# School of Mathematics Newsletter - Volume 8 - 2002

## In This Issue...

## The School Welcomes Incoming Faculty and Postdocs

It is a pleasure to welcome the new members of the School of Mathematics - Professors Douglas Arnold and Carme Calderer who are husband and wife, Professor Andrew Odlyzko, Professor Peter Polacik, Associate Professors Arnd Scheel and Alexander Voronov,Professor Doug Arnold and Assistant Professors Wojciech Chacholski and Markus Keel. Professor Arnold is also the new director of the Institute for Mathematics and its Applications (IMA), replacing the outgoing director, Professor Willard Miller, who decided to return to teaching and research. Professor Odlyzko is the first director of the newly established Digital Technology Center (DTC) and an assistant vice president for research. We also welcome the new Dunham Jackson Assistant Professors Bernard Badzioch, Junho Lee and Jianfeng Zhang, as well as Postdoctoral Associates Reka Albert, Chetan Gadgil and Maria Gracheva.

Doug Arnold
Professor Arnold, the new IMA Director, is one of the world's leaders in numerical analysis of partial differential equations, particularly those dealing with mechanicsProfessor Maria-Carme Calderer. He has made major contributions to the numerical simulation of elastic plates and shells and also of incompressible fluids. In recent years he has been working in the area of computational relativity, which seeks numerical solutions of Einstein's field equations. Douglas Arnold earned his Ph.D. in 1979 from the University of Chicago. His first position was at the University of Maryland. In 1989 he joined the faculty of Penn State University as Professor and was made Distinguished Professor in 1995. At Penn State he was also co-director of the Center for Computational Mathematics and Applications, the associate director of the Institute for High Performance Computing Applications, and a member of the Center for Gravitational Physics and Geometry. His major honors and recognitions include the first Giovanni Sacchi Landriani Prize of the Milan Academy of Arts and Letters and an invitation to give a Plenary Lecture at the International Congress of Mathematicians in Beijing in August 2002. For more about Professor Arnold, see the article about the IMA. . |

Maria Carme-Calderer
Professor Maria-Carme Calderer is a well known applied mathematician whose research interests include mathematical studies of liquid crystals. She earned her doctorate from Heriot-Watt University, Edinburgh, in 1980. She has been at Penn State since 1989 where she was promoted to the rank of Professor in 1993. She was a postdoctoral researcher at the IMA (1984-1985) as well as a visiting researcher in 1986-1987 and Professor Peter Polacik 1995-1996. She also has an active interest in mathematics education at both theundergraduate and graduate levels, as well as K-12 education. |

Peter Polacik
Professor Peter Polacik has made important contributions in the areas of partial differential equations and dynamical systems. He earned his doctorate from Comenius University, Bratislava, in 1989, where he rose to the rank of Professor. He has been a frequent visiting researcher to leading institutions throughout the world, including the IMA (Fall 1989) and Newton Institute for Mathematical Sciences (Fall 1995). |

Andrew Odlyzko
Professor Andrew Odlyzko is a mathematician of world renown whose research interests cover large areas of pure and applied mathematics and computer science, including number heory, combinatorics, analysis, probability theory, computational complexity, cryptography, coding theory, electronic publishing, electronic commerce and economics of data networks. In addition to his position on the mathematics faculty, Professor Odlyzko is the first director of the University's new Digital Technology Center (DTC), Assistant Vice President for Research, and ADC Telecommunications Chair Professor. For more details about the DTC see www.dtc.umn.edu as well as our article on the DTC. Andrew Odlyzko earned his Ph.D. from MIT in 1975 and joined AT&T Bell Laboratories, now AT&T Labs, where he held high level positions for nearly two decades, most recently, since 1996, as head of the mathematics and cryptography research department. His major honors include an invited one-hour address at the annual AMS meeting, Pittsburgh 1981, as well as an invited lecture at the International Congress of Mathematicians, Berkeley 1986. He also serves on the editorial boards of Professor Arnd Scheelmany leading mathematics, computing, communications, and digital technology journals and has been a member of advisory or governing boards for leading educational institutions throughout the country, including the IMA. |

Arnd Scheel
Associate Professor Arnd Scheel's research is in the area of dynamics of partial differential equations. He earned his doctorate from the University of Stuttgart in 1994 and joined the faculty of the Free University, Berlin. He is the recipient of the Outstanding Paper Prize of the Society for Industrial and Applied Mathematics for the year 2000. |

Alexander Voronov
Associate Professor Alexander Voronov's research interests lie in mathematical physics, algebra, algebraic geometry and topology. He earned his Ph.D. from Moscow State University in 1988, where he held a research position until 1990. In the US he has had faculty positions at MIT, University of Pennsylvania and Princeton University, among others. He was a visiting researcher at Max-Planck Institute, Institute for Advanced Study and IHES, and was awarded an AMS Centennial Research Fellowship, 1996-1998. He earned a Good Teaching Award from the University of Pennsylvania in 1995. |

Assistant Professor Wojciech Chacholski earned his Ph.D. in 1995 from the University of Notre Dame. His field of research is algebraic topology. From 1995 to 1997 he held a J.E. Marsden Postdoctoral Fellowship at the Fields Institute (Toronto), followed by a G. Faltings Postdoctoral Fellowship at Max-Planck Institute (1997-1998). From 1998 tProfessor Markus Keelo 2001 he was a Gibbs Instructor at Yale University, taking a one-year leave of absence (1999-2000) to hold a Gustafsson Fellowship at the Royal Institute of Technology (Stockholm). He is spending the current academic year there as well, on leave from our department. |

Markus Keel
Assistant Professor Markus Keel earned his Ph.D. from Princeton University in 1995. He held a Hedrick Assistant Professorship at UCLA (1995-1998), followed by Bateman and Taussky-Todd Research Instructorships at Caltech (1998-1999, 1999-2001). He held visiting memberships at MSRI Berkeley, as well as the Institute for Advanced Study. While at UCLA, he earned the Sorgenfrey Teaching Award. His research areas are partial differential equations and harmonic analysis. |

Dunham Jackson Assistant Professor Bernard Badzioch earned his Ph.D. in 2000 from the University of Notre Dame. He spent the academic year 2000-2001 as a visiting faculty member at Johns Hopkins University. His research area is algebraic topology and homotopy theory.

Dunham Jackson Assistant Professor Junho Lee earned his Ph.D. in 2001 from Michigan State University. His research area is symplectic geometry and Gromov-Witten invariants.

Dunham Jackson Assistant Professor Jianfeng Zhang earned his Ph.D. in 2001 from Purdue University. His research area is stochastic differential equations and mathematical finance.

Postdoctoral Associate Reka Albert earned her Ph.D. in 2001 from the University of Notre Dame. Her research area is mathematical biology and complex networks.

Postdoctoral Associate Chetan Gadgil earned his Ph.D. in chemical engineering from the University of Minnesota in 2001. His research area is mathematical modeling in biology.

Postdoctoral Associate Maria Gracheva earned her Ph.D. in 1998 from Moscow State Technical University. Her research area is biophysics.

## From the Department Head

In the face of a large number of recent retirements, the task of recruiting new faculty was enormous and quite challenging. The School did extremely well in this regard, thanks to the efforts of our recruiting committee and the faculty. Through our normal hiring process, we hired six faculty members: Maria-Carme Calderer and Peter Polacik (Full Professors); Arnd Scheel and Alexander Voronov (Associate Professors); Wojciech Chacholski and Markus Keel (Assistant Professors). In addition to these, Professor Douglas Arnold was hired as the new director of the IMA. The search for this position was conducted by a national search committee headed by Professor James Keener from the University of Utah with me serving as the liaison with the School of Mathematics. Another opportunity for the School of Mathematics and the University presented itself when Dr. Andrew Odlyzko from AT&T Laboratories indicated that he would be interested in the directorship of the newly established Digital Technology Center at the University of Minnesota. The search committee, headed by the Institute of Technology Dean, Regents' Professor H.Ted Davis, made an excellent decision in choosing him as the director of this center. Both Arnold and Odlyzko are eminent mathematicians and the School is their tenure home. I warmly welcome these new colleagues.

Professors Donald Aronson and Charles McCarthy will be retiring this year after many years of highly distinguished service to the School and the University of Minnesota. A dinner event in their honor is scheduled on April 12, 2002.

Two conferences were sponsored by the School of Mathematics and the IMA to celebrate the 60th birthday of Ordway Professor Nicolai V. Krylov and the 75th birthday of Regents' Professor Emeritus James B. Serrin. Many distinguished mathematicians spoke at these conferences and joined us in the celebrations.

The School held a first department retreat (with dinner) on November 13, 2001, to discuss various issues involving graduate and undergraduate education and building a community of scholars. The response from the faculty was extremely positive, and several focus groups met in discussion and presented their reports to the faculty. Much follow-up work remains to be done, but it was a great beginning. It is my hope that this will become a tradition and we will hold such a retreat every year in the fall semester.

