School of Mathematics Newsletter - Volume 9 - 2003

Welcome to Incoming Faculty and New Postdoctoral Appointees

It is a pleasure to welcome the new members of the School of Mathematics — Professor Ofer Zeitouni and Assistant Professors Tian-Jun Li and Ezra Miller. We also welcome the new Dunham Jackson Assistant Professor Christof Melcher, as well as Postdoctoral Associates Marshall Hampton, McKay Hyde and Jeremy Martin. We are also very pleased to welcome new staff members Harry Singh, who replaces Monika Stumpf as Executive Assistant to the department head, and Rhonda Dragan, who replaces Becky Johnston as Administrative Aide at the MCIM.

Professor Ofer Zeitouni is a world leader in probability theory and its applications. He has made important contributions to the theory of large deviations, random walks, random matrix theory, and filtering and statistical detection. He received his Ph.D. in electrical engineering from Technion (Israel) in 1986 and rose there to the rank of Professor of Electrical Engineering and Mathematics. He has held visiting appointments at a number of leading institutions including MIT, UC Berkeley, and ETH Zurich. His honors include the Bergmann Memorial Research Award (1991), as well as an invited address at the International Congress of Mathematicians, Beijing 2002.

Assistant Professor Tian-Jun Li earned his Ph.D. in 1996 from Brandeis University. He spent the following three years as a Gibbs Instructor at Yale University and as a Visiting Member at the Institute for Advanced Study, Princeton. From 1999 to 2002 he was on the faculty of Princeton University. His research area is symplectic topology.

Assistant Professor Ezra Miller earned his Ph.D. in 2000 from UC Berkeley and spent the past two years at MIT as an NSF Postdoctoral Research Fellow. His other honors include a Alfred P. Sloan Doctoral Dissertation Fellowship, a Julia B. Robinson Fellowship and the Charles B. Morrey Award, all of which he received while a graduate student at UC Berkeley. His research areas are algebraic geometry, combinatorics, commutative algebra and mathematical physics. He is spending the 2002 - 2003 academic year as a visiting researcher at MSRI Berkeley.

Dunham Jackson Assistant Professor Christof Melcher received his Ph.D. in 2002 from Max-Planck-Institute, Leipzig. His research areas are partial differential equations and applications to problems in continuum mechanics, magnetism and materials science.
NSF Postdoctoral Research Fellow Marshall Hampton earned his Ph.D. in 2002 from the University of Washington. His research areas are dynamical systems, celestial mechanics and image processing.

NSF Postdoctoral Research Fellow McKay Hyde earned his Ph.D. in 2002 from Caltech. His research areas are numerical solutions of PDE with emphasis on high-order methods, fast algorithms, integral formulations and spectral methods.

NSF Postdoctoral Research Fellow Jeremy Martin earned his Ph.D. in 2002 from the University of California at San Diego. His research areas are combinatorics and algebraic geometry.

From the Department Head


Naresh Jain

I will be stepping down as department head at the end of this academic year after eight years in that position. As I reflect on these years, I realize that they have been challenging and also very rewarding. I believe we have come a long way since I assumed the stewardship of the department, but the credit for all the positive changes belongs to my faculty colleagues and an outstanding staff. The spirit of cooperation that I enjoyed from all quarters makes me feel very humble and also very proud of the School of Mathematics.

During this time, a large number of faculty members retired after years of highly distinguished service to the department and the University; a few also resigned their positions. Replacing many of these outstanding scholars will never be possible, but thanks to the extraordinary efforts of my colleagues, we have been able to attract some excellent faculty members in several areas of strength in the department. The establishment of the Digital Technology Center (DTC) at the University presented an opportunity for us to establish a program in mathematical biology with the hiring of Hans Othmer as a DTC Professor with tenure home in our department. This program has attracted a large number of graduate students and postdocs and has generated close collaboration with several departments in the biological sciences, most notably with the Department of Ecology, Environment & Behavior. It was also fortuitous for us that the director of DTC, Andrew Odlyzko, happens to be a prominent mathematician with our department as his tenure home. In spite of his very busy schedule as DTC director, Andrew finds time to be seriously involved in the activities of the department and has been making significant contributions to it. We are also very fortunate to have Douglas Arnold at the helm of the renowned NSF sponsored center, The Institute for Mathematics and Its Applications (IMA). We are looking forward to the twentieth anniversary celebration of the IMA in June, 2003.

It was not too long ago that we were struggling to develop effective formats and techniques to improve our undergraduate programs. Again, due to the ceaseless efforts of many of my colleagues and financial support from the IT Dean, we now offer a new calculus curriculum to over 600 Institute of Technology students in a format that has made a real difference in the training, performance and retention rates of the students in these courses. We recently started a promising honors program in mathematics together with a ‘Junior Colloquium’ and a Math Club. We also provide opportunities for research experiences for undergraduates. This program is intended to provide year-round activities in an exciting environment for those undergraduates who wish to pursue graduate studies in mathematics. It is my hope that these initiatives will continue to flourish.

It has been a great privilege to work with a number of very able fellow administrators, John Baxter, John Eagon, David Frank, Paul Garrett, Hillel Gershenson, Lawrence Gray, Donald Kahn, Charles McCarthy, Wei-Ming Ni and Karel Prikry. I am very grateful to them for their cooperation and valuable advice over this period.

I would like to close by observing that when I decided to step down, I had imagined that with things running rather smoothly it was a good time to hand over the responsibility to someone else. My great regret is that my successor will have to deal with the very adverse consequences of the projected budget cuts. The late Eugene Fabes and I faced similar circumstances not too long ago. All of us together came through it quite well and I do hope that we will also be able to cope with the current situation.

Naresh Jain

Promotions

Mathematics librarian Kristine Fowler has been promoted to Associate Librarian with tenure. We offer Kris our warmest congratulations for a highly deserved promotion.

Awards and Recognitions


Douglas Arnold

Professor Douglas Arnold gave an invited one-hour address at the International Congress of Mathematicians held in Beijing in August 2002 . His address dealt with computer solutions  of partial differential equations underlying the simulation of a vast array of phenomena in diverse fields   such as fluid dynamics, electro-magnetics, and gravitational physics. The effectiveness of such solutions depends crucially on the development of stable numerical algorithms. In many cases the design of stable algorithms turns out to be subtly connected to geometric structures underlying the partial differential equations. This new geometric viewpoint provides a unifying understanding of a variety of innovative numerical methods developed over recent decades, in particular for the stable approximation of electro-magnetic problems. Very recently it has enabled the development of new algorithms for elasticity problems with properties previously unattainable. And it seems likely to provide an important element for the solution of numerical problems beyond current capabilities, such as the simulation of gravitational wave emission from colliding black holes.

Professor Mark Keel was awarded the McKnight Land Grant Professorship of the University of Minnesota, a major University-wide honor. Mark has also been awarded a Sloan Research Fellowship, a highly prestigious nation-wide award. Markus Keel

Tian-Jun Li Professor Tian-Jun Li has also been awarded the McKnight Land Grant Professorship of the University of Minnesota. As mentioned above, this is a major University-wide honor.


