School of Mathematics Newsletter - Volume 11 - 2005

From the Department Head

Lawrence Gray
Lawrence Gray

As I think about the current state of the School of Mathematics, I am reminded of Charles Dickens’ famous phrase: “It was the best of times, it was the worst of times …” Mathematics has never been more essential to the ways in which our society is developing, and yet we are facing tremendous financial challenges caused by dwindling governmental support of the academic enterprise. Much of the most exciting and critical progress in science and technology, from computer security to the deciphering of the human genome, from Hollywood special effects to cosmic physics, is founded on sophisticated mathematical ideas that most often began in the fertile ground of the research university environment. And yet we, like many other such institutions, are scrambling to deal with recurring cut-backs. During the past two years, salaries officially increased overall by 2.5%, but in effect, this increase was funded by an accompanying 2% retrenchment in our overall departmental budget. We are facing a similar prospect in each of the next two years, with anticipated 3% annual salary increases being funded by anticipated 2% annual cut-backs in our permanent budget. The cut-backs are necessarily taken from the “discretionary” part of our budget (non-salary), which constitutes less than 15% of the overall budget. I’ll leave the remaining calculations to you, to determine the numbers that have recently been keeping me up at night.

Aside from the money issues, things are going great! We just recently completed a successful hiring season, in which we attracted three very exciting young mathematicians to the School: Adrian Diaconu, a number theorist from Lehman College, Anne Henke, a group theorist from Leicester College in England, and Marta Lewicka, a specialist in partial differential equations who is currently a Dickson Instructor at the University of Chicago. Diaconu and Lewicka will arrive this Fall, and Henke will arrive in 2006. One of our assistant professors, Ezra Miller, received a double honor this year by getting both an NSF career grant and a University of Minnesota McKnight Land Grant Assistant Professorship. And one of our long-time faculty, Willard Miller, was honored with an Institute of Technology Distinguished Professorship, for career-long contributions in research, service, and teaching at the University. The Institute for Mathematics and its Applications had a highly successful site visit from the NSF, as part of the process of getting its funding renewed. A great deal of credit goes to its director, Doug Arnold. (Final word on the funding awaits action by Congress.)

The School continues in its efforts to serve the education needs of the state of Minnesota at all levels. Together with Professor Bert Fristedt, I have continued in my involvement with the state in connection with the K-12 math standards and statewide math tests. ITCEP, under its director Professor Harvey Keynes, continues to have a huge impact on the mathematical training of top middle and high school math students through the phenomenally successful UMTYMP. ITCEP also recently won a Math Science Partnership grant from the state as part of its ongoing in service training of K-12 math teachers. We are world-renowned for our highly ranked research faculty, but we do much, much more!

I will end this note with a bittersweet announcement. Two of our highly valued and long-time office staff members, Leane Hewitt (35 years) and Paula Dostert (15 years) have left us. Leane entered retirement, and Paula is seeking new adventures in California. We will miss them greatly and wish them all the best.

Lawrence Gray

Welcome to Incoming Faculty and New Postdoctoral Appointees

It is a pleasure to welcome the new members of the School of Mathematics—Assistant Professors Gilad M. Lerman and Daniel P. Spirn. We also welcome the new Dunham Jackson Assistant Professor J. Douglas Wright.

Assistant Professor Gilad M. Lerman earned an M.Sc. in Applied Mathematics from Tel Aviv University in 1995 and a Ph.D. from Yale University in 2000. He spent the following four years at the Courant Institute of New York University as a Courant Instructor, Assistant Professor, and a Senior Research Scientist. He also served as a consultant for the Wavelet Group at Yale as well as for the AT&T Shannon Lab in Florham Park, NJ. His honors include a Horace T. Burgess Fellowship at Yale University (1997 and 1999), and a Teaching Excellence Award from Tel Aviv University (1995). His varied research interests encompass Harmonic Analysis, Computational Harmonic Analysis, Bio-informatics, Data Analysis and Statistical Learning, and Geometric Measure Theory.

Assistant Professor Daniel P. Spirn earned his Ph.D. from the Courant Institute of New York University in 2001. He was a VIGRE Post-doctoral Fellow at Brown University and a researcher at the Theoretical Division of the Los Alamos National Laboratory before joining our department. He was awarded an NSF Research Grant for the years 2003-06. His research interests are Nonlinear Partial Differential Equations and Mathematical Physics.

Dunham Jackson Assistant Professor J. Douglas Wright earned his Ph.D. in January 2004 from Boston University. He spent the 2003-04 academic year as a Post-doctoral Fellow at The Fields Institute participating in the Thematic Program on Partial Differential Equations. His research areas are Partial Differential Equations and Applied Mathematics, especially Mathematics of Water Waves. He earned the Boston University Teaching Fellow Award for the year 2000.

Promotions

Professor Dihua Jiang was promoted to the rank of Full Professor effective September 2004. Dihua’s research area is number theory.

Professor Conan Leung was promoted to the rank of Full Professor effective September 2004. Conan’s research area is differential geometry.

Professor Arnd Scheel was promoted to the rank of Full Professor effective September 2004. Arnd’s research area is dynamical systems.

Professor Ionut Ciocan-Fontanine was promoted to the rank of Associate Professor with tenure effective September 2004. Ionut’s research area is algebraic geometry.

Professor Tian-Jun Li was promoted to the rank of Associate Professor with tenure effective September 2004. Tian-Jun’s research area is symplectic geometry.

All these colleagues have our warmest congratulations and we wish them continued success.

Awards and Recognitions

CONFERENCE IN HONOR OF ROBERT GULLIVER’S 60TH BIRTHDAY

This international conference on “Calculus of Variations and Nonlinear Partial Differential Equations” will be held June 20-24, 2005 at the Center for the Mathematical Sciences, Zhejiang University, Hangzhou, China. The conference is in honor of the 60th birthdays of Professors Gulliver, Robert Hardt and Leon Simon. Professors Hardt (Rice University) and Simon (Stanford University) are our former faculty members. Professor Fang-Hua Lin (Courant Institute) (see also below in this section), a former student of Professor Hardt in Minnesota, is one of the organizers of the conference.

MCKNIGHT PRESIDENTIAL FELLOW AWARD TO TIAN-JUN LI

Professor Tian-Jun Li is the recipient of the McKnight Presidential Fellow Award. The Award was bestowed on him in June 2004 on the occasion of his promotion to Associate Professor with tenure. This award is given each year to the most promising faculty granted tenure and promotion to Associate Professor. Professor Li is one of five faculty selected from the University. We congratulate Tian-Jun for this major recognition.

IT DISTINGUISHED PROFESSOR AWARD TO WILLARD MILLER

Professor Willard Miller is the recipient of the Institute of Technology Distinguished Professor Award. This award recognizes the outstanding contributions to teaching, research and service to the Institute of Technology. We congratulate Willard on this major recognition.

DOCTOR HONORIS CAUSA DEGREE TO JAMES SERRIN

A Conference in Honor of Regents’ Professor Emeritus James Serrin, on the occasion of awarding him the title of Doctor Honoris Causa of the University Francois-Rabelais, will be held at the University Francois-Rabelais, Tours, June 6-8, 2005. The title of the conference is “Nonlinear Partial Differential Equations and Applications.” We congratulate Professor Serrin on this great honor.

FANG-HUA LIN ELECTED TO AAAS

Professor Fang-Hua Lin, a 1985 graduate of our department, has been elected to the American Academy of Arts & Sciences. He is currently a Professor of Mathematics at the Courant Institute of New York University. Professor Lin was awarded the 2002 Bocher Memorial Prize (see the 2003 issue of this Newsletter) and is a recipient of many other major honors. Academy President Patricia Meyer Spacks announced that the newly elected members “have made extraordinary contributions to their fields and disciplines.” We congratulate Fang-Hua on this great recognition.

Featured Colleagues

In this section we give our readers a glimpse of the work and mathematical lives of three colleagues, Professors Ezra Miller, Richard Moeckel, and George Sell. The editors thank them for giving generously of their time and sharing their perspectives to make this section possible.

 

MCKNIGHT LAND-GRANT PROFESSORSHIP AND
NSF CAREER AWARD FOR EZRA MILLER

Ezra Miller
Ezra Miller

Professor Miller was awarded the University of Minnesota’s McKnight Land-Grant Professorship for the 2005-07 biennium. This prestigious award is bestowed on a few tenure-track faculty members per year, chosen from across all academic fields on the University’s multiple campuses. Ezra is also a recipient of the NSF CAREER grant (Faculty Early Career Development Grant). These grants are not limited to mathematics and represent a major national scientific recognition. The five-year award will fund Professor Miller’s research program on “Discrete Structures in Continuous Contexts”. We congratulate Ezra for both of these honors.

Ezra joined the department in the Fall of 2002, although he spent his first year on leave at the Mathematical Sciences Research Institute (MSRI) in Berkeley. We asked Ezra for some comments to provide our readers with a perspective on his research and other scientific activities. “Many objects in nature and throughout mathematics,” he responds, “are described by quantities that are allowed to vary continuously. Length, width, height, radius, volume—these are all continuous parameters. In a broad sense, Mathematics is all about relations: describe this in terms of that; decompose those as sums of these; and so on. Thus, the goal can be to describe a continuous object by way of other (perhaps simpler) continuous objects, or, as in my research, to extract the essence of the continuous by way of the discrete.”

One manner in which hidden information can be borne out is by deformation: given an initial object of study, allow yourself to alter it in some controlled way, preserving its essential properties. “After all,” Ezra asks, “how much has really changed about the abstract properties of a rubber band if it stretches a little? The hole through the middle will still be there.” For more complicated curved geometric objects, tugging this way and that can force the object to flatten out. However, the complexity that had been hidden in the curvature has to go somewhere, and this is where the discrete structure enters: the complexity becomes reflected in the object breaking into finitely many pieces, each of which is more tractable than the original. If one understands each of the pieces fully (and this conditional is often the source of much interesting research in its own right), then the objectives are (a) to describe which types of simpler pieces arise, and (b) to determine how the simpler pieces glue together. This technique is amazingly powerful, in that it can reveal enormous amounts about the original curved object: remember that the deformation was chosen so as to preserve the relevant data.

Deformation techniques are of course common throughout mathematics; it is the origin of the specific deformations and the way Ezra and his coauthors apply them that is innovative. The degenerations amount to geometric interpretations of algebra used for symbolic computation.

Another direction of Ezra’s research concerns the notion of convexity. The most basic of convex objects are the polyhedra, which have (unlike, say, a baseball) finitely many flat faces. Examples of polyhedra are the so-called Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Convexity and polyhedra—including their manifestations in dimensions higher than
three—are fundamental to certain aspects of many sciences, including computer graphics, mathematical economics, statistics, and theoretical physics, as well as to many branches of abstract mathematics. Recent research of Ezra’s with Igor Pak (at MIT), which he is currently continuing, discovers novel phenomena that are fundamental to the nature of convex polyhedra. The techniques that they use have immediate applications to algorithmic aspects of geometry, but for more theoretical purposes, their methods provide fundamental insight into the nature of convexity. As with the deformation project above, the basis of their approach is to impose discrete structures.

While much of Ezra’s work falls toward the abstract end of the mathematical spectrum, his theorems often produce concrete results—sometimes almost literally. For the convexity project, he says, “If the input is a four-dimensional polyhedron then the output is a three-dimensional jagged crystalline form that I hope to produce in plastic or wax (alas, not concrete) using modern laser technology. Such results realize the artistic aspects of mathematics in a tangible aesthetic sense; they are the kinds of things one puts on display in the front hall (of one’s home or one’s department).”

Ezra recently co-authored a book with Bernd Sturmfels (UC Berkeley), entitled Combinatorial Commutative Algebra, which has now appeared as Volume 227 in the Springer—Verlag GTM series (Graduate Texts in Mathematics). As it says on the back cover, the book provides a self-contained introduction, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. Geometric topics treated in the 18 chapters include toric varieties, flag varieties, quiver loci, and Hilbert schemes. The book has over 100 figures, and one of them even made it onto the front cover; in fact, Ezra proudly remarks “It’s the first GTM featuring cover art!” In this, the electronic age, Ezra managed to write the book while printing it just one time, a few months before it was finished. The book, and most of his papers, too, were written with coauthors in remote locations. “As long as one has control over such issues as who’s editing which of the various chapters or files at any given time, electronic collaboration can be quite efficient. Of course, it also helps to like LaTeX.” On the other hand, there is no avoiding the painful process of compiling the index, which took him three solid weeks this fall.