One final note: as you may have noticed, the newsletter has been undergoing an evolutionary change. The editorial board now consists of Professors Donald Kahn, Willard Miller and Karel Prikry (Chair). I wish to express my sincere thanks to them for their tireless effort in the production of the newsletter. I would also like to take this opportunity to thank Becky Johnston for the skillful and esthetically pleasing layout of the newsletter.

Naresh Jain, Head, School of Mathematics

## Promotions

*Professor Scot Adams* was promoted to the rank of Full Professor effective September 2001. Scot's research area is dynamics of Lie groups.

*Professor Victor Reiner* was promoted to the rank of Full Professor effective September 2001. Vic's research area is combinatorics.

*Professor Fernando Reitich* was promoted to the rank of Full Professor effective September 2001. Fernando's research area is partial differential equations and applied mathematics.

*Professor Dihua Jiang* was promoted to the rank of Associate Professor with tenure effective September 2001. Dihua's research area is number theory.

*Professor Jiaping Wang* was promoted to the rank of Associate Professor with tenure effective September 2001. Jiaping's research area is differential geometry.

## Awards and Recognitions

*Professor Douglas Arnold* will give an invited plenary address at the International Congress of Mathematicians to be held in Beijing in August 2002. For more about Professor Arnold and his work see the sections "Welcoming Incoming Faculty" and "News from the IMA."

*Professor Bernardo Cockburn* will give an invited plenary address on "Discontinuous Finite Element Methods" at the annual meeting of GAMM (Gesselschaft fur Angewandte Mathematik und Mechanik, the German counterpart of SIAM) being held in Augsburg, Germany, in March 2002.

*Professor Nicolai Krylov* was awarded the Alexander von Humboldt Prize for Senior U.S. Scientists for the year 2001.

*Professor Mitchell Luskin* will give an invited lecture at the International Congress of Mathematicians to be held in Beijing in August 2002. Professor Luskin will present his research on mathematical models, numerical analysis, and computation of crystal microstructure and phase transitions.

*Professor Mikhail Safonov* is an invited plenary speaker at the regional meeting of the American Mathematical Society to be held at the University of Wisconsin, Madison, October 12-13, 2002.

*Distinguished McKnight Professor Vladimir Sverak* will give the seventh Avron Douglis Memorial Lecture at the University of Maryland, College Park, on April 12, 2002. Previous speakers were Professors L. Caffarelli, L. Evans, P. Lax, T.-P. Liu, L. Nirenberg and H. Weinberger.

*Dunham Jackson Assistant Professor Dominik Schoetzau* is one of the recipients of the Tenth Fox Prize in Numerical Analysis. This is an international prize awarded by the Oxford University Computing Laboratory to outstanding young numerical analysts for whom the age restriction this year was that the person be born after January 1, 1970.

Our alumnus,* Professor Rui Fernandes* of Technical University, Lisbon, was awarded the Gulbenkian Basic Science Award for his paper "Connections in Poisson Geometry I: Holonomy and Invariants," published in the Journal of Differential Geometry, vol. 54 (2000). This is the most prestigious award in Science in Portugal, and is given on a rotating three-year basis to Basic Science, Social Sciences and Applied Sciences by the Gulbenkian Foundation. Fernandes received his Ph.D. in 1994 under Professor Peter Olver.

*Professor Giovanni Leoni*, currently at the Universitˆ di Alessandria, who received his Ph.D. here in 1995 under the direction of Regents' Professor James Serrin, has been awarded the Bartoletti Prize for the year 2001 by the Italian Mathematical Society (Unione Matematica Italiana), for the best young Italian mathematician under the age of 33. Previous winners have included Giuseppe DaPrato, Giorgio Talenti, Sergio Spagnolo, Mariano Giaquinta, Angelo Anile, Luigi Ambrosio and Alessandra Lunardi.

## Academic Visitors

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), Margherita Barile (University of Bari, commutative algebra), Mark de Longueville (Ph.D. Berlin Technical University, combinatorics), Douglas Hanes (Ph.D. University of Michigan, commutative algebra), Yong Jung Kim (Ph.D. University of Wisconsin, hyperbolic conservation laws, convection-diffusion equations, numerical analysis), Arthur Lim (University of Utah, harmonic analysis and representation theory), Martin Lindquist (Rutgers University, magnetic resonance), Radu Popescu (Ph.D. Columbia University, low dimensional topology), Victor Protsak (Max-Planck Institute, representation theory of Lie groups), Piotr Rybka (Warsaw University, differential equations, calculus of variations and their applications to phase transitions, mathematical models of continua and biology), Dominik Schoetzau (Ph.D. ETH Zurich, finite element methods, discontinuous Galerkin methods), Stephen Tanner (Ph.D. University of Washington, probability theory), Titus Teodorescu (Oklahoma State University, algebraic geometry, vector bundles), Carlos Tolmasky (probability, mathematical finance), Sheng Zhang (Penn State, mathematical modeling and numerical analysis), and Linghai Zhang (Ph.D. Ohio State University, partial differential equations).

*Associate Professors*: James Louisell (University of Southern Colorado, control theory, delay-differential equations)

*Professors:* Yakar Kannai (Weizmann Institute, partial differential equations), Elisabeth Logak (University of Cergy-Pontoise, France, nonlinear partial differential equations, biomathematics), Fedor Nazarov (Michigan State University, harmonic analysis), Gregory Seregin (Steklov Institute St. Petersburg, applications of calculus of variations and general theory of nonlinear partial differential equations), Bevan Thompson (University of Queensland, applications of methods from nonlinear analysis), and Thomas Zink (University of Bielefeld, algebraic geometry, arithmetic geometry).

*Postdoctoral Associates, including IMA Postdoctoral Associates who participate in the teaching activities:* Jamylle Carter (Ph.D. UCLA, image processing, computer graphics), Vittorio Cristini (Ph.D. Yale University, numerical analysis), Selim Esedoglu (Ph.D. Courant Institute, partial differential equations, computer vision), and Jianliang Qian (Ph.D. Rice University, numerical approximations to Hamilton-Jacobi equations, applied inverse problems).

Distinguished One-Month Ordway Visitors (2001-2002)

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:* Mikhail Kapranov (University of Toronto, algebraic geometry, number theory, representation theory, topology), Jean-Claude Nedelec (Ecole Polytechnique, Palaiseau, numerical methods for partial differential equations), Robert OÕMalley (University of Washington, multi-scale methods and singular perturbation analysis), and David Soudry (Tel Aviv University, automorphic forms and L-functions).

Other Visiting Scholars*Professors:* Thomas Halverson (Macalester College, combinatorial representation theory), Jay Fillmore (Professor Emeritus, UCSD, geometry), Boris Levitan (Professor Emeritus, Moscow State University, functional analysis, differential equations), Hirokazu Ninomiya (Ryokoku University, differential equations, calculus of variations), Concepcion Muriel Patino (University of Cadiz, mathematical physics), Kurt Scholz (University of St. Thomas, applied mathematics), Thomas Schwartzbauer (Assoc. Professor Emeritus, OSU, probability), Jin-Keun Seo (Yonsei University, partial differential equations), and Geanina Tudose (York University, algebraic combinatorics).

## President's Award for Outstanding Service for Professor Richard McGehee

Professor Dick McGehee is the recipient of the President's Award for Outstanding Service for his dedicated work, spanning some fifteen years, on the University of Minnesota Health Plan Task Force. His colleagues in the School of Mathematics and many across the University warmly thank him for this contribution and congratulate him on this well-deserved honor. Dick is currently Professor in the School of Mathematics and also has served as the Head of the School and as Director of the Geometry Center. Carol Carrier, Vice President for Human Resources, had this to say, in part, about his work on the Task Force: "As chair of the Task Force, he has done a first-rate job keeping the group focused on its goals. His committee meetings are very well organized and conducted in a professional manner. He is a great consensus builder."

"As part of this overall effort, Dick has spent many hours at the state as a faculty and university representative to the State of Minnesota Joint Labor/Management Committee. At the committee meetings, Dick has never hesitated to speak up on issues impacting the interests of the university."

I personally can estimate the enormity of this task because more than a decade ago I substituted for Dick on the Task Force for one year and found it very time consuming and demanding work. Thanks to Dick's effort, the University has now adopted an entirely new health care system for its employees effective January 2002. The new system is designed to deliver excellent health care for faculty and other university employees in a cost effective manner.