Mitchell Luskin

 Professor Mitchell Luskin gave an Invited Lecture at the International Congress of Mathematicians held in Beijing during August 2002 on Computational Methods for Phase Transitions and Microstructure. His talk described computational methods and mathematical analysis for structural phase transitions in crystals such as the transformation from a cubic to a tetragonal phase. Computational and mathematical challenges addressed included transformations between metastable states (local minima of the energy) and the numerical approximation of complex microstructure (the simplest microstructure is a laminate that oscillates on a fine scale between symmetry-related states).

Professor Luskin presented a numerical analysis of microstructure and used this theory to construct computational methods for the deformation of crystals that undergo a structural phase transformation. He presented computational methods and results obtained with Pavel Belik to numerically model the reversible deformation of a single crystal thin film that undergoes a structural phase transformation.


Professor Zeitouni

 Professor Zeitouni gave an invited lecture at the International Congress of Mathematicians held in Beijing in August 2002. His talk dealt with recent progress in the study of random walks in random environments. Classical random walk can be described as the trajectory a walker takes in downtown Minneapolis, where at each intersection she tosses a (fair) coin in order to decide at which direction to move next. The walk becomes a random walk in random environment (RWRE) if, at each intersection, one direction is more likely to be taken than others, and the assignment of this preferred direction is made, once and for all, randomly and independently between intersections. RWRE’s are used to model a variety of physical motions in random media, such as light scattering, and have also been used in the modeling of population growth in biology. Professor Zeitouni’s talk focused on new techniques based on the notion of regeneration times, that have played a major role in recent advances in the analysis of multidimensional RWRE’s.

BOCHER MEMORIAL PRIZE AWARDED TO ALUMNUS FANG HUA LIN


Fang Hua Lin

Professor Fang Hua Lin, who received his Ph.D. from our department in 1985, was awarded the 2002 Bocher Memorial Prize of the American Mathematical Society. The prize citation mentions “his fundamental contributions to our understanding of the Ginzburg-Landau equations with a small parameter” and “also recognizes his many deep contributions to harmonic maps and liquid crystals.” He is currently a Professor of Mathematics at New York University. His other major awards and recognitions, too numerous to list here, include the Presidential Young Investigator Award (1989-1994) as well as an invited address at the 1990 International Congress of Mathematicians in Kyoto, Japan. Even as a graduate student here Fang Hua was a legend in the department and published many papers before completing his studies. His Ph.D. advisor was Professor Robert Hardt. Over the years he has visited the department on many occasions, in particular as a Distinguished Ordway Visiting Professor in 1999. We congratulate him on this great recognition.

Academic Visitors

Distinguished Ordway Visitors (2002-2003)

The following mathematicians accepted our invitations to visit the School during the current academic year for one-month or longer visits under the Distinguished Ordway Visitors Program.

Professors:

John E. Dennis Rice University, mathematical optimization
Guiseppe DaPrato Scuola Normale Superiore di Pisa, partial differential equations, probability theory
Roger E. Howe Yale University, harmonic analysis and representation theory of Lie groups and p-adic groups
Luc Illusie Universite de Paris Sud, algebraic geometry
Maxim Kontsevich Institute des Haute Etudes Scientifiques, algebra, algebraic geometry, topology, mathematical physics
Peter Li UC Irvine, differential geometry
Michael J. D. Powell University of Cambridge, optimization and approximation theory
Christopher Sogge Johns Hopkins University, harmonic analysis, partial differential equations, geometric analysis

Continuing Postdocs and Visiting Faculty

Assistant Professors:

Alexander Alekseenko Novosibirsk State University, partial differential equations, general theory of relativity, inverse problems, optimization theory, numerical algorithms
Bernard Badzioch Dunham Jackson Assistant Professor, Ph.D. University of Notre Dame, algebraic topology and homotopy theory
Sandra DiRocco Ph.D. University of Notre Dame, algebraic geometry
Liliana Forzani Universidad Nacional del Litoral, harmonic analysis, mathematical finance
Omar Gil Faculty of Engineering Montevideo, boundary problems and partial differential equations
Mehdi Hakim-Hashemi Shiraz University, algebraic topology, homotopy theory

Shu-Yu Hsu
Ph.D. The Chinese University of Hong Kong, partial differential equations, geometric analysis, dynamical systems
Hyukjin Kwean Korea University, dynamical systems and differential equations

Junho Lee
Ph.D. Michigan State University, symplectic geometry and Gromov-Witten invariants
Arthur Lim Ph.D. University of Utah, harmonic analysis and representation theory
Simon Morgan Ph.D. Rice University, geometric measure theory, harmonic maps
Radu Popescu Ph.D. Columbia University, low dimensional topology
Victor Protsak Max-Planck Institute, representation theory of Lie groups
Carlos Tolmasky probability, mathematical finance
Jianfeng Zhang Ph.D. Purdue University, stochastic differential equations and mathematical finance

Associate Professors:

Bagisa Mukherjee Penn State Worthington Scranton Campus, liquid crystals, continuum mechanics, partial differential equations
Michael Siddoway Colorado College, module theory, commutative rings, computational algebra, history of mathematics


Postdoctoral Associates, including IMA Postdoctoral Associates who participate in the teaching activities:

Reka Albert Ph.D. University of Notre Dame, mathematical biology and complex networks
Pavel Belik Ph.D. University of Minnesota, mathematical modeling and numerical analysis of nonlinear partial differential equations in solid mechanics
Jamylle Carter Ph.D. UCLA, image processing, computer graphics
Dacian Daescu Ph.D. University of Iowa, data assimilation, sensitivity analysis, large-scale optimization techniques
Chetan Gadgil Ph.D. in chemical engineering, University of Minnesota, mathematical modeling in biology
Maria Gracheva Ph.D. Moscow State Technical University, biophysics

Daniel Kern
Ph.D. University of Illinois at Chicago, stochastic optimal control, biomathematics, mathematical modeling
Jun Seok Kim Ph.D. University of Minnesota, numerical analysis
Magdalena Stolarska Ph.D. Northwestern University, applied mathematics, mathematical biology

Other Visiting Scholars:

Jay Fillmore Professor Emeritus, UCSD, geometry
Boris Levitan Professor Emeritus, Moscow State University, functional analysis, differential equations
Thomas Schwartzbauer Assoc. Professor Emeritus, OSU, probability

Retirements

Monika Stumpf joined the School in 1987 as Executive Secretary to the department head. She gave the School fifteen years of outstanding service and was recently promoted to Executive Assistant. The faculty, staff and a very large number of visitors over the years held her in very high regard. The faculty honored her at the annual department retreat last fall on the occasion of her retirement. Her contributions to the department will be cherished by all of us for a very long time and we wish her well in her future pursuits.

Obituary

Associate Professor Emeritus Laurence R. Harper passed away July 9, 2002 at the age of 73. He lived in Minneapolis. Professor Harper earned his Ph.D. in algebra from the University of Chicago in 1959 and joined our faculty as an Assistant Professor that same year. He was promoted to Associate Professor in 1984. He was a distinguished teacher and a gracious and supportive colleague. He retired in 2000. Larry had a quiet, friendly personality, always greeting colleagues and students with a smile. We will miss him. He is survived by his wife Kathryn, four children and eleven grandchildren. The Laurence R. Harper, Jr. Scholarship Fund has been established at Paine College in Augusta, GA.