In addition to his research and writing, Ezra is active in organizing and taking part in conferences and workshops. For example, last summer he gave a series of lectures, based on his book, at the Abdus Salam International Center for Theoretical Physics in Trieste, Italy. The audience consisted of around 100 graduate students and postdocs from economically challenged countries around the world. Ezra also was one of the organizers for the Institute for Advanced Study/Park City Mathematics Institute Summer Program on Geometric Combinatorics this past July, 2004, with participants ranging from high school teachers and undergraduate students to research mathematicians.

This coming June, Ezra will be a lecturer at a summer school in Snowbird, Utah for graduate students, on the topic of D-modules and local cohomology, and is a co-organizer of a seminar session at the “every-10-year” Summer Institute in Algebraic Geometry, which will take place in Seattle, Washington this coming August.

 

RICK MOECKEL: TROPICAL CELESTIAL MECHANICS

Rick Moeckel
Rick Moeckel
The editors are very grateful to Professor Moeckel for taking time off from his busy schedule as Associate Head to offer our readers a perspective on his current research, with postdoc Marshall Hampton, in one of the most storied areas of mathematics—celestial mechanics. Rick received his Ph.D. from the University of Wisconsin in 1980. After a postdoc at ETH, Zurich, he joined the UM faculty in 1981. His research area is dynamical systems theory with emphasis on problems arising in celestial mechanics. Much of his recent work, including the problem described here, draws on techniques from computational algebra.

Tropical Celestial Mechanics

The Newtonian n-body problem has been challenging mathematicians for over 300 years. The familiar picture of planets moving in orderly elliptical orbits around the sun is misleading. In fact when three or more masses move under the influence of their mutual gravitational attraction, the results can be incredibly complicated. But simple motions are possible if the positions of the masses are chosen in a special way. For example, in 1772, Lagrange showed that if three bodies are arranged in an equilateral triangle and given appropriate initial velocities, they will always remain in an equilateral configuration — the triangle just rotates rigidly about the center of mass. When the three masses are of equal size, the existence of such a solution is clear from symmetry considerations, but when the masses have different sizes, the result is far from obvious. For example, if the three masses are the Sun, Jupiter and a small asteroid, the center of mass will be very near the sun and yet the triangle just rotates rigidly around that point (see figure 1a). It turns out that there really are asteroids moving approximately this way.

Models of planetary orbits.
Figure 1: Relative equilibria. a. Lagrange’s equililateral triangle with the Sun (red), Jupiter (blue)
and an asteroid (black). b. A surprising example with eight equal masses.

Suppose n mass values are given. Will there always be some way to arrange the bodies so that such a rigidly rotating motion is possible? For this to occur, the mutual gravitational attraction on each body due to the other masses must be exactly balanced by the centrifugal force of the rotation — a very delicate balance indeed. It turns out that no matter what masses are specified, such special relative equilibrium configurations always exist. In fact, many different shapes are possible. The relative equilibria are found by solving a complicated system of polynomial equations for the positions of the masses. When n=3 the solutions have been known since Lagrange, but for n ³4 much less is known (see figure 1b for an example with n=8). The possible shapes and even the number of relative equilibria depend on the choice of the masses. In fact, it is a long-standing open problem in celestial mechanics to show that the number of solutions of the relative equilibrium equations is finite for all masses. This question was included by Smale on his list of problems for the 21st century.

In joint work with NSF postdoc Marshall Hampton, we found a computer-assisted proof of finiteness for n=4. The method uses some recent ideas in computational algebraic geometry. The argument goes roughly as follows: because the equations are polynomial, it follows that if the number of solutions is not finite, there must be a curve (or higher-dimensional algebraic variety) of solutions. Locally, a curve of solutions can be described by writing each variable as a series in some parameter, t. In the 1970’s D.N. Bernstein pointed out that the lowest-order powers of t in these series are subject to interesting geometrical restrictions. Every system of equations in k unknowns determines a polytope in k-dimensional space, a variation on the familiar Newton polygon for an algebraic curve in the plane. Figure 2 shows such a polytope for a system of equations in three variables describing relative equilibria of the three-body problem. It turns out that the vector of exponents of the lowest order terms of the series above must be an inward-pointing normal to one of the faces of this polytope. By examining normal vectors from every face of the Newton polytope, one can systematically rule out the existence of non-constant series solutions to a polynomial system and so prove finiteness. The relative equilibrium problem for n=4 involves a system of equations in 6 unknowns. The corresponding polytope in 6 dimensions (not shown) turned out to have 12828 vertices!

Newton polytopes.
Figure 2: A Newton polytope in 3D.
The study of possible exponents of series solutions of polynomial systems is part of an active research area called tropical algebraic geometry (apparently in honor of one of its Brazilian practitioners). Given a polynomial system, there is an associated tropical variety which contains all the exponent vectors of nonzero series solutions. Our proof amounts to showing that the tropical variety determined by the relative equilibrium equations reduces to a single point (the exponent vector 0 coming from constant solutions).

 

GEORGE SELL: GLOBAL CLIMATE MODELING

George Sell
George Sell

Professor George Sell is a leader in the area of Dynamical Systems. A biography of George in honor of his 65th birthday, and authored by Professor Victor Pliss of St. Petersburg State University, was published in the October 2004 issue of the Dynamical Systems Magazine (see http://www.dynamicalsystems.org/ma/tc/toc?issue=11). It will also appear in a special issue of the Journal of Differential Equations dedicated to him. George’s extensive contributions include the Sacker-Sell spectral theory for invariant manifolds and many important results on the theory of reaction-diffusion equations and Navier-Stokes equations. His recent monograph “Dynamics of Evolutionary Equations”, coauthored with Y. You, is “a major contribution to the literature on the dynamics of infinite dimensional problems”. George’s service to the mathematical community includes being the co-founder with Professor Hans Weinberger of the Institute for Mathematics and Its Applications (IMA) and serving as the IMA’s Associate Director for several years; serving as the director of the Army Computing Research Center; serving as Program Director at the National Science Foundation, and being the founder and serving as editor of the Journal of Dynamics and Differential Equations. His many honors include an invited address at the 1982 International Congress of Mathematicians, an Honorary Doctor of Science Degree from St. Petersburg State University (1990) and a conference in his honor organized by the University of Valladolid and held in July 2002 in Medina del Campo, Spain.

Professor Sell recently developed a timely and innovative graduate level course on Global Climate Modeling. He is presenting the course for the first time during the Spring 2005 Semester and he intends to offer it on a regular basis. We thank him for sharing with our readers the following description of his course.

Global Climate Modeling

The key to building good climate models is to have a good understanding of the heat transfer phenomena in the oceans of the Earth. The physical forces driving the oceanic flows include the radiation from the Sun and the changes in the gravity due to the Earth, the Moon, the Sun and the other planets. The longtime dynamics of any climate model are located in the global attractor of the underlying oceanic model.

Since the time scales for many climate models run into the tens, or even hundreds, or thousands of years, it is natural to ask: what would happen to the longtime dynamics of a model if one were to ignore high frequency events, such as the daily rotation of the Earth or the Lunar phases? (One might use a partial time-averaging method to eliminate the physics of these events.) However, it must be noted, for example, that the daily heating and cooling of the Earth’s surface due to the Sun’s radiation is both a major physical force AND it differs widely from its mean value. In short, by adding the daily rotation of the Earth to some time- averaged model, one is introducing a large perturbation into the model. “Large” perturbations can destroy many dynamical properties. That being the case, one needs to address the issue of whether any such time-averaged model can lead to good information about the global climate of the Earth.

In this graduate-level course we describe the basic theory of oceanic flows. The lectures start with the Leray-Hopf theory of solutions of the Navier- Stokes equations (NSE) in 2D and 3D. A description of the MILLION dollar NSE problem will be an early goal in this theory.

The next step is to extend the Leray-Hopf theory to oceanic models. This will include the theory of the NSE on thin 3D physical domains. The (unfunded) 10K dollar NSE problem arises in this context! The latter open problem is to show that the global attractor for the NSE on thin 3D domains (say oceanic domains) has “good” dynamical properties.

In the climate models of interest in this course, we will examine the nonautonomous forcing of the oceanic flows due to the planets and the Sun. In order to study the diversity that is seen in the global climate, one needs to study models with many time scales. The time scales for the El Nino event, for example, differ from the time scales needed for a Kyoto protocol, or the time scales used for the onset of the next Ice Age. One challenging problem arising in all models is the effect on the longtime dynamics due to the daily rotation of the Earth. Among other theories, we will show that there is a rigorous mathematical basis for ignoring the daily rotation of the Earth in many global climate models.

IMA Related News

As our readers are well aware, the Institute for Mathematics and its Applications (IMA) is funded by the National Science Foundation and the University of Minnesota, and is closely associated with our department. September 2004 saw some changes in the leadership positions at the IMA. Professor Arnd Scheel is the new Deputy Director, replacing Professor Scot Adams who has taken on a no less challenging task as Director of Graduate Studies. Professor Fadil Santosa has stepped down as Deputy Director of the IMA, a position he held for seven years. He continues in his position as the Director of the MCIM (Minnesota Center for Industrial and Applied Mathematics). The new Associate Director is Debra Lewis, Professor of Mathematics at UC Santa Cruz, who has taken a two-year leave from UC Santa Cruz to serve in this position and as an Adjunct Professor in the School of Mathematics.

Professor Douglas Arnold continues to serve as the Institute’s Director. He wrote eloquently: “I am delighted to be working with Arnd and Debra. Their commitment and skill are already much in evidence here. I am also very grateful to Fadil and Scot for all they did in their time at the IMA. They made major contributions to the quality and reputation of the IMA, and are both continuing to serve with major roles in the department. Fadil deserves a special thanks for his exceptional commitment, having worked at the IMA not just since I came here, but also with the two previous directors. As one of the leading mathematicians worldwide in the fostering of the application of mathematical research in industry, he has built and developed IMA’s industrial programs, and has also been invaluable in almost every other aspect of the IMA: scientific program development, postdoctoral recruiting and mentoring, publications, publicity, assessment, administration, etc.”

Professor Scheel’s field of research is dynamical systems, especially the dynamics of PDE and the formation and stability of patterns. He has been involved in many IMA programs in the past, beginning with a month he spent here in 1997, before joining the department in 2001.

Professor Lewis’ research is in the area of geometric mechanics, particularly Hamiltonian and Lagrangian systems with symmetry. She received her PhD in Berkeley in 1987 and spent 1988-1989 in Minnesota as an IMA postdoc.

Each year, the work of IMA researchers focuses on one major area of applications of mathematics, with the 2004-2005 focus being on “Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities”. Professor Mitchell Luskin serves as the Chair of the organizing committee which also includes Professor Carme Calderer. In addition, as is the case each year, several department members with related specialities also participate in the program and in mentoring the IMA postdoctoral researchers. This year these include Professors Maury Bramson, Robert Gulliver, George Sell and Vladimir Sverak. Professor Luskin was kind enough to give us the following note describing the 2004-2005 program.

IMA Year on Mathematics of Materials and Macromolecules:
Multiple Scales, Disorder, and Singularities

by Mitchell Luskin

During the academic year 2004-2005, the IMA is hosting a program aimed at a synthesis of the problems at the interface between mathematics, materials science, condensed matter physics, and biology. The program organizers (including Mitchell Luskin, Chair, and Carme Calderer) have developed a program to provide rich interdisciplinary opportunities for the interplay between mathematics and emerging approaches to the study of matter and macromolecules. We are particularly focusing on phenomena that require modeling that integrates the atomic to the continuum scales.

IMA researchers are utilizing a broad spectrum of modern mathematics to understand matter. Several of the most active research efforts use nonlinear partial differential equations to model the structure and dynamics of defects and microstructure. Current research in stochastic differential equations is being utilized to model microscale and nanoscale devices and phenomena, and topological and geometric concepts are being developed to understand defects in crystals, the structure of DNA, and protein folding.