*Naresh Jain*

## Retirements

*Professor Donald G. Aronson*, who joined the faculty of the University of Minnesota in 1957, will retire this June. He received his Ph.D. from the Massachusetts Institute of Technology in 1956 under the direction of Norman Levinson, and he came to Minnesota after a year and a half as a research associate at the University of Illinois. He was promoted to Associate Professor in 1962, and to Professor in 1965. He spent the 1961-1962 academic year at Stanford University as an NSF Postdoctoral Fellow and also held numerous visiting professorships.

Don is famous for his work on the porous medium equation and on dynamical systems theory. He has also done well-known pioneering work on linear and nonlinear parabolic equations. He was an invited speaker at many prestigious conferences and gave a one-hour address at the 1987 AMS annual meeting in Salt Lake City. He is the author of 83 scientific publications. A conference in Don's honor, titled "Nonlinear Phenomena in Science," was held at the Free University of Amsterdam, June 6-8, 2001 on the occasion of his 70th birthday. At this three-day conference many distinguished speakers presented research in areas where Don has had fundamental impact. Don is a very outgoing person and enjoys collaborating with other mathematicians and scientists. Among his distinguished coauthors are James Serrin, Hans Weinberger, Rutherford Aris, Hans Othmer, Dick McGehee and John Lowengrub from Minnesota, as well as Sigurd Angenent, Luis Caffarelli, Martin Golubitsky, Nancy Kopell, Bert Peletier, Juan Vazquez and many others. Don had five Ph.D. students and seven postdoctoral students. His professed dislike of administration notwithstanding, he served for two years as Director of Graduate Studies (1969-1971), and as Associate Director of the Geometry Center in 1997-1998.

Don and his wife Claire have also played an active role in the social life of the School of Mathematics and the general community. We wish them many more happy and productive years.

*Professor Charles McCarthy*, who has been on our faculty since 1961, will retire this coming June. His specialty is Functional Analysis and Operator Theory. Charlie obtained his Ph.D. from Yale University in 1959 under Einar Hille. He spent the next two years at MIT as a Moore Instructor before joining the U of M faculty in 1961 as an Assistant Professor. He was promoted to Associate Professor in 1963 and to Professor in 1967. In 1963, he was awarded the prestigious Sloan Foundation Fellowship, which enabled him to spend the 1963-19 64 academic year at the Courant Institute of New York University. He held visiting professorships at the University of Sussex and Chalmers Institute of Technology. When the personal computers first made their appearance, Charlie played an important role in bringing this technological advance to the department. He served as Director of Graduate Studies during the 1999-2000 academic year, and for a number of years enthusiastically coached our Putnam Exam team. He and his wife Floren, who received her Master's degree in our department, look forward to low-key traveling. We wish them continued happiness in life.

*Professor Yasutaka Sibuya* retired in June 2001, after 38 years at the University. He earned his Ph.D. degree in 1959 from UCLA under Earl Coddington, and a Doctor of Sciences degree from the University of Tokyo in 1961. He joined the University of Minnesota faculty in 1963 as an Associate Professor, after holding faculty positions at MIT and the Courant Institute. He was promoted to the rank of Professor in 1965. Professor Sibuya's research is in the area of differential equations. He is the author, or co-author, of 120 scientific publications and his distinguished contributions have been highly recognized. He has had many prestigious speaking invitations, including an AMS one-hour address in 1982. He was the recipient of the Alexander von Humboldt Award for the Senior U.S. Scientists for 1985, served on the editorial boards of professional journals, and held several visiting professorships at leading research centers worldwide. He supervised eight Ph.D. students, passing on to them his high standard and enthusiasm for mathematics. A dinner in Professor Sibuya's honor, held April 10, 2001, was attended by numerous colleagues. Several of them expressed their deep appreciation for his generous sharing of time and ideas over many years. We wish him many happy and profitable years to come.

## Conference in Celebration of Nicolai Krylov's 60th Birthday

A conference on "Perspectives in Partial Differential Equations and Probability," sponsored by the School of Mathematics and the IMA, was held on Friday, Saturday and Sunday, May 25-27, 2001 to celebrate the 60th birthday of Ordway Professor Nicolai Krylov. The occasion brought here a number of distinguished mathematicians working in probability theory and partial differential equations - areas in which Krylov has been a world leader for over a quarter of a century. The conference began with welcoming remarks by the Head of the School, Naresh Jain, who reflected on Nick Krylov's great contributions to mathematics and our good fortune in having been able to attract him to Minnesota more than a decade ago. Major developments in the areas of probability theory and partial differential equations have been stimulated by the exchange of insights, problems and methods between the fields. This was exemplified by much of the research discussed in the lectures at the conference.

The invited speakers, and titles of their lectures, were Professors Luis Caffarelli (University of Texas, Austin), "Optimal transportation and Monge-Ampere equations"; Eugene Dynkin (Cornell University), "Superdiffusions and partial differential equations"; Wendell Fleming (Brown University), "Risk sensitive stochastic control and differential games"; Rafail Khasminski (Wayne State University), "Averaging principle for diffusion processes with null-recurrent fast component"; Paul Malliavin (University of Paris VI), "Construction of unitarizing measure for highest weight representations of Virasoro algebras"; Anatoly Skorokhod (Michigan State University), "Infinite systems of stochastic differential equations"; Nina Uraltseva (St. Petersburg State University), "On the regularity of solutions and free boundaries in some elliptic and parabolic problems"; and S.R.S. Varadhan (Courant Institute), "Regularity of diffusion coefficients in simple exclusion models." Professors Boris Rozovskii (University of Southern California) and Mikhail Safonov (University of Minnesota), both former students of Krylov, presented an "Overview of the work of Nicolai Krylov." The Organizing Committee consisted of John Baxter, Mikhail Safonov and Boris Rozovskii. Dinner for the conference participants was held on Saturday in the "Bistro" of the Hubert H. Humphrey Center. After-dinner speakers included Professors Dynkin, Fleming, Friedman, Jain, Malliavin, Safonov and Skorokhod, who talked about their long personal and professional associations with Nick Krylov.

## Symposium to Celebrate the 75th Birthday of James Serrin

A Symposium in honor of Regents' Professor Emeritus James Serrin's 75th birthday, sponsored by the School of Mathematics and the Institute for Mathematics and its Applications, was held November 8-11, 2001. James Serrin became Regents' Professor of Mathematics in 1969, and was one of the youngest faculty members ever to be so honored. He is the recipient of the George David Birkhoff Prize in Applied Mathematics (1973), a member of the National Academy of Sciences, the American Academy of Arts and Sciences and the Finnish Academy of Sciences and Letters. He was awarded honorary doctorates by the University of Sussex and the University of Padua. Professor Serrin continues to be very active scientifically. In 2002 he will speak at conferences in China, France and Russia.

The following distinguished mathematicians addressed the conference: Emmanuele DiBenedetto (Vanderbilt University), "Homogenization limits for a problem in visual transduction"; Haim Brezis (University of Paris VI), "New thoughts on Sobolev spaces"; Constantine Dafermos (Brown University), "Progress in hyperbolic conservation laws"; Avner Friedman (University of Minnesota), "Asymptotic behavior of solutions of systems of nonlinear evolution equations arising in chemotaxis and angiogenesis"; Jack Hale (Georgia Institute of Technology), "Regularity, determining modes and Galerkin methods"; Howard Levine (Iowa State University), "Modeling cell signaling and transduction in angiogenesis"; Hiroshi Matano (University of Tokyo), "Traveling waves in heterogeneous media and a mini-max principle"; Bert Peletier (Leiden University), "Critical powers for the unit ball in n-space"; Patrizia Pucci (University of Perugia), "Remarks on the work of James Serrin and some new results on quasilinear elliptic problems"; Paul Rabinowitz (University of Wisconsin, Madison), "Mixed states for an Allen-Cahn equation"; Grozdena Todorova (University of Tennessee, Knoxville), "Dynamics of nonlinear hyperbolic equations in the vicinity of higher modes"; Hans Weinberger (Unversity of Minnesota), "Spreading speeds in models for multispecies, growth and migration"; William Ziemer (Indiana University, Bloomington), "Sobolev mappings and co-area"; and Henghui Zou (University of Alabama, Birmingham), "A Cauchy-Liouville theorem for quasilinear elliptic equations."

Dinner for the conference participants was held Saturday in the "Bistro" of the Hubert H. Humphrey Center, with Professor Walter Littman serving as Master of Ceremonies. After-dinner speakers included the Head of the School of Mathematics, Professor Naresh Jain, as well as Professors Rutherford Aris, Jim Douglas, Roger Fosdick, Howard Levine, Chi-Sing Man, Bert Peletier, Ray Redheffer, George Sell, and Hans Weinberger, all longtime friends and associates of the honoree. The speakers commented on the depth and breadth of Jim's work and its fundamental impact on the areas of partial differential equations, calculus of variations, hydrodynamics and thermodynamics. Speakers also mentioned his steadfast loyalty to friends and commitment to the department.