Rivière-Fabes Symposium

The Rivière-Fabes Symposium on Analysis and Partial Differential Equations is held annually at the School of Mathematics to honor the memory of two distinguished former colleagues Nestor M. Rivière and Eugene B. Fabes.

The Fifth Rivière-Fabes Symposium on Analysis and PDE was held from April 5th to the 7th, 2002. Professors David Jerison (MIT), Wilhelm Schlag (Caltech), and Michael Lacey (Georgia Institute of Technology) each gave two lectures:“Carleman inequalities and the absence of embedded eigenvalues”, and “Global energy minimizers for free boundary problems and full regularity in three dimensions” (Jerison); “Energy growth for Schroedinger equations with Markovian forcing”, and “Dispersive estimates for solutions of Schroedinger equations with slowly decaying and time-dependent potentials” (Schlag); and “Carleson’s theorem with quadratic phase”, and “Product BMO and second order commutators” (Lacey). The other main speakers were: Professors Tatiana Toro (University of Washington), “Free boundary regularity below the continuous threshold”; and Nets Katz (Washington University, St. Louis), “Stickiness in the 3-dimensional Kakeya problem”.

The conference dinner was held on Saturday, April 6th at the Bistro West of the Humphrey Center. The evening gave the participants a chance to discuss some of the mathematics presented during the program, as well as recall the unique qualities that made Eugene Fabes and Nestor Rivière such an important part of our department. It was especially nice to have members of both the Rivière and Fabes families at the dinner that evening.

The Sixth Rivière-Fabes Symposium on Analysis and PDE will take place April 25th - 27th, 2003. Speakers will be Professors M. Christ (University of California, Berkeley), R. Coifman (Yale University), A. Iosevich (University of Missouri-Columbia), I. Laba (University of British Columbia), G. Mockenhaupt (Georgia Institute of Technology), and C. Muscalu (University of California, Los Angeles).

Organizers: Fernando Reitich (Chair), Carme Calderer, Markus Keel, and Walter Littman of the University of Minnesota and Carlos Kenig (University of Chicago)

For further information see the Symposium’s web page at http://www.math.umn.edu/arb/rf/

Yamabe Memorial Symposium

The First Yamabe Memorial Symposium was held at the School of Mathematics,
University of Minnesota, Friday-Sunday, September 20-22, 2002.


Yamabe speaker presenting.

The Symposium was an enormous success. There were 72 participants, including 51 out-of-town participants and 21 from the University of Minnesota. The speakers were Professors: Hubert Bray (MIT), “Inverse Mean Curvature Flow and the Yamabe Invariant of RP^3”; Ben Chow (UC at San Diego), “A result on Hamilton’s Ricci Flow”; Richard Hamilton (Columbia University), “Perturbing Precise Harnack Estimates”; Peter Li (UC at Irvine), “Minimal hypersurfaces in a nonnegatively curved manifold”; Fang Hua Lin (Courant Institute, NYU), “Faddeev knots as stable solitons: Existence theorems”; Richard Schoen (Stanford University),“An update on the Yamabe variational approach to the construction and characterization of three dimensional constant curvature metrics”; Gang Tian (MIT), “Lefschetz fibrations and symplectic isotopy”; and Brian White (Stanford University), “Singularities in mean curvature flow”.

Yamabe Memorial Symposium, in honor of the distinguished mathematician Hidehiko Yamabe (1923-1960), replaces, and continues in expanded form, the Yamabe Memorial Lecture which has been held annually since 1989, in alternating years, at the University of Minnesota and at Northwestern University. Lectures in this series have been given by Professors Neil Trudinger, Eugenio Calabi, Rick Schoen, Shizuo Kakutani, Craig Evans, Walter Rudin, Robert Hardt, Katsumi Nomizu, Fred Gehring, Richard Hamilton, Peter Sarnak, Jeff Cheeger and S.-T. Yau. The Yamabe Memorial Symposium is an enhancement of this tradition. Mathematicians

will gather every two years at the University of Minnesota for a long weekend to hear talks in an area related to geometry, to discuss the latest research and to interact with younger mathematicians. Professor Hidehiko Yamabe (1923-1960) 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. His work on topological groups, geometry and analysis were outstanding contributions to modern mathematics. The 2002 symposium organizers were Conan Leung, Jiaping Wang and Robert Gulliver. For additional information, including audio recordings of the lectures, lecture notes and the participant list with email addresses, see http://www.math.umn.edu/~gulliver/confs/yamabe.htm


Attendees milling around outside the Yamabe Memorial Symposium.

Robert Gulliver, Professor and Chair of the Yamabe Symposium Committee


Conference in Honor of Regents' Professor Lawrence Markus


Lawrence Markus

The Conference was held October 31 - November 1, 2002 at the School of Mathematics to celebrate Professor Markus’ 80th birthday and to recognize his achievements in mathematics and service to the University of Minnesota and to the University of Warwick, England.Professor Norrie Everitt (Birmingham, England) showed a video of Professor Christopher Zeeman, F.R.S., paying tribute to Larry Markus. He also delivered the Thursday Colloquium Lecture on “The Markus Harmonic Operator”. In his talk “Working with Larry” Professor Walter Littman (University of Minnesota) reminisced on his long association with the honoree. Other speakers were Professors: Bruce Lee (University of Minnesota), “ Stability degradation of dynamical systems by bounded disturbances”; John Mallet-Paret (Brown University), “Eigenfunctions of Max-Plus Operators, and State-Dependent Delay Equations”; Kenneth Meyer (University of Cincinnati), “Seeking Solenoids”;and George Sell (University of Minnesota), “Variations on a Lecture of Markus”. Organizing Committee consisted of Norrie Everitt, James Serrin (Co-chairs) and Walter Littman.

Dinner was at the Bistro West of the Humphrey Center. Walter Littman, who officiated as master of ceremonies, read a message from Professor Naresh Jain who was out of town. Kenneth Meyer entertained the gathering with some very funny reminiscences about Larry. However this was topped by Larry’s even funnier “rebuttal”.

Walter Littman, Professor of Mathematics

Conference on Current Trends in Mathematics and its Applications, in Honor of Regents’ Professor Avner Friedman’s 70th Birthday, November 8 - 10, 2002


Avner Friedman

The Conference was sponsored by the School of Mathematics and by the Institute for Mathematics and its Applications which Professor Friedman directed from 1986 to 1997. He subsequently founded, and directed, our highly successful Minnesota Center for Industrial Mathematics. Since September 2002 he has been serving as director of the Mathematical Biology Center at Ohio State University, Columbus. He is a member of the National Academy of Sciences and has earned many other major honors. Speakers and titles of their talks: Richard Brualdi (University of Wisconsin), “Matrices in combinatorics with applications”; Mort Gurtin (Carnegie Mellon), “A nonequilibrium theory of epitaxial growth that accounts for surface stress and surface diffusion”; K.H. Hoffman (Caesar, Bonn), “Mathematical modeling of an aptamer based biosensor”; Richard James (University of Minnesota), “Reversibility of phase transformations and the search for new hybrid materials”; David Kinderlehrer (Carnegie Mellon), “Diffusion mediated transport and the brownian motor”; Nancy Kopell (Boston University), “Rhythms of the nervous system: Mathematical themes and variations”; Hiroshi Matano (University of Tokyo),“Blow-up in some supercritical nonlinear heat equations”; Gary McDonald (General Motors), “Looking backwards to the future for applied mathematical sciences”; William Newman (UCLA), “Earthquakes as a nonlinear dynamical process”; George Papanicolaou (Stanford), “Scaling limits for the random Schroedinger equation and applications to imaging”; William Pulleyblank (IBM), “Proteins, petaflops and algorithms”; and Michael Steele (University of Pennsylvania), “Minimal spanning trees and the objective method”.