IMA mathematicians and materials scientists are confronting the computational challenges of multiscale modeling, singularities, and disorder. Contemporary computational algorithms for the study of matter, such as “hyperdynamics,” are often developed in the context and language of physical theories that are not part of the traditional education of computational mathematicians. This IMA program is striving to enable interactions and research between mathematicians and materials scientists on such computational problems that are important in the study of matter, but have been given little attention by the mathematics community. For more details about the annual program please consult the IMA website http://www.ima.umn.edu/

A glance at the 2004 and 2005 Summer Programs also helps to illustrate the great scope and timeliness of investigations being pursued by IMA researchers. The Program on n-Categories (June 7-18, 2004), organized by Peter May (U. of Chicago) and John Baez (UC Riverside), was of great interest to members of our department, with participants including Professors Scot Adams, Bernard Badzioch, Mark Feshbach, Mehdi Hakim Hashemi, William Messing, Victor Reiner, Fadil Santosa, Sasha Voronov, and Peter Webb, as well as graduate students Eric Harrelson, Hyeung-Joon Kim, Jonathan Rogness, James Swenson, and Javier Zuniga. As is well known to many of our readers, the category theory introduced in 1945 by S. Eilenberg and S. MacLane provided a powerful new language for mathematics. Many of the leading researchers are now working on an even more potent “higher category theory promis[ing] to allow... study of higher categorical structures that appear in a variety of specific fields. The need for such a language has become apparent, almost simultaneously, in mathematical physics, algebraic geometry, computer science, logic”.

The Principal Speakers at the Program on Computational Topology (July 6-16, 2004) were H. Edelsbrunner and J. Harer, both of Duke University. Computational Topology “grew out of Computational Geometry as researchers expanded into applications where significant topological issues arise. The two such areas discussed [were] structural molecular biology and geometric modeling. Both have connections to industries of substantial economical size.”

The Wireless Communications Program taking place June 22-July 1, 2005 will encompass short courses and research presentations in the following relevant areas of pure and applied mathematics: stochastic calculus, information theory, signal processing, optimization, and control theory. As always, the objective is to facilitate interaction between academia and industry, mathematicians and engineers.

The meeting “New Directions in Probability Theory” (August 5-6, 2005) will involve major participation by our faculty. Professors Maury Bramson and Ofer Zeitouni are among the organizers and Professor Zeitouni is also one of the main speakers. In addition, the organizers include Professor Mike Cranston (UC Irvine), a 1980 graduate of our department. The topics to be covered include Flows and Random Media; Probability, Combinatorics, and Statistical Mechanics; Stochastic Integration; Stochastic Partial Differential Equations; and Random Walk in Random Environment.

A Workshop for Graduate Students on Mathematical Modeling in Industry will take place August 1-10, 2005. The New Directions Short Course on Quantum Computation (August 15-26, 2005) will be taught by Peter W. Shor (MIT) and Alexei Kitaev (Caltech). Professor Shor is one of the founders of this new area which may have the potential to bring about yet another revolution in computing.

IMA PUBLIC LECTURES

These lectures, given by world’s leading experts in their areas, attract large audiences of the general public. The following reports on the lectures by Sir Roger Penrose and Professor James Murray were provided by Todd Wittman, a grad student in the School of Mathematics. Todd was introduced to our readers in last year’s newsletter as recipient of several awards for teaching excellence. We thank him for these lively reports.

Sir Roger Penrose
Sir Roger Penrose

 

Sir Roger Penrose, University of Oxford,
October 5, 2004:

“Does Mathematics Rule the World?”

Most scientists and certainly all mathematicians would answer the title of Sir Roger’s talk with a resounding “yes”. But there appears to be an inherent contradiction in that assertion: How could mathematics rule the world when the physical world existed long before mathematics was spawned by human imagination? Are we discovering the physical laws that describe the physical world or are we creating these laws in an attempt to order our universe? And if we are forcing a mathematical square peg into the universe’s round hole, what hope is there for the future of physical research? These questions seem a bit too philosophical for a math talk, but Sir Roger gave his opinions on the subject through a discussion of quantum physics.

Sir Roger is a world-renowned mathematician who has made significant advances in mathematical physics, specifically quantum theory. He has written several important papers in topology and introduced twistor theory to connect relativity to quantum theory. He has authored several popular books, including “The Emperor’s New Mind” and “The Nature of Space and Time”, co-authored with the physicist Stephen Hawking. Given his credentials, it may seem a bit odd for Sir Roger to speak to a standing-room only crowd that included undergraduates, high school students, families, and other non-mathematicians. The ability to communicate mathematical research to the general public is a very rare skill, and this has certainly contributed to the poor reputation of mathematics among the general public. Sir Roger rose to the occasion, using colorful illustrations he prepared on transparencies, analogies to explain complex physical phenomena, and a friendly and lively speaking tone.

Sir Roger explained some basic concepts through analogies, such as the famous Schrodinger’s cat example to describe the superposition of quantum states. If we accept the world of classical physics as being clear as the light of day, then the probabilistic world of quantum physics can be compared to the murky depths beneath the sea. Emphasizing the importance of mathematics as a bridge between classical and quantum physics, Sir Roger suggested mathematics is a mermaid, able to breathe and thrive in both worlds equally well.

To solve the paradox between reality and our attempt to describe it, Sir Roger proposed the existence of three worlds: the physical, mental, and platonic. The physical world, having given rise to humans, gave rise to the mental world. The mental world in turn created the platonic world of mathematics and physical theory. The platonic world represents our best efforts to describe the physical world in which we live. If we can accept the existence of a “real” world, then we should be able to accept that advances in mathematics and rational thought will allow us to discover that world. Those discoveries may be filtered through the mental world of the human mind, but that is just an unavoidable consequence of living on this world rather than in it.

James D. Murray, University of Oxford & University of Washington, November 18, 2004: “The Marriage Equation: A Practical Theory for Predicting Divorces and a Scientifically-Based Marital Therapy”

Prof. James Murray from the University of Washington is a mathematical biologist who holds the distinction of doing research in just about every area of mathematical biology, from epidemiology to medicine to ecology. He has been involved in many interesting and important research projects, ranging from modeling the growth of brain tumors to describing how the leopard got its spots. A few years ago, Prof. Murray engaged in his most radical and perhaps most challenging research project to date: making marriages work.

Prof. Murray was approached by a psychology professor at the University of Washington working in marital therapy. The psychologist and his team of graduate students had videotaped over 800 married couples in marital therapy sessions. The team then reviewed the tape and literally charted the course of the conversations. With a very well-defined scale taking into account tone and facial expressions, the researchers assigned a value from -10 to +10 assessing the “negativity” or “positiveness” of the response. This gave the psychologists a huge set of time series data to work with, but they weren’t sure how to work with it. So they turned to a mathematician.

Examining the data, Murray viewed each person’s response as a dynamical system. He modeled the response as a linear recurrence relation, depending on an individual's last response as well as their partner’s last response. This gave a mathematical proof of the existence of stable nodes, literally sinks into which the conversation would get stuck. The goal of a marital therapist is to ensure that the session ends positively. Mathematically speaking, if we make a 2D scatterplot of the conversation with the individual’s responses as the two axes, the marital therapist should try to ensure that the stable node lies in the first quadrant. This gave rise to a new approach to marriage counseling as well as a new area of mathematical research. Prof. Murray published, with his colleagues, the book “The Mathematics of Marriage: Dynamic Nonlinear Models.”

The conclusion of this study was that couples that work best include people with matching personalities. That is, two passive individuals will be more likely to form a stable marriage than one passive and one volatile individual. Oddly enough, two volatile individuals can form a stable marriage, although Murray warned that the relationship may consist of “alternating cycles of fighting and sex.”

Speaking to a large, mostly non-mathematical audience, Prof. Murray outlined his so-called “Marriage Equation” in simple and easy-to-grasp terms. Aware that this was a public lecture, the highest level mathematics used was the equation of a line, yet Prof. Murray still conveyed deep insight into mathematical research in the social sciences. With his lilting Scottish accent and jovial speaking style, Murray kept the audience’s interest with humorous anecdotes and mathematical insight into the human heart. To convince his audience of the accuracy of his mathematical model, his research team did a follow-up study on the 800 couples first used to gather the conversation data. With frightening accuracy, they were able to mathematically predict which couples would get divorced and which would stay together. So mathematics may not be able to make people happy, but it can predict which ones will be happy.

We recently had two additional IMA Public Lectures which will be reported in detail in next year’s newsletter. The titles and speakers were “Math Behind the Curtains: Dynamic Simulation at Pixar” (February 9, 2005), by David Baraff, Senior Animation Scientist, Pixar Animation Studios, and “Computers and the Future of Mathematical Proof” (March 30, 2005), by Thomas C. Hales, Mellon Professor of Mathematics, University of Pittsburgh.

Mathematics Fifty years ago at Minnesota: A Reminiscence by W. S. Loud

I joined the Department of Mathematics, College of Science, Literature and the Arts in the fall of 1947, when you could get a driver's license without an examination. I soon discovered that there were two departments at the University of Minnesota, which handled mathematics instruction, the other being the Department of Mathematics and Mechanics. The first of these departments was located in Folwell Hall, and the second was in Main Engineering.

I have deliberately ended this exposition at about 1952. Almost all the people named here are no longer living. After that date, the pattern of activity changed greatly with the departments finally being united in 1963.

The principal activity in both departments was undergraduate instruction because of the huge influx of students on the GI Bill following the end of World War II. The instruction was at a generally lower level because most Minnesota high schools did not offer mathematics beyond the second year of algebra (i.e. Higher Algebra). The first year of three quarters had a program of Trigonometry, College Algebra, and Analytic Geometry with calculus being postponed to the second year and carrying upper division credit (3-000 level). The text (in SLA) was Granville, Smith, and Longley. Also Calculus was taught in a three-quarter sequence: Differential Calculus, Integral Calculus, Intermediate Calculus, with the third quarter carrying graduate credit (5-000 level) because many graduate students in nonmathematical fields needed calculus at that level and also needed graduate credit. From my experience at M.I.T., this was a surprising situation, though I later learned that some very eminent mathematicians of my generation actually began their graduate study of mathematics with Intermediate Calculus. Although I did not have firsthand experience with it, I believe that the first two years in the Mathematics and Mechanics Departments followed a similar pattern.

Before I came to Minnesota, the pattern of research in mathematics was quite simple. There was one person whose duty was to be active in research and serve as adviser to most of the doctoral candidates in the department. This person had been Professor Dunham Jackson for many years. Professor Jackson died in 1946, and his functions were assumed by Professor Robert Cameron, who had come to Minnesota from M.I.T. in 1945. Professor Cameron had an active research program and was adviser to a great many doctoral candidates, some of whom later assumed positions of leadership in the Minnesota State Colleges. But there were already the signs of a significantly larger research activity. In the SLA department, there were two men in their thirties, John Olmsted and Gerhard Kalisch, who were active in research and who taught graduate courses. In the Mathematics and Mechanics Department, there was the counterpart of Professor Cameron, Professor Stefan Warschawski, and also Hugh Turrittin and Fulton Koehler. There were older people in the SLA department who had been active at one time, but had turned their attention largely to administration, textbook writing, and teaching. These included Professor Raymond W. Brink who was Chairman of the department, and had been President of the Mathematical Association of America, William L. Hart author of many widely used texts, Gladys Gibbens, and Elizabeth Carlson. Miss Carlson was Dunham Jackson’s first Ph.D student at Minnesota and was a much-respected teacher with awards from the university in recognition of her teaching. However, a great many new Ph.D’s arrived in both departments in the late forties and early fifties. Watson Fulks and James Thompson were students of Professor Warschawski. In SLA were Charles Hatheld, Jacob Bearman, Warren Loud, Bernard Gelbaum, Evar Nering, Monroe Donsker, and Ross Graves, the latter two being students of Professor Cameron. We were all interested to do research. Seminars were set up at the time and ideas were exchanged back and forth.

One thing that I did almost single-handedly was to get the University of Minnesota to participate in the William Lowell Putnam Mathematics Competition. Mr. Brink thought that Minnesota students wouldn’t stand much of a chance, but I felt they should widen their scope. There were three students who did very well: Bert Fristedt, Ian Richards, and Tai Tsun Wu. Wu was an electrical engineering student newly from China.

The graduate faculty of mathematics was composed of the active members of both departments. Graduate students took their coursework in both departments. Some committees had representatives from both departments. There had been an effort at one time to unite all mathematics in SLA, but this had failed. I was told that the engineering departments felt that a department in SLA would not be sympathetic to their particular needs.

What must be considered a major event in the mathematics research picture at the University of Minnesota was the arrival of Athelstan Spilhaus as Dean of the Institute of Technology. He was truly a mover and shaker and did much to stimulate scientific research within the Institute of Technology. He separated mathematics and mechanics, and the mathematics department became known as the IT Mathematics Department, with Professor Warschawski as head. He also persuaded the department of Physics and Astronomy to move from SLA to IT (Chemistry was already there.) He brought Paul Rosenbloom and Arthur Milgram into the IT Mathematics Department, and enabled Professor Warschawski to make several very strong appointments over the next few years.

In the period from 1953 to 1960, both departments made significant appointments, which included many of the most productive members of the departments over the years.