The final speaker was Jim himself. He spoke of his family's roots in the midwest farm country of Michigan, Indiana and Ohio. He mentioned people who had a profound effect on his undergraduate training: Ernst Hellinger at Northwestern and Harold Blair and Paul Rood at Western Michigan. He then spoke about graduate school at Indiana University where he was introduced to partial differential equations by David Gilbarg. He praised Gilbarg both as a researcher and as a man. "Of all the teachers at Indiana, I most loved David Gilbarg."

With the events of Sept. 11 in mind but never mentioned he paraphrased words of Kenneth Clark. "Order is better than chaos, creation better than destruction." He continued, "the world is full of the genius of marvelous Mathematicians, Scientists and Artists." He expressed the hope that humanity will rise above the destructive setbacks now, as it has in the past. He concluded: "Nevertheless, mathematicians in these troubled times still turn aside into unfrequented wooded lanes. Here the light filters through perfect forms. It arranges itself in lovely patternsÑthe beauty of mathematical ideas."

The Organizing Committee consisted of Haim Brezis (University of Paris VI), Walter Littman (University of Minnesota), Norman Meyers (University of Minnesota) and Patrizia Pucci (University of Perugia). Many thanks are due to Monika Stumpf, Kathy Swedell and Becky Johnston whose hard work was indispensable to the success of the celebration. Speakers noted the kindness Jim and Barbara have exhibited over their many years in Minnesota. We wish they will be rewarded by many more happy and healthful years.

## 2002 Symposium Announcements

#### The 5th Annual Rivière-Fabes Symposium

April 5-7, 2002

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 will take place April 5-7, 2002, Friday afternoon - Sunday morning. The principal speakers are Professors David Jerison (MIT) and Elias Stein (Princeton University), each of whom will give two lectures. The following invited speakers will give one lecture each: Professors Nets Katz (Washington University in St. Louis), Michael Lacey (Georgia Institute of Technology), Wilhelm Schlag (Caltech) and Tatiana Toro (University of Washington, Seattle). The organizing committee consists of Professor C. Kenig (University of Chicago), and Professors N. Jain, N. Krylov, W. Littman, F. Reitich and M. Safonov (Chair) of the School of Mathematics. For further information see the department website www.math.umn.edu/arb/RiviereFabes.html

The fourth Rivière-Fabes Symposium was held here on April 20-22, 2001. Professors Daniel Stroock (MIT) and Robert Fefferman (Chicago) gave two lectures each: "A differentiable structure on the space of probability measures" and "Hodge theory on certain non-compact Riemannian manifolds" (Professor Stroock), and "Some issues in harmonic analysis related to the work of Fabes and Rivière on non-isotropic dilations: I) Maximal functions, and II) Singular integrals" (Professor Fefferman). The other main speakers were: Professors P. Daskalopoulos (UC Irvine), "Gauss curvature flow with flat sides: geometry and regularity of the interface"; S. Hoffman (University of Missouri, Columbia), "The solution of the square root problem of Kato"; M. Mitrea (University of Missouri, Columbia), "Elliptic boundary value problems on Sobolev-Besov spaces"; and Terence Tao (UCLA), "Global regularity of wave maps." A dinner for the participants was held Saturday, April 21, 2001.

First Biennial Yamabe Memorial Symposium

September 20-22, 2002

The Yamabe Memorial Lecture, in honor of the distinguished mathematician Hidehiko Yamabe (1923-1960), 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.

In the future we will continue this fine tradition in a different and more extended form. Thanks to a gift to the School of Mathematics from a very generous anonymous donor, a permanent endowment has been set up to suppport a biennial conference, which will be known as the Yamabe Memorial Symposium. This Symposium will be held for the first time Friday-Sunday, September 20-22, 2002 at the School of Mathematics. The Memorial Lecture, in its original form, will continue to be held at Northwestern in alternate years.

The 2002 symposium organizers are Conan Leung, Jiaping Wang and myself. This first Yamabe Symposium will be a high-level conference on aspects of geometry and analysis. The organizers expect to have a very distinguished list of speakers and an exciting symposium.

*Robert Gulliver, Professor and Chair of the Yamabe Symposium Committee*

Conference to Celebrate the 70th Birthday of

Regents' Professor Avner Friedman

November 8-10, 2002

Avner Friedman is a member of the National Academy of Sciences. He served as director of the Institute for Mathematics and its Applications from 1986 to 1997.

The conference will be held at the University of Minnesota, Minneapolis. The organizing committee consists of Professors Nicolai Krylov, Walter Littman (chair), Fernando Reitich, and Fadil Santosa.

## Speaking Invitations & Other Notable Activities

*Professor Bernardo Cockburn* has been invited to organize a minitutorial for the SIAM Annual Meeting to be held in Philadelphia, July 7-12, 2002, on the occasion of the 50th anniversary of the founding of SIAM. The title of the tutorial is: "Discontinuous Galerkin methods for Partial Differential Equations." He has also been invited to organize a minisymposium on this topic for the 5th World Congress on Computational Mechanics (WCCM V), to be held in Vienna, also July 7-12, 2002 Ñcoinciding with the SIAM meeting. Professor Clint Dawson (University of Texas at Austin) is a coorganizer. Professor Cockburn will divide his time between the two meetings. The Discontinuous Galerkin methods are robust and accurate methods that have recently made their way into the mainstream of computational fluid dynamics and are quickly finding use in a wide variety of applications outside that area. Practical applications include weather-forecasting, oil recovery, oceanography, design of turbomachinery, transport of contaminant in porous media, semiconductor device simulation, and many others.

*Professor Peter Olver* is helping to organize two major, interrelated programs at the University of Minnesota this summer. The IMA Summer program on "Special Functions in the Digital Age" will assess the current state of the art in special function theory and digital libraries in general. Highlighted will be the soon-to-appear Digital Library of Mathematical Functions (DLMF) at the National Institute of Science and Technology (NIST), a project led by his father, Frank W.J. Olver, a math professor at the University of Maryland and at NIST. This is the first time the two have worked together on a committee! The IMA program will lead in to a large meeting of the Society for the Foundations of Computational Mathematics, featuring outstanding plenary speakers and numerous workshops. At that time, Peter Olver will be taking over as co-managing editor, with Prof. Arieh Iserles of the University of Cambridge, of the new Springer journal, "Foundations of Computational Mathematics" sponsored by the Society.

Peter is also a member of the organizing committee for the Workshop on Under- and Overdetermined Systems of Algebraic or Differential Equations, Karlsruhe, Germany, March 18-19, 2002, and served on the organizing committee of the European Summer School on "What is Integrability?" held at the Newton Institute, Cambridge, England, August 13 - 24, 2001.

*Professor Victor Reiner* was one of the two principal speakers at the Special Session on Algebraic and Topological Combinatorics at the AMS meeting at Williams College, October 13-14, 2001. The other principal speaker was Richard Stanley of MIT, Vic's Ph.D. advisor. The title of Vic's lecture was "Recent progress in the topology of simplicial complexes."

*Professor Alexander Voronov* accepted the invitation to join the editorial board of a new journal in algebra "Stacks, Categories, and Applications." He also gave an invited series of lectures on "Universal Algebra" at the Conference in honor of Dennis Sullivan's 60th birthday held at SUNY at Stony Brook, June 7-14, 2001, and is serving on the advisory committee for the International Symposium on Kac-Moody Lie Algebras and Applications, to be held at the Ramanujan Institute, University of Madras, January 28-31, 2002.

*Professor Rachel Kuske*, who is also the Associate Director of the Minnesota Center for Industrial Mathematics (a center in the School of Mathematics), has recently set up a math mentoring network for women and girls. For more details, see the article "AWM Mentor Network."

## Undergraduate Program: Teaching Communication Skills

Those of us who have been teaching for some years will probably agree that students often lack sufficient communication skills. Teaching such skills tends to be an incidental part of imparting mathematical knowledge. This is especially true of beginning courses where emphasis has traditionally been on learning basic concepts and techniques. However, over the last few years we have seen developments in our department, and in the University as a whole, that place learning communication skills on a more even footing with gaining command of the course material itself. This is a desirable change, since there is a real need for good communication skills in the workplace as well as in graduate study. In this note we would like to outline some related developments.