At the dinner event, Professor Fernando Reitich who chaired the organizing committee read the following message from the department Head Professor Naresh Jain who was unable to attend.

Conference attendees.

Dear Avner,
On behalf of the School of Mathematics, I would like to express our deep admiration for your accomplishments as Director of the IMA and member of the School of Mathematics. Even though Hans Weinberger,
as the founding director, laid a solid foundation for the Institute, you greatly expanded its focus and turned it into a world-class center for mathematics and its applications. The success of the outreach program to industry led to the establishment of the Minnesota Center for Industrial Mathematics, known as the MCIM, through your initiative. As part of the School of Mathematics, this center currently guides 20-25 students in our industrial mathematics program. The most important component of this program is an industrial internship for Ph.D. and Master’s students which gives them firsthand experience of real-world problems. This was accompanied by some very interesting course development at the graduate and the undergraduate levels and often you played a key role in such developments.

As IMA Director, and later as a Regents’ Professor in the School, you mentored a large number of Ph.D. students and postdocs and were instrumental in the hiring of several excellent faculty members in analysis and applied mathematics. I, together with my colleagues, have always marveled at the amount of energy that you possessed to bring so many great ideas to a successful conclusion.

You always liked new challenges and embarked on the creation of the math-biology center at Ohio State. You have our best wishes for the success of this new venture, and we know you will succeed. We also know that you will never lose interest in the IMA; it is forever a part of you. You should be very pleased that your successor, Willard Miller and Associate Director Fadil Santosa carried forward your programs, with innovations of their own, very successfully. You can also be sure that the current Director, Doug Arnold, with support from Fadil Santosa and Scot Adams, is providing the leadership to the Institute that it deserves. A great tradition of excellence was established and the new generation of leaders will not only continue that, but will also strive to achieve greater heights.

Avner, thank you for your great contributions to both the IMA and the School of Mathematics. Kusum and I wish you and Lynn a very happy 70th birthday.

Members of the Organizing Committee were Professors N. Krylov, W. Littman, F. Reitich (chair), and F. Santosa.

International Conference on DYNAMICAL METHODS FOR DIFFERENTIAL EQUATIONS in honor of Professor George R. Sell’s 65th birthday, September 4 - 7, 2002

We would like to thank Professor Russell Johnson, of the University of Firenze, for the following remarks about this conference and Professor Sell’s work. Professor Johnson received his Ph.D. from our department in 1975.

This international meeting was held in Medina del Campo (Spain). George has made numerous mathematical contributions which lie at the interface between dynamical systems and differential equations. In particular, he has authored fundamental papers in the field of non-autonomous dynamical systems, an area which was well-represented at the meeting. So it seems particularly appropriate that the conference carried his name. A scientific committee was responsible for selecting the speakers and fixing the sections of the meeting. Its members were A. Delshams (Barcelona), R. Johnson (Firenze), R. Obaya (Valladolid), and R. Ortega (Granada). There were around 100 participants from 24 countries. Numerous themes of ordinary, partial, and functional differential equations and their applications were discussed during the main talks and sessions. The organization of the meeting was carried out by A. Alonso, S. Novo, C. Nunez, R. Obaya, and J. Rojo of the Universidad de Valladolid. The invited speakers were as follows: Viviane Baladi (CNRS - IHES, Bures-sur-Yvette), Fritz Colonius (Universitat Augsburg), Lorenzo Diaz (PUC, Rio de Janeiro), Paul Glendinning (University of Manchester), Angel Jorba (Universidad de Barcelona), Gerhard Keller (Universitat Erlangen), Urs Kirchgraber (ETH Zurich), Peter E. Kloeden (J.W. Goethe Univ., Frankfurt), Raphael Krikorian (Ecole Polytechnique, Paris), Yuri Latushkin (University of Missouri-Columbia), Rafael De la Llave (University of Texas at Austin), Roberto Markarian (IMERL, Montevideo), Welington de Melo (IMPA, Rio de Janeiro), J. Angel Rodriguez (Universidad de Oviedo), Wolfgang Ruess (Universitat Essen), George R. Sell (University of Minnesota, Minneapolis), and Yingfei Yi (Georgia Institute of Technology, Atlanta)

George Sell

The Conference on Foundations of Computational Mathematics

The Institute for Mathematics and its Applications and the School of Mathematics hosted this major international meeting on August 5-14, 2002.

There were 18 three-day workshops and 18 plenary speakers, covering fields of research at the interface of Numerical Analysis, Computer Science and Mathematics. The last such meeting was FoCM’99 (July 1999) in Oxford, England. Details of the program and copies of many of the presentations can be found on the conference web site http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/. The conference was supported by the National Science Foundation, the Office of Naval Research, IBM, the American Institute of Mathematics, the Number Theory Society and the Digital Technology Center at the University of Minnesota.

One of the highlights of the meeting was the “Panel Discussion on the Future of the Foundations of Computational Mathematics,” aimed at forecasting the mathematics of the future, and discussing outstanding problems on which young researchers should focus. Endre Suli (Oxford) moderated the session. Panelists were Lenore Blum (Carnegie Mellon), Ron DeVore (South Carolina), Peter Olver, and Steve Smale (Berkeley). Smale discussed relevant outstanding problems from his famous list of 18 + 3. (A solution of one of the problems was announced at the meeting.) For copies of the presentations see http://www.ima.umn.edu/~miller/FoCM_panel.html

Planning for the meeting took two years. Willard Miller and Peter Olver co-chaired the Local Organizing Committee for FoCM’02; the other committee members were Carme Calderer, Bernardo Cockburn, Victor Reiner, and Jianhong Shen. Among other local participants, Andrew Odlyzko was a plenary speaker and Dennis Hejhal, Mitch Luskin, Peter Olver, Guillermo Sapiro and George Sell were workshop organizers. Graduate students Burhan Biner, Jeongoo Cheh, Hongjie Dong, Hazem Hamden, Anton Leykin, and Ji Hoon Ryoo participated in the meeting and helped at the registration desk.

A major new project of the Society for the Foundations of Computational Mathematics (SFoCM) is the Journal in Foundations of Computational Mathematics, published by Springer-Verlag on behalf of SFoCM. The first issue appeared in January 2001. The journal contains research and survey papers of the highest quality that further the understanding of the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis and computer science. At FoCM’02 Peter Olver and Arieh Iserles (Cambridge, England) became Managing Editors of the Journal. The Journal operations are managed through the Minnesota website, see http://www.math.umn.edu/~focm/

As a lead-in to FoCM’02, the IMA 2002 Summer Program, Special Functions in the Digital Age, was held July 22 - August 2, 2002. Willard Miller and Peter Olver were also the principle local organizers for this event. (Another member of the Organizing Committee was Frank Olver, Peter’s father!) See http://www.ima.umn.edu/digital-age/ for details. The theme of the IMA summer program was carried over to FoCM’02 with a plenary talk and FoCM workshop on special functions, 5-7 August.