There was much contact with the mathematics faculty at the various small colleges about the state. The Minnesota Section of the Mathematical Association of America was active, and there was the opportunity to meet and interact with colleagues from around the state and in North and South Dakota.

Professor Boris Levitan

Professor Boris Levitan

Our distinguished colleague, Professor Boris Levitan, died in Minneapolis on April 4, 2004. He was 89 years old. Probably his most important contribution to Mathematics is the Gelfand-Levitan equation. Gelfand and Levitan introduced this equation to study inverse scattering problems. For more details about his life, please refer to the April 14, 2004 Star Tribune obituary by Neal Gendler. This obituary also contains remarkable stories of his life, such as when he fought in the battle of Stalingrad and he was nearly shot in a strafing attack so close that he could see the pilot’s face.

He came to Minnesota at the invitation of Professor Fabes and he worked with one of our colleagues Professor Max Jodeit. Thanks to Max for contributing the reminiscences that follow.

Working with Boris Levitan
by Max Jodeit, Jr.

Sometime in the mid-nineties, Boris Levitan came to my office, then in Murphy Hall, with a question he wanted help with. I was able to deal with that question and he insisted, over my objections, that I be a coauthor. David Sattinger was still here then and he suggested a place to send it. The result was:

The isospectrality problem for the classical Sturm-Liouville equation, Max Jodeit, Jr. and B. M. Levitan, Advances in Differential Equations 2(1997)297 - 318.

One important keyword for Boris Levitan: focus! He invited me to continue with some further questions of his, and we met at the place he shared with our emeritus faculty at that time. He had to work hard to teach me the Gelfand-Levitan method!

Boris wanted to make that method work in the context of vector-valued Sturm-Liouville problems rather than the “classical,” or scalar-valued case. This led to:

A characterization of some even vector-valued Sturm-Liouville problems, Max Jodeit, Jr. and B. M. Levitan, Matematicheskaya fizika, analiz, geometriya 5(1998)166 - 181.

During our work together I learned some new phrases. Something “has place” if it holds. If an idea did not work, Boris would say “I am destroyed!” These came up often in the next phase, the vector-valued analog of the first paper. The work was announced in a note in 1998:

Isospectral Vector-Valued Sturm-Liouville Problems, Max Jodeit, Jr. and B. M. Levitan, Letters in Mathematical Physics 43 (1998)117 -122.

The last paper we worked on took some time and much effort.

The Isospectrality Problem for Some Vector-Valued and B. M. Levitan, Russian Journal of Mathematical Physics 6 (1999)375 - 393.

Though Boris had many other ideas and problems, his health kept him from his mathematical life. I remain glad to have known him and grateful that I actually had the chance to work with him.

Retirements and Resignations

RETIREMENT OF DAVID STORVICK

David Storvick

David Storvick retired at the end of the 2004 school year after a career of 47 years at the University of Minnesota. David received his Ph.D. in 1956 from the University of Michigan, and after a short time at Iowa State University moved to the University of Minnesota in 1957, achieving the rank of Full Professor in 1966. During his many years of service he was Associate Head of the School of Mathematics 1964-70, and he later served as Associate Dean of the Institute of Technology (1979-83) and Interim Associate Dean for Academic Affairs of IT (1993-94). He was also Interim Director of the Gray Freshwater Biological institute in the College of Biological Sciences 1989-90.

A dinner was held on April 29, 2004 honoring both David Storvick and Morty Harris, who was retiring at the same time (see issue 10 of this Newsletter). The dinner was held in the West Bank Bistro and over 60 people attended. We were entertained by several speakers, including Larry Markus and Jim Serrin, who reminisced about David’s long career and spoke on his mathematical contributions in analysis, dwelling particularly on his expertise with the Feynman integral. It was an extremely pleasant occasion, providing the opportunity to meet colleagues and acquaintances not just from the Mathematics Department but from other departments and from outside the University. As has become the custom for such occasions, Walter Littman served as master of ceremonies.

Leane Hewitt  

 

LEANE HEWITT RETIRES AFTER
35 YEARS OF SERVICE

Leane Hewitt, the department’s Administrative Director, retired in December 2004 after 35 years of dedicated service. She joined the department in 1969 at a youthful age as a Secretary and held a number of key positions during her career. With her skill and judgment, as well as her thorough understanding of university procedures and her attention to detail, Leane became as close to indispensable as any single individual can ever be and set a standard of service that most of us can only aspire to. She will certainly be missed professionally.

We will also miss Leane’s old-fashioned friendliness and courtesy, of the kind often associated nowadays with another, less hurried era. She always had a friendly greeting for everyone she would run into in the hallways, and without doubt all members of the department view her as a very good friend. Leane's spouse, Jim Hewitt, received his Ph.D. in mathematics here in 1979 and teaches nearby at Inver Grove Heights Community College. She and Jim have shared a life-long passion for running and Leane finished many marathons over the years, clocking some enviable times.

This year’s Faculty Retreat dinner, December 1, 2004, in the Mississippi Room of Coffman Memorial Union also provided a suitable occasion to recognize Leane for her dedicated service. The Head of the School of Mathematics, Professor Gray, as well as a number of colleagues took the opportunity to express their appreciation.

Although the department presented Leane with a hardwood rocking chair bearing the University’s emblem, it would be naive to assume that she will use it much any day soon. Rather, we wish her and Jim many active years enjoying their varied interests, and, as runners might say, happy running, Leane!

WOJCIECH CHACHOLSKI RESIGNS

We note the resignation of Assistant Professor Wojciech Chacholski. Woitek joined the School of Mathematics in 2002, coming from Yale University. He specialized in algebraic topology, specifically in the areas around homotopy theory and model categories. Both he and his wife Sandra Di Rocco have permanent positions in mathematics at the Royal Institute of Technology, Stockholm,Sweden. We note that during his short stay here, Chacholski played an active role in bringing very interesting visitors to our department.

STEVE WINCKELMAN, INFORMATION TECHNOLOGY MANAGER, RESIGNS

This year saw considerable changes in our computer system staff. Our computer manager, Steve Winckelman, accepted the position of Program Director for the Law School's computer system's office. Steve joined the School of Math in the fall of 1995 and guided the continual expansion of our computer facilities since then.

The department Head Professor Gray commented as follows:”Steve is a very talented individual and was instrumental in building our system to what it is today. He will truly be missed and we wish him the best of luck in his new position.”

In addition to operating system, hardware and software issues, Steve’s expertise and ingenuity were often needed in a wide range of areas, including upgrading our network and building computer classroom labs in a cost-effective manner. We are fortunate that he was able to attract very talented staff to the School of Mathematics who will carry on the development of our computing system in the future.

PAULA DOSTERT RESIGNS

The School of Mathematics has been fortunate to enjoy Paula Dostert’s creativity and dedication to provide quality service to students and faculty for 15 years. Often the first person of contact for questions and problems, Paula’s wealth of knowledge and insight has been very valued and much appreciated. She leaves a legacy of well organized records and systems that provides a lasting testament to her substantial abilities and contributions. Most of all, Paula will be remembered for her hunger for adventure and growth. Such stories as performing tango dances, working part time for an airline at the airport, traveling to London on a shoestring, taking a helicopter ride in the Badlands, driving down Pike’s Peak while wondering if brakes will hold, and attending and volunteering at personal growth conventions will be missed. March 25th was Paula’s last day on staff in the department. Paula is moving to San Diego to fulfill a life-long dream of living by the ocean. Warm wishes go with her and an awareness she will succeed in this newest adventure.

Academic Visitors

Distinguished Ordway Visitors (2004-2005)

The following leading mathematicians accepted our invitations to visit the School during the current academic year under the Distinguished Ordway Visitors Program. The program brings highly distinguished mathematicians to Minneapolis for prolonged periods, significantly enhancing the creative environment of the School. The visitors typically give several lectures, including a colloquium lecture and several seminars, and the exchanges of ideas with our faculty and students often result in research collaborations.

Professors:

Stuart Antman, University of Maryland, College Park, analysis and mechanics, March 2005
Louis Billera, Cornell University, discrete geometry and combinatorics, October 2004
Erwin Bolthausen, Universitat Zurich, probability theory, September 2004
Alain Chenciner, University of Paris VII, dynamical systems, April 2005
Jack Hale, Georgia Institute of Technology, differential equations, September 2004
Michael Harris, University of Paris VII, number theory
Pierre-Louis Lions, University of Paris IX Dauphine, analysis and partial differential equations, September 2004
Robert Pego, University of Maryland, College Park, partial differential equations, applied mathematics, January 2005
Yongbin Ruan, University of Wisconsin, Madison, geometry, topology, and mathematical physics, October 2004

Professor Sasha Voronov has kindly given us the following note about the April 2004 Ordway visit by the Fields’ Medalist Maxim Kontsevich.

Ordway Lectures visit by Maxim Kontsevich

By Sasha Voronov

In April 2004, Professor Maxim Kontsevich paid us a week-long visit with a series of three Ordway Lectures. He was the second distinguished mathematician (after Professor Hillel Furstenberg, who visited us in February 2003) and the first Fields’ Medalist to visit the School of Mathematics on the new Ordway Lectureship program. Since then Professor Pierre-Louis Lions, who also holds a Fields’ Medal, gave Ordway Lectures in September-October 2004.

Below is a short biographical reference, which was compiled from an entry in Encyclopaedia Britannica, the American Mathematical Society web site, and other online sources.

Maxim Kontsevich (born 25 August 1964) is professor at the Institute des Hautes Etudes Scientifiques (IHES) in France and visiting professor at Rutgers University in New Brunswick, New Jersey. After studying at the Moscow State University with I. M. Gelfand and beginning research at the “Institute for Problems of Information Processing,” he gained a doctorate at the Max-Planck-Institut, Bonn, Germany in 1992 with D. B. Zagier as his advisor. He then received invitations to Harvard, Princeton, and Berkeley.

In 1998 at the 23rd International Congress of Mathematicians in Berlin, Germany he received the Fields Medal together with R. E. Borcherds, W. T. Gowers, and C. T. McMullen.

Maxim Kontsevich has established a reputation in pure mathematics and theoretical physics, with influential ideas and deep insights. He has been influenced by the work of Richard Feynman and Edward Witten. Kontsevich is an expert in the so-called “string theory” and in quantum field theory. He made his name with contributions to several important problems of geometry. He was able to prove a conjecture of Witten and demonstrate the mathematical equivalence of two models of so-called quantum gravity. The quantum theory of gravity is an intermediate step towards a complete unified theory. It harmonizes physical theories of the macrocosm (mass attraction) and the microcosm (forces between elementary particles).

Another result of Kontsevich relates to knot theory. Knots mean exactly the same thing for mathematicians as for everyone else, except that the two ends of the rope are always joined together. A key question in knot theory is, which of the various knots are equivalent? Or in other words, which knots can be twisted and turned to produce another knot without the use of scissors? This question was raised at the beginning of the 20th century, but is still unanswered. It is not even clear which knots can be undone, that is, converted to a simple loop. Mathematicians are looking for ways of classifying all knots. They would be assigned a number or function, with equivalent knots having the same number. Knots which are not equivalent must have different numbers. However, such a characterization of knots has not yet been achieved. Kontsevich has found the best “knot invariant” so far, which is now generally called the Kontsevich integral. Although knot theory is part of pure mathematics, there seem to be scientific applications. Knot structures occur in cosmology, statistical mechanics, and genetics.

Kontsevich also proved a deformation quantization conjecture, which had been open for more than twenty years. To solve the problem, he came up with an ingenious formula motivated by the Feynman diagram expansion of a string theory model. Another noticeable contribution of Kontsevich is in the field of mirror symmetry, an important duality between two quantum field theory models from the physical point of view and between two types of geometry, complex and symplectic, from the mathematical perspective. Kontsevich’s “homological mirror symmetry” turned out to provide an adequate mathematical description of this physical phenomenon.

As Ordway Lecturer in the School of Mathematics, Kontsevich gave three lectures on Affine Structures and Non-Archimedean Geometry, in which he described his recent work on mirror symmetry. The lectures gathered a big crowd of people, packing the colloquium room, Vincent Hall 16. At times it seemed like even the experts were lost, but the excitement of novel, state-of-the-art mathematics grabbed the attention of the audience.

Kontsevich’s visit was short, barely one week, but quite full of activity. Between the lectures, he managed to engage himself in mathematical discussions with a number of faculty. Apart from organizing a reception and dinner in his honor at Bistro West, Humphrey Center, we took him for a stroll along the pedestrian bridge across the Mississippi next to the Mills District, facing St. Anthony Falls. He seemed to be excited to recognize flour brand names on tops of the surrounding grain mills and compared the mill ruins to the remains of the Roman Empire. He also was very interested to see downtown St. Paul from our 29th floor apartment, and to visit the Lowertown area where my wife’s art studio is located.