To begin with, we are happy to say that our department has been somewhat ahead of the curve. Thus when the University's new writing requirement of at least one writing intensive course in each student's major took effect in the Fall 1999, we had just the right kind of course for this purpose. It was Math 2283, "Sequences, Series and Foundations," developed by Professor Wayne Richter about ten years ago as a transitional course between lower level courses emphasizing basic manipulative skills and more advanced courses with more attention to proofs. In this course students have been expected to make a serious effort to write simple proofs in a setting familiar to them from the first two years of calculus. In Fall 1999 this course was upgraded to Math 3283W where students are expected to carefully write proofs of theorems and expositions of the subject matter. In order to get the maximum benefit from their assignments, students in writing intensive courses must typically rewrite their papers at least once after getting the instructor's feedback. Most math majors are now satisfying their writing requirement by taking this upgraded course. We also continue to offer the original course, Math 2283, for students who satisfy their writing requirements in other ways. Another way to satisfy the writing requirement is by writing a Senior Project paper (Math 4997W. All CLA math majors are required to do a Senior Project). A faculty member guides the student in the writing of the paper which must be at least ten pages long. It is also required that the project demonstrate acquisition of new mathematical material. Extra one-on-one student-faculty contact is an added benefit of the senior projects.

Here are the titles of the Senior Projects carried out to date, together with the names of the faculty advisors. Professor Paul Garrett supervised three such projects: "The content of sports statistics," "The Enigma Cipher," and "The NP-completeness of well-posedness of positions in the game of Minesweeper." Professors Bert Fristedt and Max Jodeit have supervised one project each: "WallisÕs attempt to prove the parallel postulate," and "The definition and properties of the complex exponential function." In the articles "Thoughts on Writing Skills" and "Senior Project Goals," Professors Garrett and Fristedt share their thoughts about teaching writing skills and about the goals of the projects.

We would also like to mention some other approaches involving interactive learning that our faculty are using to improve student communication skills in our IT Calculus and Mathematics for Elementary School Teachers courses. In IT Calculus the in-class time is divided into two hours of large lecture, one hour of recitation and two hours of lab/workshop each week, compared to three hours of large lecture and two hours of recitation in the traditional format. Both faculty and TA's participate in the lab/workshop sessions but not in the recitation sessions, thus there is an additional one hour of faculty-student contact per week in the new format. In the lab/workshops students develop verbal technical communication skills by interacting with each other as well as with TA's and faculty, while at the same time "learning by doing." Use of graphing calculators, Matlab and Mathematica during the second year allows treatment of more interesting applied problems than can be done in the traditional course. And, from the very inception of this format, students have been required to write more: already in the January 1998 issue of this newsletter it was noted that in the fourth-quarter course in fall 1997 students wrote up four lab reports.

In the elementary school teachers' course there is no formal division into lectures and recitations (or labs). Rather, the professor briefly explains a concept, assigns a suitable problem illustrating it, and then students break up into groups of four to work on the problem. After a few minutes, typically not more than ten, a student presents the work done by her/his group at the blackboard. Another problem is then assigned, or a new concept explained, and so on. The expectation is that any student in a group should be able to do the blackboard presentation. Therefore, even those students who contribute somewhat less to solving the assigned problems have to communicate, both within the group and at the blackboard. The examinations are more traditional, requiring individual work.

*Larry Gray, Professor and Director of Undergraduate Studies*

## Undergraduate Program: Some Thoughts on Teaching Writing Skills

A number of upper-division courses have increased the emphasis on coherent writing and presentation of technical mathematics. My structuring of Math 5248 (Cryptography) and Math 5251 (Error-correcting Codes) gives students weekly assignments in which they must give precise verbal descriptions of algorithms, as well as logically complete narratives to accompany the execution of the algorithms. A written term project is also a significant part of the course. All his writing is intended not only as exercise in technical writing for its own sake, but also as a stepping-stone to the greater linguistic demands of writing proofs, for those students who will continue in that direction.

The need for a transitional stage in mathematics writing was perceived after some years of observation of students' discomfort with careful general writing, much less precise writing in a technical context. Further, at the level of careful description of algorithms, explicit writing demands that students be more conscious of what they're doing, rather than being able to do it but without sufficient understanding so as to be able to describe it effectively to anyone else. Many students have expressed appreciation for and interest in the increased emphasis on the linguistic aspects, and for insisting on the point that mathematics must be well-enough understood so that it can be communicated to others.

*Paul Garrett, Professor and Director of Graduate Studies*

## Undergraduate Program: Senior Project Goals

In order to help a student choose a senior project, it is important for the faculty member to keep two things in mind: (1) the goal of the project, as opposed to the variety of goals in mathematics courses; (2) the level of difficulty of the project, which should be appropriate for the student's mathematical background. My view is that the primary goal of the senior project is to provide the student an opportunity to create a coherent story involving several proofs or calculations, each of which is at a level that the student has already shown he or she can handle.

It is not reasonable to ask a student who has typically earned B's or B-'s on tests to now create a coherent story involving the types of problems that on tests are used to decide who deserves an A or A-. Rather the goal is a to provide a capstone experience in which the student combines mathematics that he or she already understands with some new mathematics or applications at the same level.

*Bert Fristedt, Professor of Mathematics *

## Undergraduate Program: Reflections on Changing from Quarters to Semesters

We are now in the midst of the third academic year under the semester system, the switch from quarters to semesters having occurred in September 1999. The semester system has certain benefits. For instance, it has enabled us to change some 4-credit quarter courses into more leisurely paced 3-credit semester courses. A second example concerns many of our year-long sequences. Under the quarter system, we generally felt that a student who took only the first of the three quarters was not getting a sufficiently rich experience, while those who would take two of the three quarters in the sequence would have difficulty finding a good alternative course if they did not want to continue with the third quarter of the sequence. On the other hand, the first of two semesters is typically a satisfying educational experience even if the second semester is not taken. There is also another kind of benefit that resulted from the switch from quarters to semesters. It gave us an opportunity to re-think and improve our curriculum and the structure of our courses in ways that are only incidentally connected to semester conversion.

When the University of Minnesota converted from quarters to semesters for the academic year 1999-2000, the School of Mathematics and the School of Statistics decided to make their beginning 5xxx-level courses in probability and statistics identical. These courses, which had been somewhat similar under the quarter system, are often taken by undergraduate majors in the two disciplines and also by graduate students in a variety of areas. The reason we decided to make the courses identical was to simplify the structure of our programs for students and give them more flexibility in their planning. After these changes were made, the number of students taking the courses has grown; it is approximately 225-250 for the current academic year, approximately double what it was in the last year on the quarter system.

The merged courses, which now use the same textbook and course outline, are Math 5651, called "Basic Theory of Probability and Statistics," and Stat 5101, called "Theory of Statistics I." There are eight sections being given during the current academic year. Four of the eight are taught as Math 5651 by mathematics faculty and the other four are taught as Stat 5101 by statistics faculty. The flexibility gained by merging the courses lies in the fact that now the course under either designator is an appropriate prerequisite for each of the following three courses: Math 5652, "Introduction to Stochastic Processes"; Math 5654, "Prediction and Filtering"; and Stat 5102,"Theory of Statistics II." Thus, for instance, a student can take Stat 5101 in order to prepare for Math 5654; similarly he or she can take Math 5651 to prepare for Stat 5102. And a student who knows that he or she wants to eventually take Math 5652 or Stat 5102 but who is yet undecided between them can proceed by taking either Math 5651 or Stat 5101 as a first course for both potential directions.

*Bert Fristedt, Professor of Mathematics*

## Undergraduate Program: NCS-MAA Team Math Contest November 10, 2001

Each fall, the North Central Section of the Mathematical Association of America holds a mathematics contest for undergraduates. Teams of at most three students work collectively on a set of ten problems for three hours. The problems are scored at ten points for each, so that a perfect set of solutions gives a score of 100. This year, there were 66 teams from 22 schools located in Minnesota, the Dakotas, Alberta, and Manitoba. The Unversity of Minnesota (Twin Cities) sponsored four teams for the contest this year.

We are pleased to report that one of our teams, with team members Brian Jacobson, Derek Larson, and Kristin Shimin, took first place with perfect score of 100 - the only team to obtain a perfect score. Our other three teams, which included Ian Bui, Philip Carlton, Peter Dryud, Michel D'Sa, Michael Erlewine, Tim Lee, John Pham and Mathew Steuck, also placed well. We note that in the year 2000 contest, one of our teams also took first place. The members then were Brian Jacobson, Derek Larson and Jon Moon.

On behalf of the School of Mathematics, I would like to congratulate the teams members who did so well. Thanks also go to Professors Charles McCarthy and Karel Prikry who administered the test.