Willard Miller and Peter Olver

Speaking Invitations and Other Notable Activities

Professor Sergey Bobkov was an invited speaker at the Conference in Functional Analysis in Honor of 70th Birthday of Professor A. Pelczynski. The conference was held September 22-29, 2002 in Bedlewo (near Poznan, Poland) and was organized by the Institute of Mathematics of the Polish Academy of Sciences.

Professor Dihua Jiang was an invited speaker at a number of events: The Midwest workshop in Lie theory, representation theory and automorphic forms, University of Notre Dame, April, 2002; a conference in honor of Professor J. Shalika, on L-Functions and Automorphic Forms, the Johns Hopkins University, May, 2002; a conference on Recent Progress in the Langlands Program, Centre International de Rencontres Mathematiques (Marseille, France), June, 2002; A Satellite Conference on Number Theory, International Congress of Mathematicians 2002, Zhejiang Univ., Hangzhou, China, August, 2002; and A Satellite Conference on Number Theory and Arithmetic Geometry, ICM 2002,Weihai, China, August, 2002. He serves on the scientific committees of: a conference in honor of Professor S. Rallis, on Automorphic Representations, L-functions and Applications, March 27-30, 2003, Univ. of Ohio, Columbus; and the First Summer Graduate School, the Center of Mathematical Sciences, Hangzhou, China, July 2003. The famous mathematician S.-T. Yau is the Center’s director. Professor Jiang will give an invited lecture at the first of the two events, and he will give a series of lectures on automorphic forms at the second.

Professor Mark Keel gave an invited lecture at the meeting, “Equations aux Derivees Partielles”, in Forges-les-Eaux, France. June 3-7, 2002.

Ordway Professor Nicolai Krylov was a co-organizer, with Professor Guiseppe DaPrato (Scuola Normale Superiore di Pisa), of the session on Kolmogorov equations, at the first joint meeting of the American Mathematical Society and the Union of Italian Mathematicians, Pisa, June 12-16, 2002. The speakers were Professors: Marc Freidlin (University of Maryland), Alessandra Lunardi (Universita' di Parma), Boris Rozovskii (University of Southern California at Los Angeles), Franco Flandoli (Universita' di Pisa), Sandra Cerrai (Universita' di Firenze), Sergey Lototsky (University of Southern California at Los Angeles), and Lorenzo Zambotti (Scuola Normale Superiore di Pisa).

Professor Peter Olver was a Visiting Professor at the Swiss Federal Institute of Technology, Lausanne, Switzerland (January-June, 2002). He was a plenary Speaker at the International Symposium on Symbolic and Algebraic Computation (ISSAC), Lille, France, July, 2002. ISSAC is the foremost computer algebra conference in the world. He was an invited course lecturer twice during the summer of 2002, giving a series of lectures for graduate students, postdocs and researchers on applications of moving frames, at Fields Institute Special Meeting on Symbolic and Numeric Computation in Geometry, Algebra and Analysis, University of Western Ontario, London, Ontario, Canada, July, 2002 as well as at Summer School in Geometric Numerical Integration, Fevik, Norway, August, 2002. He co-chaired, with Professor Willard Miller, the Local Organizing Committee for the Conference on Foundations of Computational Mathematics which was held here August 5-14, 2002; a note about this conference authored by Professors Miller and Olver appears above in this Newsletter. He was also a member of organizing committees for a workshop on Under- and Overdetermined Systems of Algebraic or Differential Equations, Karlsruhe, Germany, March 18-19, 2002. Furthermore, with Professor Gloria Mari-Beffa (a 1990’s Ph.D. graduate of our department), he organized a Special Session on Geometric Methods in Differential Equations at the Meeting of the American Mathematical Society, Madison, October 12-13, 2002. Currently he serves on the organizing committees for the following two conferences: Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine, June 23-29, 2003; and Differential Invariants and Invariant Differential Equations, Banff International Research Station, Canada, July 19-24, 2003.

Professor Mikhail Safonov gave an invited plenary address “General Properties of Solutions to Second Order Elliptic and Parabolic Equations” at the meeting of the American Mathematical Society, University of Wisconsin, Madison, October 12-13, 2002.

Professor Sell was a co-organizer for a Workshop on Computational Dynamics, which was held in conjunction with the Conference on Foundations of Computational Mathematics described above.

Regents’ Professor Emeritus James Serrin is co-editor, along with Cathleen S. Morawetz and Yakov G. Sinai, of a new book “Selected Works of Eberhard Hopf, with Commentaries”. In June he will also give the Lezione Leonardesca in analysis, sponsored by the Departments of Mathematics of the Universities and Politecnico of Milan.

Professor Alexander Voronov served on the Organizing Committee for a “Ramanujan Mathematical Society” conference, held at Banaras Hindu University, Varanasi, India, June 10-13, 2002. He will be the main lecturer at the workshop on “Geometric Methods in Physics” June 29 - July 6, 2003, in Bialowieza, Poland, and will deliver a mini-course of five lectures on “String Topology” at a school on “Algebraic Topology” at the University of Almeria, Spain, in September, 2003. At the department, he developed a one-semester graduate course “Topics in Mathematical Physics” (Math 8390) and taught this course for the first time in the Fall 2001. The goal is to present recent developments in mathematics related to quantum field theory. The lectures are posted at http://www.math.umn.edu/~voronov/8390/index.html
An informal description, by Professor Voronov, of this very interesting course, appears in the Graduate Program section of this newsletter.

Undergraduate Program

UNDERGRADUATE PROGRAM

Junior Colloquium

In the Fall semester of 2002 the department began a new weekly afternoon seminar called the “Junior Colloquium” on Tuesdays. It is intended for talks of broad mathematical and scientific interest, given by both faculty and graduate students, at a level that bright undergraduate math majors can follow. Undergraduates, graduate students, and faculty are all encouraged to attend. Refreshments are served before the colloquium.

The offerings in this inaugural semester were deliciously diverse: celestial mechanics, the Banach-Tarski paradox, Latin squares, nonlinear waves, Fibonacci numbers, pattern formation in oscillator arrays, computer object recognition, Morse theory, Fourier transforms, homotopy theory, coin-tossing and Brownian motion, the Langlands program, and Penrose tilings.

So far, the core audience has consisted of lower-level graduate students, with occasional strong showings by undergraduates. We would like to see the undergraduates take over! On many Tuesdays the Junior Colloquium is followed by meetings of the new Undergraduate Math Club, meeting in the new Math Majors Lounge in Vincent Hall 116.

The Junior Colloquium is co-organized by Vic Reiner (faculty), and graduate students Jon Rogness and James Swenson. The current schedule can be found by a link from the main math page or Reiner’s web page. Contact any of the organizers if you are interested in speaking.

Vic Reiner, Professor of Mathematics

New Honors Sequence

This fall, the mathematics department initiated a new honors math sequence in multivariable calculus. This three course sequence is designed to help develop the mathematical potential and ability of promising undergraduates (and area high-school students). The sequence has a much higher requirement of mathematical rigor explicitly including proofs in the treatment of topics than in the analogous IT sequence. The students are excellent. They are both talented and hardworking. Our biggest challenge is to increase our pipeline of promising math majors.