Perhaps, the most unusual event during Kontsevich’s visit took place on that Thursday afternoon in Vincent Hall. It was a Russian-style, secret seminar, announced strictly by word of mouth, exclusively to the members of the cult. The idea behind such “misorganization,” as it may appear to a side observer, is that the speaker may allow himself to be very informal and get straight to the point, without spending half an hour on initiation of the laymen. Perhaps, because of the time elapsed since then, we may feel safe to disclose the topic of that seminar, From an A_infty-Algebra To a Topological Conformal Field Theory. Kontsevich described the idea of a construction, which generalized a conjecture of Deligne on Hochschild cohomology and related algebra with physics in a mind-blowing shot. In a way it was a mathematical gift to the distinguished audience; there was still some work to be done, and we were free to go ahead and complete it. Unfortunately, Kontsevich had given a similar informal talk elsewhere, and the work is completed by now, also elsewhere, see a paper by K. Costello of Imperial College, London, on topological conformal field theories and Calabi-Yau categories, available on the web at http://front.math.ucdavis.edu/math.QA/0412149.

2004-05 Continuing Postdocs and Visiting Faculty

Assistant Professors:
Jesus Carrero (Ph.D. UCLA, numerical analysis of partial differential equations, scientific computation)
Jamylle Carter (Ph.D. UCLA, image processing, computer graphics)
Huiqiang Jiang (Ph.D. Courant Institute, partial differential equations)
Simon Morgan (Ph.D. Rice University, geometric measure theory, harmonic maps)
Chian-Jen Wang, Dunham Jackson Assistant Professor (Ph.D. Ohio State, automorphic forms and representation theory)
Jennifer Wagner (Ph.D. UCSD, algebraic combinatorics)
Stephen Watson (Ph.D. Carnegie Mellon University, dynamical systems)
Tobias Weth (University of Giessen, numerical analysis)

Associate Professors:
Victor Padron (Universidad de Los Andes, Merida, Venezuela, differential equations and applications)
Raja Sridharan (The Tata Institute of Fundamental Research, commutative algebra, algebraic geometry)

Professors:
Tepper Gill (Howard University, mathematical physics, nonlinear dynamical systems, probability theory)
Ernie Kalnins (University of Waikato, New Zealand, mathematical physics)
Alexander Tikhomirov (Bielefeld University and Syktyvkar University, probability theory)

Postdoctoral Associates and Postdoctoral Fellows, including IMA Postdoctoral Associates who participate in the teaching activities:
Yassine Boubendir (Universite Paris 13, acoustics and electromagnetics, applied mathematics, numerical methods)
Mihail Cocos (University of British Columbia, differential geometry, geometric analysis)
Marshall Hampton, NSF Postdoctoral Fellow (dynamical systems, celestial mechanics, image processing)
McKay Hyde, NSF Postdoctoral Fellow (numerical solutions of partial differential equations, fast algorithms, spectral methods)
Jeremy Martin, NSF Postdoctoral Fellow (Ph.D. UCSD, combinatorics and algebraic geometry)
Anastasios Matzavinos (Ph.D. University of Dundee, applied mathematics, mathematical biology, optimization)
Magdalena Stolarska (Ph.D. Northwestern University, applied mathematics, mathematical biology)
Thomas Wihler (ETH Zurich, numerical analysis)

Symposiums & Conferences

The Seventh and Eighth Riviere-Fabes Symposia on Analysis and PDE

The Symposia take place annually to honor the memory of our former colleagues Nestor Riviere and Gene Fabes. The seventh Symposium was held April 23-25, 2004 at the School of Mathematics. The principal speakers and titles of their lectures were: Haim Brezis (Rutgers University), two one hour lectures, on “New estimates for the Laplacian, the div-curl, and related elliptic systems” and “Nonlinear elliptic equations involving measures”, respectively, Srinivasa S.R. Varadhan (Courant Institute, NYU), two one hour lectures on “Homogenization of Random Hamilton-Jacobi-Bellman equations and applications to large Deviations in a quenched Random Environment”, Alexander Kiselev (University of Wisconsin Madison), “Spectrum and dynamics of Schroedinger operators with decaying potentials”, Alexander Nagel (University of Wisconsin Madison), “Regularity of the Kohn-Laplacian in decoupled domains”, Jill C. Pipher (Brown University) “Perturbations of elliptic operators”, and Sijue Wu (University of Michigan Ann Arbor), “Recent Progress in Mathematical Analysis of Vortex Sheets”.

The Conference Organizers were Nicolai Krylov (Chair), Carlos Kenig, Walter Littman, Fernando Reitich and Ofer Zeitouni.

The eighth Riviere-Fabes Symposium was held April 8-10, 2005. The speakers this year were: Vladimir Maz’ya (Ohio State and Linkoeping Universities), two one hour lectures on “Unsolved mysteries of solutions to PDEs near the boundary”, Stephen Wainger (University of Wisconsin Madison), two one hour lectures on “Some discrete operators arising in Harmonic Analysis”, Luca Capogna (University of Arkansas), “Mean curvature flow and the isoperimetric problem in the Heisenberg group”, Svetlana Jitomirskaya (University of California, Irvine), “The ten martini problem”, Natasa Pavlovic (Princeton), “Dyadic models for the equations of fluid motion”, and Yu Yuan (University of Washington), “Global solutions to special Lagrangian equations”. The conference dinner was held April 9 in the Mississippi Room of the Coffman Union.

The Organizing Committee consisted of Naresh Jain, Mark Keel, Carlos Kenig, Walter Littman and Mikhail Safonov.

Yamabe Symosium is a great success
The Second Yamabe Memorial Symposium was held at the School of Mathematics, University of Minnesota, Friday - Sunday, September 17 - 19, 2004. (Sept. 17, incidentally, is Riemann’s birthday.) The Symposium was an enormous success. There were 71 participants, including 52 out-of-town participants and 19 from the University of Minnesota. For the schedule, abstracts, preprints related to the talks and the participant list with email addresses, see www.math.umn.edu/yamabe.
Paul Seidel
Paul Seidel

The theme of the Symposium this time was “Geometry and Physics”.

The speakers, and the titles of their talks, were:

Robert Bryant, Duke University: “Gradient Kähler Ricci Solitons”, Sheldon Katz, University of Illinois: “Donaldson-Thomas and topological string invariants”, Kefeng Liu, U.C.L.A.: “String Duality and Localization”, Duong Phong, Columbia University: “Superstring Perturbation at Two-Loops”, Paul Seidel, University of Chicago: “Khovanov homology and the symplectic geometry of nilpotent slices”, Isadore M. Singer, M.I.T. “The projective Dirac operator and its fractional analytic index”, Karen Uhlenbeck, University of Texas: “Virasoro Actions on Harmonic Maps”, Shing-Tung Yau, Harvard University: “Positive quasi-local mass in general relativity”.

This list of speakers consists of highly distinguished world-class mathematicians. Here are a few of the honors the more senior speakers have received: Karen Uhlenbeck, Isadore Singer and S.-T. Yau have been awarded the National Medal of Science; Yau is a Fields medalist; and Singer is one of the first recipients of the Abel Prize, which is equivalent to a Nobel Prize for mathematicians.

Isadore Singer
Isadore Singer

The Symposium honors Prof. Hidehiko Yamabe (1923—1960), who was an active and highly collaborative mathematician in the School of Mathematics at the University of Minnesota from 1954 until 1960, the year of his untimely death.

The Yamabe Memorial Lecture has been held for a number of years, through support from a fund created by Etsuko Yamabe and through contributions from a number of mathematicians. The lecture has been held in alternating years at the University of Minnesota and at Northwestern University. A recent, generous contribution from an anonymous donor made it possible to expand the Minnesota half of the annual lecture series into a weekend symposium, held every two years.

By Robert Gulliver

Notable Activities of the Faculty

Some of our colleagues have been kind enough to update us on their recent activities. We know that many of our other colleagues have significant achievements and we hope to report on those in future newsletters.

During the month of April 2005 Professor Douglas Arnold gave a series of lectures, in connection with the 2005 Mathematics Awareness Month and the centenary of Einstein’s famous 1905 papers, on the subject of “Math and the Cosmos: The New Mathematical Gravitational Astronomy”. The lectures include the William Marshall Bullitt Lecture at the University of Louisville and the Lonseth Lecture at Oregon State.

Professor Sergey Bobkov was organizer and chair of the session “Concentration Inequalities” at the 6th World Bernoulli Congress on Probability Theory and Mathematical Statistics held in Barcelona, Spain, July 26-31, 2005.

Professor Mark Keel gave an invited Mini Course at the Summer School and Workshop on Nonlinear Wave Equations, co-sponsored by the Wolfgang Pauli Institute and the Erwin Schroedinger Institute for Mathematical Physics in Vienna during July 2004. He also gave invited lectures on nonlinear waves at a number of conferences in Europe and North America.

Professor Walter Littman is a co-organizer of a conference on Control Methods in PDE-Dynamical Systems to be held in Snowbird (Utah), July 3-7, 2005. The conference is intended for two distinct research communities in partial differential equations (PDE): (1) the PDE-control community, which is focused on the study of control-theoretic properties of PDEs (e.g., well-posedness, interior and boundary regularity, controllability, stabilization, and optimization); and (2) the PDE-dynamical systems community, which is focused on the long-time behavior of solutions (e.g., global attractors and their geometric, topological, and structural properties). The main goal is to develop mutual stimulation and joint interactions betweenresearchers in these two areas. For more information see Notices of the A.M.S., Nov. 2004, p.1296.

Professor Peter Polacik was a co-organizer of a special session ”Qualitative Studies on Parabolic and Elliptic Equations” at the AIMS’ Fifth International Conference on Dynamical Systems and Differential Equations in Pomona, California, June 16 - 19, 2004. Asymptotics (in a broad sense), blow up, and geometric properties, were among the issues considered. He is organizing a minisymposium “Qualitative Studies in Parabolic Equations” at EQUADIFF 11, an international conference on differential equations, to be held in Bratislava, Slovakia, July 25 - 29, 2005. He is also a co-organizer of a conference on “Infinite dimensional dynamical systems”, in honor of the 70th birthday of P. Brunovsky, to be held at Luminy, France, July 4 - 8, 2005. This conference will be devoted to dynamics in infinite dimensions, with special emphasis on problems related to partial differential equations.

Undergraduate Program

UNDERGRADUATE PROJECTS

Senior projects involve substantial one-on-one student-faculty interaction and enhance greatly the students’ learning experience. Below is a list of the faculty members who recently supervised such projects, together with the titles of the projects.

Stephen Agard: “Decision Theory based on Bayes’s Theorem”, “Statistical Inference and Estimation”, “On the reasons for Interest as an Institution”, and “Proof of the Black-Scholes Formula for European Put-Options”;
John Baxter: “Counting partition matrices” and “Rigid motion”;
Paul Garrett: “Independence Results in Set Theory”, and “The role of the history of mathematics in the curriculum”;
Tian-Jun Li: “Symplectic vector spaces and symplectic matrices”;
Willard Miller: “Constructing Grids using a Density Function to Determine Concentration”;
Victor Reiner: “Critical groups of graphs”, and “Critical groups and line graphs”;
Joel Roberts: “Pedagogy of Gifted Students and UMTYMP”, “Postulates and Theorems in High School Geometry and in Math 5335”, “Archimedes’ Method Proposition 14: Archimedes’ place in the history of calculus”, “Quadric Surfaces: theory and computer drawings”, and “Comparing and contrasting high school and college calculus”;
Dennis Stanton: “Extra accuracy in some alternating series”.

The theses supervised by Professor Reiner were follow-ups to the students’ REU (Research Experiences for Undergraduates) work done under Reiner’s guidance during the summer of 2003. Both theses dealt with the notion of the critical group of a graph. This is a certain finite abelian group naturally associated to the graph, whose order equals the number of spanning trees of the graph. One of the students solved some open problems about this critical group, including one posed by Greg Kuperberg of UC Davis. The other student, who in the meantime began graduate studies, obtained results that were suggested by his REU data on the critical groups of regular line graphs. This has led to a further conjecture which is a subject of ongoing investigations by the student, Professor Reiner, and another grad student of Reiner.