*Gennady Lyubeznik, Professor of Mathematics & University of Minnesota contest coordinator*

## Undergraduate Program: Research Experiences for Undergraduates (REU)

The summer 2001 REU program involved even more undergraduates than in summer 2000, and we had weekly presentations of students' work, after Friday pizza lunch. Scot Adams' group, Filip Matejka, Andrew Liesch, and Michael Lieberman, modeled traffic to understand whether metering is effective in improving the flow of traffic. They began by modeling traffic on a simple Y-shaped road system, with cars traveling down the Y, so that two lanes of traffic would merge into one, using Mathematica. Cars were produced at both sides of the top of the Y according to an exponentially distributed waiting time. If the rate of production was sufficiently large, then a traffic jam would occur at the merge point, as in real life. Thus the cars would leave the merge point with an initial velocity of zero, and if the maximum acceleration is set small enough, then cars leaving the merge point would be widely spaced from one another producing a low flow off the bottom of the Y. They found that by implementing metering this flow could be increased. They then analyzed more complicated road models, developing a Java program with which a user could draw a road system using the mouse, and be prompted for parameters such as maximal acceleration, speed limits, rate of production of cars, rate of metering. Their basic result is that, while in some situations metering is clearly advantageous, in complicated road systems choosing efficient metering is hard, and perhaps not feasible.

Vic Reiner's group, Hans Christianson and Hyung Kim, continued a project that his Summer 2000 REU group (Paul Bendich and Tristram Bogart) began. In 2000, his students performed computer experiments to determine the structure of the critical group (a finite abelian group which is a subtle graph-isomorphism invariant) for a certain class of graphs (threshold graphs). They did a great job on this, and conjectured a description for "almost all" threshold graphs. This summer, Hans Christianson produced an elegant proof of their conjecture, and Hyung Kim did more experiments which led them to extend the statement of their conjecture to all threshold graphs. Christianson and Vic have written a paper based on this work, submitted to Linear Algebra and Its Applications. It is linked-to from Vic's web page at www.math.umn.edu/~reiner/.

In Rachel Kuske's group, Jessica Myers (University of Minnesota) combined linear stability analysis with numerical simulations to study the effects of coupling on a canonical model of neurons with bursting (alternating active/silent) dynamics. She developed predictive rules for synchronization and considered different models for coupling. Justin Douglas (University of Minnesota) developed code for studying stochastic effects on models of elasto-plastic behavior. His code involved determining the stability of equilibria and then testing the effects of external random effects on transitions between equilibria. Michael Hsieh (University of California, Berkeley) analyzed pricing of the American put option. He incorporated asymptotic results for the behavior near expiry into an iterative method adapted for the Black-Scholes partial differential equation.

Paul Garrett's group, Laura Chasman (Caltech), Ben Chastek (St. Mary's), Kevin Costello (Caltech), Lee Dicker (McGill), Michael D'Sa (U of M), Ali Elgindi (U of Wisconsin), McKenzie Lamb (Beloit College), Natalie Linnell (U of M), Christina Mulligan (Harvard), and Mohammad Zaki (MN State U), studied a variety of problems related to number theory and its applications, such as random number generation, distribution of prime numbers, local-to-global principles (Hasse-Minkowski theorem), fixed-point theorems (aiming toward Weil conjectures), partitions, and general structure of algebraic number fields. We started by developing a common ground of Fourier analysis, complex analysis, abstract algebra, and some specific number-theoretic ideas such as the gamma function, zeta-functions and L-functions, Gauss sums, quadratic reciprocity, algebraic integers, elliptic functions, theta series, and modular functions. We continued talking about modern developments in number theory and its applications while individuals worked on their own projects, to get a little idea about the Wiles-Taylor proof of Fermat's last theorem via the Taniyama-Shimura conjecture, as well as trying to think of parts of Langlands' conjectures as being extensions of quadratic reciprocity and other (known) reciprocity laws of classfield theory.

For details about the Summer 2002 program please see the department web page at www.math.umn.edu/arb/reu.

*Paul Garrett, Professor of Mathematics and REU Coordinator *

## Graduate Program

In July and August we welcomed 38 new TAs, from all around the world. Eight among these were more advanced students already working with mathematicians who are joining our faculty this year. As usual, the international TAs arrived first for the program conducted by the English as Second Language Department that helps orient them in the ambient language and culture. The ESL people also assess communication skills, in addition to English fluency, and make recommendations about readiness to work in a classroom.

After the ESL orientation, the School of Mathematics conducted its own orientation, introducing students to the mundane but important facts that they'll need in order to function in the School of Mathematics, and having videotaped practice sessions in which they presented material as a TA would. Several senior TAs (Dan Drake, Ryan Berndt, Gabe Soto, John Hall, and Upali Karunathilake) assisted, lending their insights and perspectives. Play-acting scripted and acted by the grad students made it all more memorable.

The Written Preliminary Ph.D. exams were given the week before classes, and as expected several 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 this requirement. Diane Trager, the graduate secretary, organized things for the School of Mathematics picnic. She continues to learn the many details and conventions that play a role in the graduate program.

The Graduate Studies Committee awarded the Thesis Prize to Dr. Mireille (Mimi) Boutin for her thesis "On Invariants of Lie Group Actions and their Application to some Equivalence Problems." She worked under the supervision of Peter Olver, and is now at Brown University working with David Mumford.

In addition to Mimi Boutin, students who finished Ph.D.'s this year were (the institution in parentheses indicates the current position):

Paul Castillo (advisor Bernardo Cockburn), "Local Discontinuous Galerkin Methods for Convection-Diffusion and Elliptic Problems," (Lawrence Livermore National Lab)

Wonjae Chang (advisor Nicolai Krylov), "Numerical Schemes for BellmanÕs Equations with Free Boundary," (Columbia University)

Kuo-Chang Chen (advisor Rick Moeckel), "Variational Methods and Periodic Solutions of Newtonian N-Body Problems," (Northwestern University)

Natasha Dobrinen (advisor Karel Prikry), "Generalized Distributive Laws in Boolean Algebras and Issues related to a Problem of von Neumann," (Penn State)

Xun Dong (advisor Vic Reiner), "The Topology of Bounded-Degree Graph Complexes and Finite Free Resolutions," (Caltech)

Kristina Garrett (advisor Dennis Stanton), "Lattice Paths and Generalized Rogers-Ramanujan Type Identities," (Carleton College)

Eduardo Goes Leandro (advisor Rick Moeckel), "Bifurcations and Stability of Some Symmetrical Classes of Central Configurations," (U. Federal De Pemambuco)

Cristian Rios (advisors Carlos Kenig and Mikhail Safonov), "Sufficient Conditions for the Absolute Continuity of the Nondivergence Harmonic Measure," (McMaster University)

Seong-A Shim (advisor Wei-Ming Ni), "Uniform Bounds and Global Behaviors of Solutions of Cross-Diffusion Systems," (McMaster University)

Tamas Wiandt (advisor Richard McGehee), "Conley Decomposition for Closed Relations," (Rice University).

In addition, the following students graduated from the Master's degree program:

Elisa Ferretti (advisor Mikhail Safonov), August 2000

Jennie Manrodt (advisor David Frank), September 2000

Caixia Ge (advisor Stephen Agard), May 2001

Luis Yunes (advisor Fadil Santosa), May 2001

Hung Quang Ngo (advisor Dennis Stanton), June 2001

Ulyana Babanova (advisor Paul Garrett), August 2001

Jonathan Marshall (advisor Fadil Santosa), August 2001

In closing, we have asked two of our graduating Ph.D. students to tell us briefly about their student experiences here. Their comments follow.

*Professor Paul Garrett, Director of Graduate Studies*

I have many good memories from the time I spent in Minnesota. When I arrived in 1996, the math department was full of students coming from all over the world and with very different backgrounds. We taught each other English, we wrote our homework together, we helped each other for the preliminary exams, we practiced giving talks together and we graded late through the night at the same table. The strong bond we built over the years even manifested itself when we applied for jobs, sharing files, information and tips. As you can imagine, our application material looked suspiciously similar! But we eventually had the joy to see each of us get a great offer and that is probably the best proof of the high quality of this department.

Mireille Boutin (Ph.D. 2001)

I started my studies in 1995 and earned my degree in 2001. My advisor was R. McGehee. I am very grateful that I had the chance to learn from excellent teachers at the U of MN. I was also lucky to teach the whole spectrum of classes offered to undergrads, from College Algebra to Honors classes and UMTYMP. I think the experience I acquired helped me to get my current position. I will always remember the non-mathematical times, too: it was great to get to know my professors during the picnics and to get together with my friends during the soccer games of the math department's team, the Eagles. I will always look forward to going back to the University to meet all my friends again.

Tamas Wiandt (Ph.D. 2001)

## Minnesota Center for Industrial Mathematics

With the Center's Director Professor Avner Friedman being on leave, Professor Fadil Santosa is the Acting Director and Professor Rachel Kuske is the Associate Director. During the past summer the Center placed twelve mathematics graduate students as interns with 3M, IBM, Unisys, Symbol and Corning, as well as Vital Images, a local medical imaging company, which hosted two students. During the Fall Semester these students gave reports about their research at our Industrial Problems Seminar, which is run jointly with the Institute for Mathematics and its Applications (IMA). For example, two of the students who did their internships at Corning reported about their research on problems arising in optical communications. In addition to the student presentations, the Industrial Problems Seminar features talks by scientists from industry introducing students, and IMA postdocs, to problems in which mathematics plays a significant role, often leading to collaborations between these scientists and members of the Center. Some such recent collaborations included scientists from Deluxe, Vision-Ease, Cardinal Glass and Symbol. More information about internships can be found on MCIM's web site at www.math.umn.edu/mcim.