Steve Sperber, Professor of Mathematics

The New Undergraduate Math Club

The Undergraduate Math Club meets on Tuesdays, after the Junior Colloquium, in the new Undergraduate Lounge located in 116 Vincent Hall. The goal of the club is to provide students with a forum to discuss and share information on topics such as graduate school, curricular issues, careers in mathematics, summer internships and participation in math competitions. To have fun is also one important goal of the Club; pizza is served at most meetings of the Club. The Club meetings are organized by faculty members Carme Calderer and Jackie Shen. Every meeting features a guest visitor to hold informal discussions with students. Several faculty members from the School of Mathematics visited the Club in the Fall of 2002. Students took the opportunity to ask questions about the research field of each visitor. We are always on the lookout for speakers.

Carme Calderer, Professor of Mathematics

Research Experiences for Undergraduates

The summer 2002 REU program involved 18 students from the U.S. and Canada. We had weekly presentations of students’ work, after Friday pizza lunch, in addition to presentations within groups during the week. Faculty mentors were Professors Carme Calderer, Paul Garrett, Rachel Kuske, Vic Reiner, and Sasha Voronov.

Carme Calderer supervised two participating undergraduate students: Phil Mendelsohn (Univ. of Minnesota) and Pearl Sandwick (New York Univ.). Phil Mendelsohn did numerical simulations of time dependent problems of phase transitions. For special geometries, the problems lead to nonlinear ordinary differential equations. Phil studied long-time behavior and bifurcation of solutions. Pearl Sandwick studied nonlinear elasticity and calculus of variations. Such topics provided her with mathematical and physical background to analyze models of elastomers. These are anisotropic materials that experience large deformations in the presence of electric fields. Such materials are investigated in connection with modeling of artificial tissues. Pearl studied extensional elastic deformations resulting from an applied electric field.

The topic of Vic Reiner’s group, consisting of Scott Hirschman (Univ. of Northern Iowa), Brian Jacobson (Univ. of Minnesota), Minseung Kim (Univ. of Pennsylvania), and Andy Niedermaier (Harvey Mudd College), was “Trees, determinants and Pfaffians”. They explored some results related to the enumeration of spanning trees and Kirchoff’s celebrated Matrix-Tree Theorem which counts spanning trees in a graph via a determinant. S. Hirschman and Professor Reiner found a new, direct proof of the recent Pfaffian Matrix-Tree Theorem of Masbaum and Vaintrob, which counts spanning trees in 3-graphs via a Pfaffian. They submitted their work as a note to “Graphs and Combinatorics”. A. Niedermaier and B. Jacobson worked on computing the structure of a certain finite abelian group (“the critical group”) associated to a graph, whose order equals the number of spanning trees. For some families of graphs, when they were able to calculate this number of trees, they could determine the structure of this group very explicitly. These results are likewise being submitted for publication.

Paul Garrett’s group, Jacob Bernstein (Univ. of Michigan), Anna-Marie Bohmann (M.I.T.), Lee Dicker (McGill Univ.), Amanda Febey (St. Olaf’s College), Joshua Green (Univ. of Arizona), Roxanne Johnson (Northland College), Michael Lieberman (Reed College), Stephen Lu (Princeton Univ.), Ben Rosenfield (Middlebury College), and Kristen Shaw (Univ. of British Columbia), investigated a variety of issues related to number theory, modular forms, and computations, both practical as well as theoretical. Projects included Amanda’s C++ code for some cryptographic applications, Jacob’s survey of Siegel modular forms, Kristen’s discussion of Goodstein sequences and inaccessible cardinals, Ben’s overview of Tate’s thesis, Anna-Marie’s treatment of Sylow theorems and related ideas about group actions, Roxanne’s cryptology course development outline, Michael’s introduction to Hecke L-functions, Stephen’s examples of Rankin-Selberg integrals, and Josh’s investigation of how one would or wouldn’t prove the Riemann Hypothesis. Sasha Voronov’s group shared Scott Hirschman (Univ. of Northern Iowa) and Brian Jacobson (Univ. of Minnesota) with Vic Reiner’s group. First, the students learned some basics of topology, algebra, and combinatorics, necessary to study graph homology. Then they studied ribbon graph homology, which produces a combinatorial description of the homology of the moduli spaces of algebraic curves. Scott Hirschman looked at different ways of defining orientation on a graph and showed they all were equivalent. Brian Jacobson wrote a computer program in GAP (Groups, Algorithms and Programming) which lists all ribbon graphs with a given number of edges, computes the automorphism group of a ribbon graph and the ribbon graph homology. If not for the natural time limitations of the algorithm, this would solve the tantalizing problem of computing the homology of moduli spaces. In a 30 minute computer time, the program was able to correctly compute the homology of some low-dimensional moduli spaces, in several known cases. This program is a first step towards computer computation of graph homology. Further improvement of the algorithm should not only produce new computations, but also gather evidence for a number of conjectures on moduli spaces, which have been motivating research in this new and exciting area of mathematics.

Paul Garrett, Professor of Mathematics and REU Coordinator

News About the Graduate Program

From Professor Paul Garrett, Director of Graduate Studies

In March 2002 we gave our first Open House for recruiting new graduate students. Thirty students from all around the country came to socialize and hear talks from several of our faculty: Carme Calderer, Paul Garrett, Claudia Neuhauser, Vic Reiner, Fadil Santosa, Arnd Scheel, and Vladimir Sverak. Despite the ice storm that weekend (which did indeed amaze visitors from the South), the Open House was very effective in introducing prospective students to our department and to each other.

In July and August we welcomed 27 new TAs, from all around the world. The international students arrived first for the program conducted by the Center for Learning and Teaching Services that helps orient them in the ambient language and culture. The CTLS people also assess communication skills, in addition to English fluency, and make recommendations about readiness to work in a classroom. The domestic students arrived soon after, to participate in our newly-created intensive mini-courses, as an academic orientation prior to our already-well-established orientation aimed at TA duties. Over two weeks, several of our faculty spoke to the new students, touching upon central topics in mathematics and their relation to ongoing research. (Larry Gray, Paul Garrett, Don Kahn, Markus Keel, Al Marden, Willard Miller, and George Sell all gave several talks.) Given the very positive response from students and faculty alike, we will continue and try to expand this new part of our orientation in future summers.

In addition to the CTLS orientation and the academic orientation, the School of Mathematics conducted its own TA orientation, introducing students to the mundane but important facts that they’ll need in order to function as Teaching Assistants in the School of Mathematics, and videotaping practice sessions in which they presented material as a TA would. Several senior TAs (John Hall, Hande Metin, Michael Galbraith, Jon Rogness, Gabriel Soto, James Swenson, Pang-Yen Weng, and Dan Drake) assisted, lending their insights and perspectives. Play-acting scripted and acted by the grad students made it all the more memorable.

The Written Preliminary Ph.D. exams were given the week before classes, and as expected many students made progress toward completion of this requirement. Apart from making progress toward the Ph.D., TAs also get a pay raise for completion of the Written Prelims.