CRYPTOLOGY AND CODING THEORY COURSES

These two popular courses were developed by Professor Paul Garrett and taught by him since 1995. Since there were no completely satisfactory texts covering the subject matter in a manner appropriate for our undergraduates, Paul even wrote his own books—”Making, Breaking Codes, and Intro to Cryptology”, and “The Mathematics of Coding Theory: Information, Compression, and Error-correction”, both published by Prentice-Hall. The cryptology book was recently translated into Chinese for distribution in Asia. Because of the high student interest in these courses (well over one hundred students take each of the two courses each year), three other faculty members (Mark Feshbach, David Frank, and Vic Reiner) taught crypto in Fall 2004, with Paul serving as the Course Supervisor. Don Kahn and Gennady Lyubeznik are teaching the Coding course in the spring of 2005. Steve Sperber taught Coding two years ago. Crypto and coding theory are vital areas of application of pure mathematics to internet commerce and to data storage. Owing to Paul’s dedication, our department is one of the few mathematics departments in the country with such a substantial undergrad course offering in these subjects.

News about the Graduate Program

From Scot Adams, Director of Graduate Studies

This year there are 22 incoming students, the same number as last year. Ten are international; eight are women.This year’s orientation continued the long tradition of placement exams, begun by Paul Garrett. Results of these exams are a tool to help incoming students (with the aid of their advisors) decide which of the standard first year courses they are prepared to take, and which will likely require additional preparation.

We congratulate our graduating PhD students (Oct. 2003 to Dec. 2004):

Radek Erban ("From Individual to Collective Behavior in Biological Systems.", Hans Othmer, advisor; Oxford University)
Michael L Galbraith (“Geometric Optics, Convex Functions, Carleman Estimates and Interfaces in the Boundary Control of the Wave Equation.”, Robert Gulliver, advisor; National Security Agency)
Oleg Alexandrov (“Wave Propogation in Optical Fibers: Analysis and Optimization.”, Fadil Santosa, advisor; UCLA)
Youngae Han (“An Efficient Solver for Problems of Scattering.”, Fernando Reitich, advisor; CalTech)
Nicolae Tarfulea (“Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein’s Equations.”, Doug Arnold, advisor; Purdue University Calumet)
Kyeong-hun Kim (“On Stochastic Partial Differential Equations with Variable Coefficients in C1 domains.”, Nicolai Krylov, advisor; University of Utah, Salt Lake City)
Jae Hyouk Lee (“Geometrics Motivated from Normed Algebras.”,Naichung Conan Leung, advisor; Washington University, St.Louis)
Kijung Lee (“Lp Theory of Stochastic Partial Systems.”, Nicolai Krylov, advisor; University of Rochester)
Jens Rademacher (“A Mechanism for Periodic Secondary Wave Bifurcation of Pulses in Reaction-Diffusion Systems.”, Arnd Scheel, advisor; University of British Columbia)
We congratulate our graduating Master’s Degree students (Oct. 2003 to Sept. 2004):
Hyeung-Joon Kim (Naresh Jain, advisor)
Lin Fan (Stephen Agard, advisor)
Yang-Jin Kim (Hans Othmer, advisor)
Guang-Tsai Lei (Walter Littman and Peter Rejto, advisors)
Fan Yang (Stephen Agard, advisor)
Mingyan Lin (Mitchell Luskin, advisor)
Zahra Al Shamrani (Paul Garrett, advisor)
Lisa Rassel (Fadil Santosa, advisor)
Shagufta Nazir Ahmad (Bernardo Cockburn, advisor)
Leah P Prom (Harvey Keynes, advisor)
Adam Galambos (Victor Reiner, advisor)

Yang-Jin Kim, Shagufta Nazir Ahmad and Zahra Al Shamrani continue as graduate students in our department. According to an analysis done by the Graduate School, our graduate program’s completion statistics have a favorable comparison with the general results in Engineering, Physics, etc. For example, the six year completion rates for our PhD graduate students entering in 1994,1995, 1996 and 1997 are, respectively 58%, 67%, 85% and 73%. The general figures for the same years are 44%, 48%, 49% and 37%.

Application for admission to our graduate program shows a favorable trend. According to the Graduate School, we had 176 completed applications in 2000-2001, then 207 in 2002-2003 and then 249 in 2003-2004. We are hoping for another great year!

We have begun a long process of trying to determine the current whereabouts of our 285 Mathematics PhD graduates since 1981. For 184 of these 285, we have a last-known email address, and will soon begin testing to see how many of these addresses are currently functional.

NEW GRADUATE COURSE OFFERINGS

Professors George Sell and Tian-Jun Li developed interesting new graduate level courses on Global Climate Modeling and on Symplectic Structures on Manifolds. We thank them both for sharing with our readers their descriptions of these innovative courses. Professor Sell is presenting his course for the first time during the Spring 2005 Semester. It is his intention to make this course a regular graduate level offering in the School of Mathematics. The description of Professor Sell’s course appears in the section “FEATURED COLLEAGUES”. Professor Li taught the course for the first time during the 2003-04 academic year. He has written a book on the subject, based on the lecture notes of his course. The title is “Moduli spaces of symplectic structures” and it will be published by the World Scientific Publishing Company.

SYMPLECTIC STRUCTURES ON MANIFOLDS

The course covers an important and rapidly developing new area of mathematics and mathematical physics. Symplectic structures originated in classical Hamiltonian mechanics, including the mechanics of the solar system as well as rigid body systems. Over the years, they have become important in many branches of mathematics. This development is an excellent example of how physics inspires mathematics. In modern terms, a symplectic structure is given by means of a non-degenerate closed differential form of degree 2. Every 2-manifold has such a structure, via a volume form. One rich source of symplectic manifolds comes from a beatiful branch of mathematics, namely algebraic geometry. In the last few years it has become apparent that symplectic geometry is also closely linked to low dimensional topology.

The course organization is as follows. In the fall semester (and part of the spring) the aim is to develop basic concepts and describe various important constructions. Prerequisites include some familiarity with differential forms and manifolds. The rest of the course focuses on recent directions of research such as applications of pseudo-holomorphic curves and Seiberg-Witten theory to classifying symplectic structures on four-dimensional manifolds.

Tian-Jun Li

GRADUATE STUDENT TOPOLOGY CONFERENCE

A topology conference intended specifically for graduate students was held at the School of Mathematics on April 24th, 2004. Twenty-one students from around the nation gathered to meet their colleagues, give research talks, and listen to the keynote address by Professor Fred Cohen of the University of Rochester.

The first Graduate Student Topology Conference was held at the University of Notre Dame in 2003; Northwestern University has offered to host it in 2005. Based on the success of the topology student conference, the School of Mathematics will host the first-ever Graduate Student Combinatorics Conference in April of 2005 (see below).

The organizers would like to thank Harry Singh and Kathy Swedell for their help, and to the department itself for providing funds for this unique conference.

James Swenson, Jonathan Rogness

GRADUATE STUDENT COMBINATORICS CONFERENCE

On the weekend of April 15-17, the department will host the first-ever Graduate Student Combinatorics Conference. This conference — modeled after the annual Graduate Student Topology Conference which was held here in 2004 — will feature over 30 participants and 25 graduate student speakers from across the U.S. and Canada. The conference will have two keynote speakers: Richard Ehrenborg and Margaret Readdy, both of the University of Kentucky. The conference is being organized by Dan Drake, John Hall, Ning Jia, Sangwook Kim, and Muge Taskin. Funding has been provided by the department and the Institute of Technology. The organizers hope that this conference will follow in the footsteps of the Student Topology Conference and become an annual event hosted at universities across the country.

Minnesota Center for Industrial Mathematics

INDUSTRIAL PROBLEMS SEMINAR

The MCIM/IMA Industrial Problems Seminar for the academic year 2003-4 featured 16 speakers representing various industries. Topics for the seminars were quite varied as well. Richard Derrig spoke about a mathematical model for insurance fraud detection. Apo Sezginer from Invarium, a Silicon Valley startup, spoke about how to advance lithographic methods in chip making. Former MCIM student Scott Shald gave a presentation about Coherent Technology’s effort in detecting leaks in gas pipelines. Many of the talks are recorded and available in streaming media from the IMA web site.

INTERNSHIPS

Seven students went on internships during the summer of 2004. Tara Rangarajan worked with medical researchers at the Hennepin County Medical Center on a method for measuring brain bloodflow in trauma patients. Thomas Hoft’s project at Coherent Technology was on scattering of light by aerosols. Chuan Xue developed a signal processing algorithm for data smoothing and interpolation for Medtronic. Other projects are described in MCIM’s web page.

STRENGTHENED COLLABORATION WITH MEDTRONIC

Cooperation between MCIM and leading medical device maker Medtronic, based in Fridley, MN, dates back to the summer of 1996 when the company started engaging mathematics graduate students as interns. Over the years, students have worked on projects as diverse as analysis of data for health management, to computing stresses in wire-rope cables. During the summer of 2004, Professor Carme Calderer, together with graduate students Brandon Chabeau and Hang Zhang, started a collaboration with Medtronic scientists on a materials modeling project. Both students are supported as research assistants in the School of Mathematics by a research grant from Medtronic. The project is likely to lead to scientific publications, proprietary intellectual properties, as well as two PhD theses for the students.
Medtronic expressed its appreciation for the value MCIM brings to the company by making a donation of $50,000 in April 2004.

Drs. Becky Bergman, VP for Research, and Darrel Unterecker, Director for Research, at Medtronic, with Larry Gray, Carme Calderer, Fernando Reitich, and Fadil Santosa.
The accompanying photograph, taken at the Campus Club, shows Drs. Becky Bergman, VP for Research, and Darrel Unterecker, Director for Research, at Medtronic, with Larry Gray, Carme Calderer, Fernando Reitich, and Fadil Santosa.

NEW FACULTY

Gilad Lerman, Assistant Professor in the School of Mathematics since Fall 2004, is a new faculty associated with MCIM. He received his PhD from Yale University and was postdoc at the Courant Institute for Mathematical Sciences at New York University before joining the department. Gilad works in several areas including harmonic analysis, multiscale data analysis, and learning theory. He is involved in many of the center’s activities and interacts with industry visitors as well as students.

 

INTERVIEW WITH YI-JU CHAO (PHD 1999)

Yi-Ju Chao
Yi-Ju Chao, who left after her PhD in 1999, moved back to Minnesota about a year ago. During her studies at the University of Minnesota she took part in the activities offered by MCIM. She was an intern at Medtronic in the summer of 1997, and finished her MS degree in Mathematics with emphasis in Industrial and Applied Mathematics in 1998. In the summer of 1998 she did an internship at Motorola. Both her MS and PhD thesis topics were based on the work she did as an intern. Currently a partner in the firm Morton Consulting Corporation, she recently spoke with Fadil Santosa about her experience after leaving the School of Mathematics.

Fadil Santosa: You were a student on the regular Mathematics track when you started here in 1994. What made you decide to take an internship?

Yi-Ju Chao: I heard a lot of buzz from other students about the industrial internships that were offered by MCIM. A lot of the students that have done it really enjoyed the experience. I also felt that it was the easiest way for me to find out what it would be like to work in industry.

FS: What was your first internship?

YC: I was an intern at Medtronic. I worked with Teresa Ruesgen on developing a predictive health model from heart-failure patient data.

FS: Did you feel you were well prepared for the project?

YC: Not at all. In the beginning, I was just trying to use existing mathematical tools to solve the problem. I found that I needed to understand the problem first. So, I read a lot of medical literature, and then developed a model based on the data.

FS: Do you think that what you did there was valuable to Medtronic?
YC: I remember the final presentation I made at Medtronic. The people in the audience asked a lot of questions, and were very excited. They expressed interest in continuing the research I started there.

FS: You must be happy about your contribution.

YC: Well, overall I felt I was ignorant about medical science and wished to learn more. But on the other hand, I did feel some satisfaction. It’s not the same satisfaction that I feel after proving a theorem. It’s different. I felt that I have used mathematics to answer a relevant problem from the real world. I ended up writing a Master’s thesis based on this work.

FS: Your second internship was at Motorola, and the research you did there ended up as part of your PhD thesis. How did you get connected with Motorola?

YC: I met Dr. Philip Fleming when he came to speak at the IMA Industrial Problems Seminar. You thought that there was potentially a good match and introduced me to him. I had an extended discussion with him about his research afterwards. Later he invited me to work with his team at Motorola as a summer intern.

FS: What was the project?

YC: Actually, it was quite a mathematical project. Phil Fleming, who was trained in mathematics at the University of Michigan, had posed a problem in queueing theory arising from communication networks. I was able to identify it as a mathematical problem. What I had to do was to prove that a certain type of semi-martingale weakly converges to a diffusion process. Much to Phil’s surprise, I solved this problem, which back then, was an open problem, within a few weeks.