In conclusion, we asked Dr. John Hoffman from Lockheed Martin Corporation to tell our readers about his experiences as a mathematician in industry. His stimulating contribution follows.

*Rachel Kuske, Associate Director Fadil Santosa, Acting Director *

#### What's it Like to be a Mathematician in Industry?

Hi, I'm John Hoffman, I graduated from the U of MN with a Ph.D. in Probability in 1993. I was recently asked by Fadil Santosa of the IMA to write about how I decided to become a mathematician in industry, describe my work, and to describe how (or if) a Ph.D. prepared me for my job. The event of my life that made me even consider getting a Ph.D. was a summer internship at Eli Lilly & Co. (one of the larger pharmaceutical manufacturers) between my junior and senior years of college at Rose Hulman Institute of Technology in Indiana. As summer interns we received special treatment, and got to tour a number of the corporate facilities, and meet a wide variety of people working in many aspects of the company: research, production, finance, and operations. Every person I met that summer, who had a job that I found interesting, had a Ph.D. Clearly, this implied that I needed to get a Ph.D.! So, my motivation for attending graduate school had never been to become a professor (which, at that time, I interpreted as being a teacher instead of a researcher). Later, I learned the only people in academia who made any money were those that did research, so if I were to stay in academia, I'd have to become a researcher. I enjoy research immensely; but in the early 1990's opportunities for academic researchers were extremely limited, paid poorly, often required extensive moving, and had little job security. Since I had had enough of all that in graduate school, I decided to work as a researcher in industry.

Presently I work at Lockheed Martin in Eagan MN. I'm in the Advanced Signal Processing and Algorithms Group. Ostensibly, our group's mission is to monitor sensor technologies, and algorithm developments that could impact the P-3 Orion Maritime Surveillance Aircraft and its missions. Eagan has been responsible for all the electronics systems (including sensors) on this aircraft for the past 50 years (The P-3 is one of the older aircraft in the inventory). Our group has a number of core technical competencies which we use to pursue research programs sponsored by various government agencies. Our goal is to develop (or learn about) new technologies that can be applied to the missions of the P-3. Since the sensor suite on a P-3 is quite broad, we are usually able to make a solid business case for a wide variety of technologies, and for how those technologies would aid our divison. To give a feel for the breadth of projects that I've worked on in my two years at Lockheed Martin:

- I have worked with particle systems techniques for solving non-linear filtering equations.
- I have worked in information theory, developing techniques for measuring the performance of data fusion algorithms (an example of a data fusion algorithm is an air traffic control system with a wide variety of distributed sensors working together to present a single cohesive picture of the airspace. Thus, the question becomes how do you measure the performance of an algorithm whose output is a finite set?).
- I have worked with fuzzy logic, random set theory and robust statistics to develop (then test) Automatic Target Recognition (ATR) algorithms for Synthetic Aperture Radar (SAR).
- I have developed a new method for rapidly approximating a permanent (a function of a matrix similar to a determinant, except it is an NP-Complete calculation instead of O(N^3)). This work can be summarized as focusing on the algorithmic issues of taking advanced mathematical techniques, and making them work on real, or synthetic data.

How has my Math Ph.D. prepared me for the work I do now? My math Ph.D. really accomplished two things. First, it gave me a set of credentials to get in the door; having a Ph.D. is strong evidence to any knowledgeable (and not all are knowledgeable!) employer, that I have the tenacity to wrestle with a problem until it gets solved, and that I can work on hard problems. In addition, my area of specialty, probability theory, is a crucial component in much of the work performed in our group at Lockheed Martin. Secondly, solving my thesis problems educated me in the language of mathematics research. When I came to the University of MN, I had none of the knowledge or skill needed to understand research articles. I in essence learned how to think mathematically. Again a vital skill for my current employer.

But what about the skills that didn't come with the Ph.D.? It takes more than a piece of paper to get (and keep) a job in industry. Probably the most crucial skill in industry is communication. In industry I have almost always worked with a group on a project. Thus communicating within the group and "playing nice with others" are vital to success. In addition, since our work always has a customer (who often doesn't understand, nor cares about the details) we need to communicate to them in words they understand our accomplishments, and show them the value we add to the project. Communication skills are important to any job, it just cannot be emphasized enough.

So, in closing I decided to get a Math Ph.D. and work in industry to have a fun job, do research, and make some good money. Getting my Ph.D. aided me in obtaining this goal by getting my foot in the door, while my work ethic, communication skills, and the knowledge that I have allowed me to keep it. I hope you found this article interesting. I sure enjoyed writing it.

Editor's comment: Whereas the academic job market was bad in the early 1990's, as John Hoffman points out, it is much better now due to increased college enrollments and many faculty retirements. Salaries are also much improved, particularly at the entry level. At present mathematics provides very attractive career opportunities in both academia and industry.

## Mathematics Library

The Mathematics Library's collection continues to grow, with over 42,000 book and journal volumes and ever-increasing access to electronic resources. Price inflation for mathematics and science materials, however, continues to outstrip the modest fund increases provided by the University. As a result, 16 subscriptions had to be cancelled from among the 300 journals received; they were carefully selected, based on faculty comments and evaluative data, to minimize the adverse effect on teaching and research. One strategy was to cut a journal costing several thousand dollars in exchange for new subscriptions to more cost-effective journals in the same area. It is hoped that such action, in combination with researchers' and editorial boards' efforts, will moderate the unsustainable publishing practices that contribute to the problem.

The Librarian and the Mathematics Library Faculty Committee encourage the evolution of scholarly communication, while also advocating for an improved funding system. We continue to refine the balance of resources provided by the Mathematics Library, to use our resources most effectively so that students' and researchers needs for books as well as networked information and services are met.

*Kristine Fowler, Mathematics Librarian*

## AWM Mentor Network

In spring 2001 the AWM (Association for Women in Mathematics) Mentor Network, which has its "headquarters" in the School of Mathematics, officially got off the ground. The goal of the Network is to match mentors with girls and women who are interested in mathematics and/or are pursuing careers in mathematics. The network is intended to link mentors (both men and women) with a variety of groups: recent Ph.D.'s, graduate students, undergraduate students, high school and grade school students, and teachers. Matching is based on common interests in careers in academia or industry, math education, balance of career and family, or general mathematical interests. Contact is usually through email, phone, or regular mail. The Network has been steadily growing, thanks to the financial assistance and office support given by the AWM, the School of Mathematics, the IMA, the Office of University Women, and ITCEP. At the time that this article is written, there have been approximately 120 requests for mentors, and about 100 mentor volunteers, nearly all of which have been assigned to a "mentor pair." The network has been advertised through several means Ð some targeted advertising through university contacts, advisor referrals, notices on the AWM web site and in the AWM newsletter, and a very common way, word of mouth.

Mentor requests have been received from high school students through recent Ph.D.'s, with the bulk of the requests coming from undergraduate and graduate students. Some of the requests have come from other countries, including Canada, Romania, Argentina, South Africa, India, and Australia. Some requests are very specific, looking for a mentor on a particular topic, such as "How do I get my thesis in shape for publication?", or "What types of non-academic careers are available to a person with a statistics degree?". Others are more general, such as "I love doing math" and "What should I expect as I start a tenure track job?". Recently weÕve been increasing our contact with high school groups, so the range of requests has continued to grow. Because of the broad range of requests, we are always looking for additional mentor volunteers, both men and women!

The different mentoring styles have also "shaped" the network. In at least one case, two mentors have combined their pairs to form a joint mentor group. Some mentors with more than one mentee communicate with them both jointly and separately. We're always open for suggestions and comments for improving the network. As we increase the publicity for the network, we expect it to grow and develop.

A recent expansion has been a cooperative effort with the Institute for Mathematics and its Applications (IMA) to set up research topic-related mentoring and discussion forums at the IMA Research Communities web site: www.ima.umn.edu/research/AWM.html.

*Rachel Kuske, Professor and Associate Director of MCIM*

## News from the Institute for Mathematics & its Applications

The Institute for Mathematics and its Applications has a new director as of Aug. 27. Douglas N. Arnold, a Distinguished Professor of Mathematics at Pennsylvania State University, replaced Willard Miller, who returned to the mathematics faculty. In addition, Doug's wife, Carme Calderer, also a professor of mathematics at Penn State, joined the Minnesota mathematics faculty. Doug and Carme are very familiar with the IMA program: Doug, a numerical analyst was in residence at the IMA pursuing research in scientific computation (1986-1987) and materials science (1995-1996). He also recently served on the IMA Board of Governors. Carme, whose research interests include mathematical studies of liquid crystals, was a postdoctoral researcher (1984-1985) and a visiting researcher in 1986-1987 and 1995-1996 at the IMA.