In Fall 2002 we gave our first Fall Open House for prospective students from local colleges and universities. Several of our faculty (George Sell, Vic Reiner, Arnd Scheel, Vladimir Sverak, Fadil Santosa, Carme Calderer, and Paul Garrett) gave talks about a variety of aspects of current research in our department.

Ph.D.’s granted 2001-02:

Kyle Calderhead (advisor Professor Victor Reiner)
Won Jae Chang (advisor Professor Nicolai Krylov)
Vladimir Itskov (advisor Professor Peter Olver)
Kyung-Keun Kang (advisor Professor Vladimir Sverak)
Jun-Seok Kim (advisor Professor John Lowengrub)
Nathan Reading (advisor Professor Victor Reiner)
Jaiok Roh (advisor Professor George Sell)
Cetin Urtis (advisor Professor Paul Garrett)
Jing Wang (co-advisors Professor Robert Gulliver, Professor Fadil Santosa)
Nathan Wodarz (advisor Professor Donald Kahn)

M.S.’s granted 2001-02:

Hassib Amini (advisor Professor Joel Roberts)
Hua Bai (advisor Professor Dennis Stanton)
Kevin Collins (specialization in Industrial Math, advisor Professor Fadil Santosa)
John Eian (advisor Professor Peter Rejto)
Melissa Everson (specialization in Math. Ed., advisor Professor Harvey Keynes)
Miriam Freedman (specialization in Applied Math, advisor Professor Rachel Kuske)
Michael Galbraith (advisor Professor Robert Gulliver)
Thomas Hoft (specialization in Applied Math, advisor Professor Fadil Santosa)
Justin Jacobs (specialization in Math. Ed., advisor Professor Harvey Keynes)
Minchul Kang (advisor Professor Hans Othmer)
Cunbo Liu (specialization in Actuarial Science, advisor Professor Stephen Agard)
Nataliya (Kerbel) Mazo (advisor Professor Rachel Kuske)
Ivan Osipkov (advisor Professor Wei-Ming Ni)
Karen Riga (specialization in Math. Ed., advisor Professor Harvey Keynes)
John Yap (specialization in actuarial science, advisor Professor Stephen Agard)


“Physical Mathematics” Course for Graduate Students

Interaction of Mathematics and Physics has been very fruitful for both subjects from very early on. While in the ages from Newton and Leibniz to Euler, to Lagrange and Laplace, the two fields were practically indistinguishable, further development brought not only incredible depth, but also contributed to certain divergence of interests, methods, and motivations. The situation in the 20th century was marked by periodically discovering that methods developed solely for the sake of one field could also be used to make unexpected breakthroughs in the other. In the late 20th century, when string theory came about and the theoretical physicists proved to be at times more abstract than the fellow mathematicians, the history of science got an unusual shift: the vague ideas of physics found their place within the rigor of mathematics and produced new methods, fields, and of course, remarkable theorems.Examples include statistical and quantum mechanical methods in knot theory, gauge theory methods in low-dimensional topology, instanton ideas throughout geometry, Feynman integral and diagram techniques in algebra and combinatorics, the inverse scattering problem and quantum group theory, mirror symmetry and enumerative algebraic geometry, to name a few. Perhaps, these exciting developments created a field that may be called Physical Mathematics: Mathematics no longer plays a service role; it is rather Physics which is being applied to Mathematics.

Physical methods thereby became indispensable in training the modern mathematician, and one of the main goals of the graduate course Math 8390 “Topics in Mathematical Physics” developed in the Fall of 2001 was to introduce the graduate students to the world of Physical Mathematics. The course was designed as a one-semester topics course for advanced graduate students, and was in fact attended not only by students, but also by several faculty members.

The course is centered around recent applications of ideas from quantum field theory to pure, “mainstream” mathematics, presented in a form accessible to graduate students. Topics include operad theory, moduli spaces, homotopy algebra, algebraic structures in string theory, deformation quantization, and graph homology. Lecture notes are posted on the course web page http://www.math.umn.edu/~voronov/8390/

Alexander Voronov, Professor of Mathematics

Mathematics Library

Over the summer the university libraries introduced a new version of MNCAT, the online catalog system, with enhanced features such as the ability for an individual to check due dates and renew books after signing in. Thanks to the mathematics department systems office, wireless internet access is now available for those working on their own computers in any corner of the Mathematics Library, as in other parts of Vincent Hall. Thus the accessibility and usability of the library’s various networked resources and services continue to improve. In addition to its many electronic journals and databases, the Mathematics Library now contains over 43,000 volumes of journals and books. Special acquisitions in 2002 included 12 new books purchased with private donations, as well as many gifts of older books, some out of print, that are useful additions or replacements for the collection. The library continues to develop effective ways of supporting the learning and research needs of the mathematics and statistics community in light of the challenges and opportunities of scholarly publishing.

Kristine Fowler, Mathematics Librarian
310 Vincent Hall
E-mail:
Phone: (612) 624-9395

Minnesota Center for Industrial Mathematics

Led by Prof. Fadil Santosa (Director) and Prof. Fernando Reitich (Associate Director), the Minnesota Center for Industrial Mathematics (MCIM) continues to provide internship opportunities for mathematics students and to develop collaborative projects with industry. In its ninth year, the Center has garnered a reputation as a valuable resource for industry, and receives inquiries about possible projects from local companies on a regular basis.

In cooperation with the IMA, the Center runs the Industrial Problems Seminar. The seminar typically features speakers from industry who present their work and problems to our faculty and students. It also serves as a stage for the students to present their results upon completion of their internships. The seminar has thus become a successful forum for interaction between industrial scientists and our faculty, students and visitors. The list of speakers for 2002-3 series can be found at www.ima.umn.edu/industrial. Several students were placed in internships last summer. Companies hosting our students include Symbol Technologies, Parker Hughes Cancer Institute, Schlumberger, and Signature Bioscience.

Alumni of our Applied and Industrial Mathematics Program have consistently done very well professionally upon graduation, and we try to keep informed about their career paths. Among those that have pursued industrial careers, Scott Shald (MS 1997, PhD 1999) recently moved from Lincoln Lab to Coherent Technologies in Lafayette, CO, to join the company’s effort in the development of laser radar systems for imaging and remote atmospheric measurements. Also, Sam Albert (MS 1998, PhD 2000) is now back in the Twin Cities area working for Cargill’s financial management group after a short stint at Interactive Data Corporation in New York.

In the following note, our student Maria Ponomarenko writes about her internship experience at Schlumberger-Doll Research in the Summer of 2002.

Fernando Reitich, Professor and Assoc. Director of MCIM,
Fadil Santosa, Professor and Director of MCIM

y Internship Experience

I am a third year graduate student in the School of Mathematics working towards a PhD degree in Mathematics with emphasis in the Applied and Industrial Mathematics. Last summer I was fortunate to participate in an internship at Schlumberger-Doll Research, Ridgefield, CT. For PhD students interested in industrial mathematics an internship is highly recommended. I was particularly excited because I was very eager to step into the real world and try to work in an industrial research facility (especially one belonging to such a major company as Schlumberger). I thought at the very least, it would give me an idea whether I would like to pursue a career in industry after my graduation.