FS: Did you publish this work?

YC: Yes, it has appeared in Queueing Systems, and it constitutes a major part of my PhD thesis, which was supervised by Professor Nicolai Krylov.

FS: How do you think you ended up with a job offer from Motorola after you finished your PhD?

YC: I always believe people are hired for a combination of reasons including also non-technical aspects. I think my boss believed that I could be trained and made valuable to the company even though I knew little about engineering. I also showed enough willingness to learn the engineering system that they were working on at the time. The project I described wasn’t the only thing I did at Motorola during my internship. After I finished it, I did some analysis of network data with heavy tailed distribution. The second project allowed me to work with other people on a problem which was very different, more practical. It proved to the people there that I could do more than solve math problems.

FS: What was your job title at Motorola?

YC: Lead software engineer. I guess that was the closest title they had for applied mathematician.

FS: How long did you work there and what did you do?

YC: I worked there for a little more than 18 months, and then moved to New York with my husband. When I first got to Motorola, I was given a tour of the projects they were doing. My first project was related to analysis of heavy tailed distribution, which was a hot topic during the Internet boom. But I soon realized that what I was doing had little to do with real product development. So I took on a project involving a new wireless network standard, doing performance analysis of wireless communication systems. This project later evolved into network architecture design. This turned out to be good training as it led to my second job.

FS: And where was that?

YC: The company is called InterDigital Communications Corporation. It is involved in wireless network design and wireless technology platforms. I was there for more than two years, developing network architecture designs, and representing the company in a standard organization of next generation mobile wireless networks.

FS: Now you are back home in Minnesota, and you established a consulting firm. What’s it like to have your own business?

YC: Having your own business is both exciting and challenging. We started out by doing consulting in financial engineering. We are now more focused on doing consulting in distributed control. Working for yourself you have a lot more freedom to choose, but it can be a challenge because your choice must make good business sense.

FS: It’s been over 5 years since you finished. In that period you have gone through several industries. What lessons have you learned that you could share with our students?

YC: Be prepared to keep learning when you leave school and enter the workforce, but not the same way as you have done in school. Mathematical skill is only a small part of what you need to succeed in industry. In the work place, your mathematical training will give you some advantages over your colleagues: one is the ability to reason rigorously and another is the ability to think deeply. But you will be at a disadvantage in other ways: one is ignorance of technology and the reality of the business world, two is lack of training working as part of a team, and three is lack of experience communicating with non-mathematicians. While your mathematical ability may get you a job in the first place, you have to improve yourself in the areas where you are weak. Someone who works hard to learn these other skills and who is a fast learner can advance very quickly.

FS: Should we do more training in non-mathematical skills such as those you described?

YC: First of all, the good news is that university does train students in mathematics very well and industry cannot provide this type of training that leads to rigorous and deep abstract thinking. These skills really do give an edge to mathematicians in industry. On the other hand, universities are not better than industry when it comes to teaching these other skills. The best approach is for the university to concentrate on doing what they do best in the classroom while providing students opportunities to interact with industry to develop other skills. I think I benefited a lot by talking to industrial speakers who visit the department, and of course, from the internships that I did. I recommend internship to every student, whether they will end up in academia or in industry.

Alumni and Friends

Letter from J. Allen Cox

December 28, 2004

Over the years Honeywell scientists and engineers have maintained various forms of relationships with universities in general and the University of Minnesota in particular. In many cases these relationships were spawned at the individual level between a professor and a Honeywell employee familiar with the professor’s work, and frequently they took the form either as consultative agreements or as collaboration on specific government contracts. However, in 1982 the establishment of the IMA offered a completely new approach to promote university-industry collaboration by formally creating an organization for that very purpose and driving the process by requiring industry’s “buy-in” from the start. The buy-in by industry came in two forms: hard cash for membership and student support and specific problems in applied mathematics. The IMA responded by delivering outstanding performance at a great value to the industrial partners; the best evidence of this is found both in the continued strong support for the IMA after 24 years and in the number of similar centers that have been created around the country based on essentially the same model.

My own personal involvement with the IMA started in 1981 as the point-of-contact in the Honeywell Laboratories. Initially, my participation consisted of presentations at the IMA on problems in my field of interest (optical systems and photonics), attending seminars, and recommending Honeywell on the governing board. Frankly, there was a bit of a struggle in the first few years trying to define an optimum mechanism to establish specific collaborative projects within the IMA. The industrial postdoctoral program turned out to be just the answer and, starting with the initial year in 1990, led to four consecutive postdoctoral appointments through 1996 under my mentorship and directed by Avner Friedman.

All four positions supported technology development within the Photonics section at the Honeywell Labs generally concerned with optoelectronic components and systems for very high speed data communications and specifically in the fields of diffractive optics and optical waveguides. The first two postdocs, David Dobson and Gang Bao, developed several design and modeling codes for diffractive elements. These codes played a direct role in winning, and executing, a ~$5M DARPA program to develop a MEMS-based, tunable spectral filter for infrared imaging. The software was also used in a number of other projects to design antireflective structures, polarizing elements, special laser mirrors, and laser beam homogenizing elements. The work that the last two postdocs, Nathan Katz and Lei Wang, did on modeling mode propagation in optical fibers and coupling of VCSELs* to optical fibers was used in one DARPA program, but it was much more valuable for Honeywell in developing a number of VCSEL products for high speed data communications. In total, the effort of these four collaborations resulted in at least twelve patents awarded to Honeywell. The VCSEL business was sold in early 2004 to Finisar for $75M, and although we can’t claim the IMA work was critical to the sale, it did result in a number of patents and product designs which certainly contributed to the overall value.

Other Honeywellers have also had significant involvement with the IMA (and MCIM, for that matter). Blaise Morton, Gunter Stein, and Tariq Samad are especially noteworthy for coordinating a number of collaborations in the area of control systems. Tariq is currently the Honeywell representative on the governing board and is a strong proponent for continuing Honeywell’s participation in the IMA, and I think the future of this relationship looks both secure and promising.

*VCSEL = vertical-cavity surface-emitting laser

J. Allen Cox, Ph.D.
Senior Research Fellow
Honeywell Laboratories

Letter from Tariq Samad

Every major technological advance in modern times can be attributed in significant part to investment in mathematics and its applications. From computers to communications, genetics to geophysics, our understanding of nature—and of our own artifacts—is actionable to the extent it is formalized. We seek to model phenomena through mathematics, to optimally design and operate our engineered systems using mathematical techniques, to foster worldwide intellectual collaborations through the universal language of mathematics, and even to capture the limits of our understanding and abilities with mathematical precision.

In this case, what’s been true in the past will doubtless hold in the future. Organizations—whether at the level of states or corporations or academic centers—that invest in mathematics will be the ones that will be at the forefront of technological progress, to their advantage over their peers and competitors and with attendant economic and societal benefits for their stakeholders.

Our state has a true jewel in this regard. The Institute for Mathematics and Its Applications (IMA) at the University of Minnesota is internationally recognized as a truly one-of-a-kind center that connects expertise in all subfields of mathematics with problems in numerous spheres of industry, government, and society. The IMA’s distinguished cadre of visiting scientists, its annual thematic programs and numerous workshops, the IMA Public Lectures, and other mechanisms have all been designed to increase the impact of the abstract discipline of mathematics on the real world and real-world problems. The IMA privileges the organizations (including the State of Minnesota) that support and engage with it, not only through the Institute’s worldwide recognition for excellence but, and more importantly, by affording them competitive advantages as a result of the scientific and technological developments accruing from IMA participation.

Tariq Samad

Tariq Samad is a Corporate Fellow at the Honeywell ACS Advanced Technology Laboratory, and represents Honeywell on the Industrial Advisory Board of the IMA.

Mathematics News from Normandale Community College

We thank Julie Guelich, Dean of Normandale, for the following update on their very active mathematics programs.

 

Peggy Rejto, Julie Guelich
Peggy Rejto, Julie Guelich

Normandale Community College and the University of Minnesota Department of Mathematics have had a close relationship for many years. More than 50% of the mathematics faculty members at Normandale received their graduate mathematics training at the U of MN. The joint Mathematics/Computer Science Department at Normandale has 32 faculty members, 4 of whom are adjunct members. Faculty members who received their graduate training at the U of MN are well-prepared to teach the mathematics courses offered at Normandale. All faculty members at Normandale have at least a master's degree, and many have a doctorate. New faculty members at Normandale have a three-year period of probation, during which time they create a teaching portfolio. Faculty members are not required to carry out mathematical research as a condition of employment, since the emphasis at Normandale is on the scholarship of teaching. Many faculty routinely give presentations at professional conferences relating to the curriculum and teaching of lower division coursework. Increasingly of late, assessment of student learning is a major focus of post-secondary education. Colleges are required to report on assessment efforts to the North Central Section of the Higher Learning Commission, the accrediting body for colleges and universities in the United States. Knowledge of and experience with the process of assessment for mathematics coursework is important for new faculty members who wish to teach at Normandale or any other two- or four-year college.

Many of the students in the Math/CSci Department at Normandale transfer to the Institute of Technology at the U of MN. The Normandale curriculum was designed with the University in mind, and coursework transfers easily. During the past year, a new degree, “Associate of Arts with Emphasis in Mathematics,” was created. It includes the lower division coursework for a baccalaureate degree in mathematics. Normandale also offers two other degrees – the Associate of Science in Engineering Foundations and the Associate of Science in Computer Science – that articulate with programs at the Institute of Technology. In August 2004, Normandale received a four-year National Science Foundation CSEMS grant of $400,000 for scholarships for mathematics, engineering, and computer science students. The Normandale mathematics faculty members hope that these scholarships will support Normandale students who are strong in math and science, allowing them to attend college full-time without working at outside jobs.

Our Alumnus, Joe Schumi - A Career in Actuarial Science

I received a Bachelor of mathematics from the Institute of Technology in 1966. At the time, it seemed this best prepared me for graduate school in mathematics. It was a good time to be in math or the sciences as the race to the moon provided generous funding.

However five years later, after Nixon was elected president, money was not so plentiful. While previously a Minnesota Ph.D. graduate could obtain a tenure-track position at a school with a nationally ranked football program, though perhaps not a nationally ranked math department, by 1971, when I received my Ph.D., some were fortunate to obtain a position at a division III school.

But not everyone was so fortunate. While teaching part time, I had become aware of the actuarial profession through on campus Actuarial Career Day presentations by the Twin Cities Actuarial Club. As a result, I took and passed the first two actuarial exams and obtained a few interviews. Unfortunately, the sentiment expressed by potential employers was that someone like me would leave the actuarial profession as soon as the academic market improved.

In the early 70’s, the St. Paul Companies was expanding its actuarial department. This was driven to a large extent by changes in the insurance industry restricting the ability of companies to share resources and requiring companies to do more on their own. St. Paul, unlike the life insurance companies I had spoken with previously, was a property-casualty insurance company, so taking a position at St. Paul represented a career choice between the two major ‘brands’ of actuaries in the United States. (Note from the editors: Joe eventually rose to the rank of Vice President.)

[Most people are probably aware that attaining recognition as an actuary requires passing a series of nine or ten exams. While the early topics are mathematical, the latter exams include accounting, taxation, regulation as well as specific insurance topics. While advanced mathematics is not required, good study habits are, as the exams are mainly self study. And while the companies support the program with exam passing bonuses and some on the job study time, the actuarial student is expected to study 300 to 400 hours on their own time every six months until the exams are completed. As the pass ratio is generally close to 40%, good students will often complete the exams in under 10 years.]

New recruits at the St. Paul were assigned to pricing units that helped develop rates for insurance policies or corporate units that worked mainly on reserves for insurance claims that had occurred but had not yet been paid. In my first assignment, I worked with the underwriters of our products for farmers and ranchers. The work included analyzing the recent results to determine if rates needed to be changed to meet the companies' profit objectives and trying to project future results. Early on, my job was to computerize rate-making formulae, first using Fortran in a mainframe environment, and after about ten years, moving to a personal computer environment.

As one progressed through the exams, the areas of responsibility broadened and newer actuarial staff were assigned as subordinates.

By the 1980’s there were many people with advanced mathematical training entering the financial professions and there were changes taking place in nature of the products a company was expected to deliver. Customers were looking for insurance products that were more closely tailored to their needs — policies that covered only very large losses or unusual accumulations of small losses. Insurance companies were looking for ways to more efficiently purchase the insurance they buy to protect themselves from catastrophic losses. Competition required that these estimates be increasingly precise. These products presented more mathematically challenging problems, which were often not solvable in tidy closed forms, but with the advent of powerful desk top computers, were computationally tractable. This was also the time that the so called ‘rocket scientists’ were entering the financial markets with tools such as the Black-Scholes formula for pricing options.

While these new models were very sophisticated, they rely on estimates of parameters and the basic assumptions that underlie insurance. The proper use of these tools then requires the actuary to improve the quality of the parameter estimates and continuously test the validity of assumptions in an ever changing environment. One of the basic principles underlying insurance is that combining the random financial results of number of similar but statistically independent entities reduces the aggregate uncertainty. Sometimes these assumptions can be taken for granted. [Until a 9.0 earthquake struck off the coast of Indonesia, who would have thought that buildings in Thailand and Somalia didn’t represent very independent risks.]

Competition continued to drive the insurance industry, the narrowing of margins driving more and more companies to the brink and/or into the arms of suitors which often led to the elimination of positions deemed redundant. Eventually, my former employer merged with one company, then another. Fortunately, I had a sufficient number of years of age and years of service to retire.

In any case, it was a fascinating time to be a mathematician in a non-traditional setting.

Joe Schumi

Talk by Michael Postol

Dr. Michael Postol, a 1990 Ph.D. graduate of our department who is employed by the National Security Agency, visited in July 2004 and gave an interesting talk on his ongoing work on “Intrusion Detection”. His presentation was attended by colleagues from several departments. Mike wrote his Ph.D. thesis in the area of algebraic topology. An abstract of the talk follows.

Title: Computer Intrusion Detection Using Features from Graph Theory and Algebraic Topology

This talk describes the problem of profiling the users of a network for the purpose of intrusion detection. We look at three graphs associated with each session on a Windows NT machine. A number of features are extracted from these graphs and fed to a classifier which uses “random forest” techniques for distinguishing between the graphs associated with one user and those associated with another. The features can be taken from the properties of the graphs themselves as well as from a variety of simplicial complexes which can be built using the information contained in the graphs.

The talk presents some initial results as well as a number of ideas we plan to pursue in the near future.

IT Center for Educational Programs (ITCEP)

ITCEP programs have a major impact on education throughout Minnesota. Our Master’s Degree Program in Mathematics with Emphasis in Education is administered in cooperation with ITCEP, with ITCEP’s Director Professor Harvey Keynes serving as advisor for the students enrolled in the program. Our faculty and graduate students are also enthusiastic participants in the UMTYMP program. ITCEP’s Communications Coordinator Alexandra Janosek reports below on these programs as well as on an exciting ITCEP program to enhance the mathematics skills of public school teachers. We are grateful to Alexandra for providing these articles.

MASTERING MATHEMATICS & EDUCATION

Though students of the Master’s Degree Program in Mathematics with Emphasis in Math Education come from diverse backgrounds and continue on to various careers, the factor they have most in common is their love of mathematics.

Through the program, these students have the opportunity to indulge their higher math craving, gain invaluable teaching experience, receive financial aid, and earn a teaching license – all in just two years – giving them an advantage in any number of career fields.

The program, housed in the School of Mathematics as a Master’s of Science Degree program, requires students to take a year each of advanced math courses and math education courses, including a semester of student teaching in a high school. In addition, all students have a paid TA position in college-level classes offered by the School of Mathematics or the University of Minnesota Talented Youth Mathematics Program (UMTYMP). “Students aren’t accepted into the program unless they are qualified for a TA position in the School of Math,” says Harvey Keynes, the advising professor for program students. This means they were successful in their undergraduate programs, have a primary focus on mathematics, and a strong interest in teaching.

These qualifications are evident in the students, according to Terry Wyberg, an instructor in the Math Education Department who works closely with Keynes and program students. “The students’…math content knowledge is exceptional. They are so excited about math and discuss it with such enthusiasm that the classes are more vibrant for having them there.” With their experience in both high school and college settings, graduates of the program “really have a feel for what teaching is like,” says Wyberg.

And these are qualities schools are seeking. “I easily found a job,” states Justin Jacobs, a 2002 alumnus. “I taught…at Westwood Middle School…[and] Park Center Senior High... I feel that I have been successful at both schools, and I have to give much of the credit for my success to my college experience.” Melissa Morgan, also a 2002 graduate, adds, “With a Master’s degree, I am paid more and I have been able to teach more advanced classes, which I enjoy very much.” After 6 years teaching, Carraig Hegi, a graduate of the first class in 1998, is a high school teacher, math team advisor and creates “new materials as needed” for his school.

But the program prepares graduates for other career paths too. “It gives me a lot of options for my career,” says Chris Robinson, a current first-year student. “I see myself teaching in a junior high or high school over the next 5 or 6 years, but I also have an interest in developing curriculum.” Sarah Cherry, one of Robinson’s classmates, also sees herself developing curriculum and teaching but in a non-classroom setting, such as a museum or a university center. John Hall, one of Hegi’s classmates, is now finishing his Ph.D. in Mathematics. He says “I am a much better Ph.D. student than I would have been coming straight from undergraduate work.”

Considering the quality of students emerging from the program, it is no wonder those closely involved hold it in such high regard. It has proved a, “constructive, sustainable and worthwhile master's program,” according to Professor Paul Garrett. “This program potentially could change the way math is taught in Minnesota. It has resulted in a leadership group who really understand mathematics.”

MATH PROGRAMS FOR PROMISING YOUTH

The programs for mathematically promising elementary and secondary school students developed by the IT Center for Educational Programs (ITCEP) continue to thrive. These academic year and summer programs provide students with a supportive environment in which to explore challenging mathematics at the University of Minnesota.

In 2004-05, five hundred-seven (507) students are participating in ITCEP’s five-year premier academic program, the University of Minnesota Talented Youth Mathematics Program (UMTYMP). UMTYMP offers a rigorous mathematics curriculum that allows highly motivated, talented students in grades 5-12 to learn complex topics and gain meaningful insights at a high level and accelerated pace. The courses are taught by math department familiars such as post doctoral fellows Jennifer Wagner and Simon Morgan, doctoral students John Hall and Jonathan Rogness, and by Professor Harvey Keynes. The first year calculus course has a record enrollment of 85 students, 18 of whom are in the eighth grade or below.

In addition to UMTYMP, ITCEP offers enrichment programs at several levels during the school year and in the summer. About 500 students enroll each year in the 5 academic year programs for students in grades 3-10. These programs provide opportunities to learn and enjoy mathematics and introduce students to the role of mathematics in society through meeting and working with scientists, engineers, and mathematicians. Students also have the opportunity to meet and interact with U of MN undergraduate students, most of whom are majoring in mathematics, engineering, or science. Young students tend to base their educational and career goals on what they have experienced and the role models they emulate. ITCEP continues to offer these experiences to students in the summer. In conjunction with Youth & Community Programs of the University’s Department of Recreational Sports, ITCEP provides math classes varying from Geometric Art (8-9 year olds) to more advanced classes in Algebra and Geometry (13-15 year olds).

In 2005, ITCEP will launch a new summer course that will lay a solid foundation of analysis, geometry and vectors from which calculus-ready students can springboard into a calculus course, especially UMTYMP Calculus I. Jonathan Rogness, who will receive his doctorate from the Department of Mathematics in June 2005, will develop and teach the course in collaboration with Professor Harvey Keynes. In 2006 and 2007, ITCEP plans to develop and introduce prequels to this course – Algebraic Reasoning and Connections to Geometry and Geometric Reasoning and Connections to Algebra – with the help of ITCEP post-doctoral fellows.

These post-doctoral fellows, together with University faculty and doctoral students, will also help with the continuation of ITCEP’s rising Math Seminar series. In these monthly seminars, accelerated high school and college students actively participate in a dynamic discussion of concepts beyond calculus and innovations in mathematical research.

Another innovative ITCEP enrichment program on the 2005-06 horizon is a “Math Circle” where middle and high school students can delve more deeply into geometric reasoning through group problem solving, mathematical discussions and contests. Students will be encouraged to lead their own explorations into the mathematical topics.

For further information on these programs, contact the IT Center for Educational Programs or visit our website: www.itcep.umn.edu/.

THE MATHEMATICS WITHIN

Ours is not to question why,
Just to invert and multiply!

As a teacher participant in the 2003-04 Improving Teacher Quality (ITQ) Mathematics Within program, John Weimholt modified the well-known quote to illustrate common elementary school approaches to teaching mathematics. Fellow public school teachers enrolled in the 2003 summer course and the instructional team working with them appreciated this quip and the reality that it reflects.

The ITQ Mathematics Within Program, started in 2002, combines teachers’ experiences with faculty knowledge to increase teachers’, and therefore students’, understanding of grade 3-7 mathematics concepts and how these concepts relate to one another and with concepts throughout K-12 education.

The partnership between public school teachers and IT Center for Educational Programs (ITCEP) faculty is invaluable, according to Jennifer Tolzmann, a Forest Lake Public School District Coordinator who has progressed from teacher participant in 2002 to instructional team member in 2004. The program fosters mutual learning and sharing, says Professor Harvey Keynes, Director of ITCEP and leader of the Mathematics Within instructional team. “Faculty members learn to respect teachers’ abilities to model pedagogical technique and teachers appreciate faculty efforts to share their knowledge of core mathematical topics.”

“No one ever explained to me the 'whys' of mathematics before,” revealed one 2003 teacher participant. “Asking why a rule works instead of just applying it – it’s a totally new way of thinking for most of the teachers,” says Assistant Professor Simon Morgan, one of the instructional team members. For example, one of the techniques used to explore concepts was drawing models that explain why commonly known rules, like ‘dividing by ½ is the same as multiplying by 2,’ are true. “Visual representations used to explain why actually helped me ‘get it,’” reports one of the teacher participants.

More elementary teachers ‘getting it’ is the key to nurturing student achievement, says Tolzmann. “I feel more comfortable answering students’ questions and letting them explore,” explains a teacher after taking the 2004 summer course. A 2003 summer teacher participant states: “Taking time to look at some of the [mathematical] patterns and relationships helped me deepen my understanding and ability to relate them to my students.” In grades 3-6, students learn foundational mathematics concepts; understanding these concepts will facilitate the rest of their education.

When teachers of these grades appreciate what an impact they have on their students’ mathematical future, they realize “they can make a difference in their job,” says Tolzmann. Morgan can tell something has changed in the teachers when they return to the University for their Spring Follow-up Workshop – “they are more confident, their students are more confident and that leads to more success in the classroom.” “I am a changed person!” exclaims a teacher participant.

The Mathematics Within program not only increases teacher confidence in their ability to teach mathematics, it motivates them and helps them take leadership roles at whatever level they want – school, district, state or nationally, according to Keynes. To date, 66 elementary school teachers from 18 Minnesota public school districts have participated in the program. Among these are some of education’s leaders of tomorrow.

The ITQ projects are funded in part by a grant from the Minnesota Higher Education Services Office. For more information, visit www.itcep.umn.edu/profdev.

Contact Us

School of Mathematics
University of Minnesota
127 Vincent Hall
206 Church Street S.E.
Minneapolis, MN 55455
http://www.math.umn.edu
e-mail: dept@math.umn.edu
telephone: (612) 625-5591
fax: (612) 626-2017

Department Head:
Lawrence Gray (612) 625-5591

Graduate Studies:
Scot Adams, Director,
(612) 625-1306
adams@math.umn.edu

Undergraduate Studies:
David Frank, Director,
(612) 625-4848
frank@math.umn.edu

IT Center for Educational Programs (ITCEP)
Harvey Keynes, Director
4 Vincent Hall
206 Church Street S.E.
Minneapolis, MN 55455
telephone:(612) 625-2861
fax:(612) 626-2017

Institute for Mathematics and
its Applications (IMA)
Douglas Arnold, Director
Arnd Scheel, Deputy Director
Debra Lewis, Associate Director
400 Lind Hall, 207 Church Street S.E.
Minneapolis, MN 55455-0463
http://www.ima.umn.edu
telephone: (612) 624-6066
fax: (612) 626-7370

Minnesota Center for
Industrial Mathematics (MCIM)
Fadil Santosa, Director
Fernando Reitich, Associate Director
http://www.math.umn.edu/mcim
e-mail: mcim@math.umn.edu
telephone:(612) 625-3377
fax:(612) 624-2333

The Math Newsletter is published annually for the members,
alumni and friends of the School of Mathematics.

Editorial Board: Rhonda Dragan, Donald Kahn (Chair), Karel Prikry, Peter Rejto, Peter Webb