During my internship I worked on an optimization problem involving an oil reservoir simulation. It was extremely interesting but also quite challenging since I have not worked in the field of optimization (in fact, I used to major in algebra during my master’s studies at Kiev Taras Shevchenko University, but here shifted my focus to applied math and took a variety of courses in this area). A major and perhaps the most exciting part of my project has been the development of a surrogate function approach based on the artificial neural network. I had to write and test a C++ code based on the method which had to interface with other existing software. Incidentally, this required me to learn C/C++ — something I long wanted to do.

Maria Ponomarenko

As a result of my internship I have gained insight of a new and exciting field in applied math that has a great potential and is full of yet uncharted territories. Indeed, I plan to pursue some of the questions that arise in this internship work in my thesis research. I also greatly enjoyed interaction with my supervisor and coworkers, the whole environment at the lab, and realized that I definitely made a right choice when I decided to work towards a career as an industrial researcher. Overall, this internship has been a most happy and fruitful experience and I recommend it to anyone.

Maria Ponomarenko

News from the IMA

The theme of this year at the IMA is “Optimization”, which seeks not to run the world but, rather, to show the best way in which the world might be run. This is a subject which has undergone enormous advances over the last ten years, partly due to improvements in computing machinery, but also due to many new mathematical ideas, new algorithms and new implementations of old algorithms.

The IMA continues to operate by quarters, and, in the fall, we ran workshops on the general theme of “Supply Chain and Logistics Optimization”. The term “supply chain” refers to the network of suppliers, distributors, transportation means, storage facilities, and retailers needed to deliver products to the right locations at the right time in the right quantities. That is to say, we want the trucks to get the goods to the right places, at the right times, at the lowest possible total cost - or variants of that basic problem. A complex supply chain gives rise to many opportunities to apply optimization techniques to achieve greater efficiency, but also to very challenging problems both to formulate and solve mathematically, and also to implement because of the non-mathematical, business aspects.

The winter term is devoted to “New Optimization Paradigms and Approaches”, all about the above-mentioned improvements in algorithms and ideas. In the spring, we present “Information Technology and Optimization” which discusses telecommunication optimization and optimization in data mining.

Integer Programming is a part of Optimization which seeks to minimize a linear functional along the integer points in a convex polytope, often of extremely high dimension. One of my own favorite topics this year has been the interaction between Integer Programming and Computational Algebraic Geometry. I lectured on this in the Junior Colloquium in February. For more information on the Optimization year, please go to http://www.ima.umn.edu/optimization/

Since Doug Arnold has taken the reins of the IMA, there have been many changes, both in programs and in operations. The workshops now involve fewer talks, with a greater emphasis on interaction, both formal and informal. In 2004, we will have a summer program on n-categories. We are currently considering a proposal for an annual program in Computational Algebraic Geometry. Pending approval of NSF funding, we are beginning a “New Directions” initiative, which seeks to smooth the way for established mathematicians who wish to branch into new directions and increase the impact of their research. For more information, go to http://www.ima.umn.edu/new-directions/

Scot Adams, Professor of Mathematics and IMA Associate Director

News from the Institute of Technology Center for Educational Programs

ITCEP’s director, Professor Harvey Keynes, continues to be the advisor for the five-year-old Masters Degree Program in Mathematics, emphasis in Mathematics Education. John Hall, one of its twelve graduates, continues in the math PhD program. Melissa Everson, Justin Jacobs, Karen Riga, and Nathan Van Dyke graduated in 2002 and now have jobs in Middle and High Schools, mainly in the Twin Cities metro area. During Summer 2002, Melissa, Justin, and Carraig Hegi, also a masters’ program graduate, were members of the instructional team for the 2002-03 Professional Development Program funded by an Eisenhower grant and implemented by ITCEP.

This program, titled “Mathematics Within”, aims to improve the mathematics content knowledge and understanding of the connections within mathematics of fourth through seventh grade teachers. Thirteen elementary school teachers participated in each of the two summer courses (Algebraic Patterns and Shape; and, Space and Measurement) and now are in the process of presenting the lessons they prepared as program participants to their elementary school students and members of the ITCEP instructional team. Several of these teacher participants and masters program graduates are involved with the proposed 2003-04 “Mathematics Within” Professional Development Program.

Working on both these program teams is Simon Morgan, ITCEP’s new post-doctorate assistant professor. In addition, Simon is a workshop leader for the University of Minnesota Talented Youth Mathematics Program (UMTYMP) Calculus I and III courses.

In this, UMTYMP’s twenty-second year, UMTYMP has an enrollment of 468 students in grades 6-12 (Twin Cites 373; Outreach 95), 184 of whom are calculus students. Twenty-eight students are in Twin Cities Calculus III and several others are enrolled in advanced mathematics or IT honors course work. Eight alumni are in the new mathematics honors program. For a second consecutive year, Assistant Professor R. Hesse, a School of Mathematics Ph.D. Graduate, is teaching UMTYMP calculus at St. John’s University, St. Cloud. Assistant Professor M. Keel, an UMTYMP alumnus, is teaching the UMTYMP Advanced Topics course, likewise for a second consecutive year. Professor H. Keynes, and Adjunct Professor T. Schwartzbauer, continue teaching Twin Cities’ UMTYMP calculus; Professor Schwartzbauer also teaches calculus at the Rochester site.

Professor Keynes and Dr. A. Olson, ITCEP’s Associate Director, together with other IT participants, are collaborating with several urban and suburban districts on a NSF MSP (Math Science Partnership) grant proposal. The four overall goals of this extensive five-year proposal are to: 1) Improve the mathematics content knowledge of elementary/middle school teachers, 2) integrate physical science and engineering applications based on the newly acquired math content knowledge of targeted teachers, with the possibility to extend to all K-12 later in the initiative, 3) build the leadership capacity of these teachers, and 4) create a teacher leadership network with IT, supported by ITCEP.

We are pleased to report that Matthew Landreman, a St. Paul native and a physics major from Swarthmore College was named as a 2002 Rhodes scholar, the oldest international fellowship. Matthew attended the UMTYMP program for 6 years until 1998 before attending Swarthmore. Only 32 people from the United States are selected each year to receive this prestigious award.

Alexandra Janosek,
ITCEP Communication and Public Relations Coordinator

Contact Us

School of Mathematics Contact Information

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

Naresh C. Jain
Ph: (612) 625-5591

Undergraduate Studies

Lawrence Gray, Director
Ph: (612) 625-4848

Graduate Studies

Paul Garrett, Director
Ph: (612) 625-1306
Minnesota Center for Industrial Mathematics (MCIM)

Fadil Santosa, Director
Fernando Reitich, Associate Director
Ph: (612) 625-3377,
Fax: (612) 624-2333

www.math.umn.edu/mcim

IT Center for Educational Programs (ITCEP)

Harvey Keynes, Director
4 Vincent Hall
206 Church Street S.E.
Minneapolis, MN 55455
Ph: (612) 625-2861,
Fax: (612) 626-2017

Institute for Mathematics
and its Applications (IMA)

Douglas Arnold, Director
Fadil Santosa,
Deputy Director
Scott Adams,
Associate Director
400 Lind Hall
207 Church Street S.E.
Minneapolis, MN 55455
Ph: (612) 624-6066
Fax: (612) 626-7370
gopher: gopher.ima.umn.edu
anonymous ftp: ftp.ima.umn.edu
www.ima.umn.edu