In the new administrative structure of the IMA, Doug Arnold is the director, Fadil Santosa the deputy director and Robert Gulliver the associate director.

During his four-year term as director, Willard together with associate director Fadil Santosa led the IMA through a successful recompetition for funding of math institutes by NSF. They also established the industry-related HOT TOPICS program and accelerated the Internet distribution of IMA programming.

The IMA's mission is to demonstrate the power of sophisticated mathematics in solving problems that arise in other sciences, engineering and industry. The IMA is host to more than 100 long-term postdocs, visiting scholars and other experts each year, with nearly 1,000 more attending a dozen weeklong workshops.

Through a unique industrial postdoctorate and seminar program, led by Deputy Director Fadil Santosa, the IMA helps students and other mathematical researchers learn about research opportunities in industry and allows corporate participants to benefit from the mathematicians' expertise. For details about this program see www.ima.umn.edu/ industrial/index.html .

Doug's vision for the IMA includes an increased emphasis on computation: "The digitalization of all areas of science and technology means that there is a place for computation in all programs of the IMA" (interview with Allyn Jackson of the AMS Notices, August 2001). He is very interested in continuing to develop the institute's role as a training center where people can learn about new areas of research in which the mathematical sciences can make significant contributions. He will continue the HOT TOPICS workshops and expand them to include problems coming from other sciences. We in the School of Mathematics are especially pleased to hear that Doug plans to continue the close relationship that exists between the School and the IMA.

During the 2000-2001 academic year IMA researchers focused on "Mathematics in Multimedia," including vision, speech and language modeling, digital libraries, computer graphics and geometric design. There were also industry-related "Hot Topics" Workshops on "Mathematics of the Internet: E-Auction and Markets," December 3-5, 2000, "Analysis and Modeling of Industrial Jetting Processes," January 10 - 13, 2001, "Mathematical Opportunities in Large-Scale Network Dynamics," August 6-7, 2001 and "Wireless Networks," August 8-10, 2001. The summer program was "Geometric Methods in Inverse Problems and PDE Control," July 16-27, 2001. In addition there were two special workshops intended to encourage greater participation of women and minorities in mathematics research: "Connecting Women in Mathematical Sciences to Industry," September 8-10, 2000 and "Minorities and Applied Mathematics - Connections to Industry and Government Laboratories," May 4-6, 2001. There is extensive documentation of these programs on the IMA web site www.ima.umn.edu, including copies of transparencies, power point presentations and in some cases, streaming audio and video.

The September 2001-June 2002 annual program is "Mathematics in the Geosciences." During the Fall Quarter (September-December, 2001) the focus is on Dynamical Systems and Ergodic Theory, followed by Multiscale Phenomena and Renormalization during the Winter Quarter (January-March, 2002), and Inverse Problems and the Quantification of Uncertainty during the Spring Quarter (April-June, 2002). For further details see: www.ima.umn.edu/geoscience/index.html.

IMA UPDATE, a periodic notice concerning the activities of the Institute for Mathematics and its Applications, is available as an HTML/email document. The UPDATE contains hyperlinks to information about past, present and future IMA programs, as well as links to materials presented at IMA workshops: video, audio, movies, slides, etc. If you would like to be added to the mailing list, please send a message to .

Doug Dokken, who earned his Ph.D. from our department in 1985 under the direction of Professor Robert Ellis, was kind enough to give us a report about his work at the IMA during the current academic year, 2001-2002. His lively report gives a good picture of this year's IMA activities and their relevance to one very interesting area of applications. We note that Doug is the vice-president of the Twin Cities Chapter of the American Meteorological Society.

#### Professor Doug Dokken Visits the IMA

I am a Professor of Mathematics at the University of St Thomas, and I am a visitor at the IMA during the 2001-2002 academic year. My primary areas of interest are topological dynamics and ergodic theory. During the past several years I have been involved with meteorology-related projects supported by UST's Center for Applied Mathematics: the building of a vortex simulator, and the study of vortex breakdown using James Serrin's swirling vortex model. My interest in meteorology began when I witnessed an F5 tornadic thunderstorm demolish parts of Fargo, North Dakota on June 20, 1957. The storm was studied in detail by Ted Fujita in his landmark paper, "A Detailed Analysis of the Fargo Tornadoes of June 20, 1957." I am currently working with Rich Naistadt and Bill Togstad of the National Weather Service office in Chanhassen and Kurt Scholz of St. Thomas on the modeling of the Granite Falls tornadic storm of July 25, 2000. I am also involved in the co-advising the building of a Ward chamber by the St. Thomas Physics Department.

The current year at the IMA is a great opportunity to see how mathematics is applied in the geosciences and learn successful techniques that could also be applied to the study of severe local storms. The Fall quarter's emphasis on dynamical systems and ergodic theory has seen the use of celestial mechanics, bifurcation theory, stochastic differential equations, and singular spectrum analysis of time series in the study of climate dynamics. Many other exciting topics have also been covered, for example, the study of earthquakes and their prediction. I am looking forward to participating in workshops during the next two quarters, in particular, learning about data assimilation techniques, slow manifolds, and applications of recently developed numerical techniques in the geosciences.

*Professor Douglas Dokken*

## Andrew Odlyzko: Director of the new Digital Technology Center (DTC)

The University of Minnesota has recently hired Andrew Odlyzko as the first director of the new Digital Technology Center (DTC); Assistant Vice President for Research; ADC Telecommunications Chair Professor; and Professor of Mathematics. He is the second mathematician to be hired as part of this initiative. Professor Hans Othmer, a distinguished expert in computational biology, who joined the math faculty two years ago, is also a member of the center. The Digital Technology Center which, effective winter 2002, will be located in a newly remodeled Walter Library building, is the cornerstone of the university's digital technology initiative. The center has three main objectives: to advance the university as a national leader in digital and information technology; to enable the university to produce graduates able to meet the workforce needs of high-technology industries; and to build alliances between the university, government, other educational institutions and industry. In addition, it will house the Minnesota Supercomputing Institute, the Laboratory for Computational Science and Engineering, and the Telecommunications and Advanced Networking Laboratory. The research foci of the center include telecommunications and advanced networking, software storage and Internet technologies, data storage and visualization, electronic commerce and digital publishing, bioinformatics and computational biology.

Odlyzko comes from AT&T Labs, where he was head of the mathematics and cryptography research department since 1996 and held other high level positions there for nearly two decades. A world-renowned expert on computational complexity, cryptography and coding theory, he has been quoted in the Economist, the Wall Street Journal, Scientific American, U.S. News and World Report, Fortune and Business Week, among others. "Andrew Odlyzko is not only a brilliant, internationally renowned mathematician, he also has the vision and interest in the broader aspects of digital technology, such as e-commerce, software engineering, telecommunications, computational science and distributed systems, that will enable him to lead the Digital Technology Center to world prominence," said H. Ted Davis, Dean of the Institute of Technology and chair of the search committee for the director of the Digital Technology Center. "He is a tremendous intellectual addition to the University of Minnesota." (See also the section "Welcoming the Incoming Faculty" at the beginning of this Newsletter.)

## News From the Institute of Technology Center for Educational Programs (ITCEP)

This year, the University of Minnesota Talented Youth Mathematics Program (UMTYMP) has an enrollment of 507 students from grades 6-12 (Twin Cities, 398; Outreach, 109), 197 of which are calculus students. In the Twin Cities thirty students are in Calculus III and several others are studying advanced math or doing IT honors coursework. As always, the level of cooperation between ITCEP and the School of Mathematics continues to be high - we note that UMTYMP, the ITCEPÕs flagship program, was started by ITCEP's Director, Professor Harvey Keynes, as a program within the School of Mathematics, twenty one years ago. As usual, some of the School of Mathematics faculty teach the more advanced UMTYMP courses. We note especially Professor Markus Keel, who joined the School this September and who himself graduated from the UMTYMP program in its early years. Professor Robert Hesse, a School of Mathematics Ph.D. graduate, is teaching UMTYMP calculus at St. John's University, St. Cloud.

Professor Keynes continues to be the advisor for the four-year-old Master's Degree Program in Mathematics, with emphasis in Mathematics Education. While the majority of the program's ten graduates have found rewarding positions as high school teachers, one of them, John Hall, decided to continue on in the Ph.D. program, specializing in combinatorics. This semester, he is a TA for Calculus for Biology majors and a workshop leader for UMTYMP Calculus III. Two current students in the program, Melissa Everson and Justin Jacobs, will graduate in 2002. They are TAs for the School's single-variable calculus courses, and for UTMYMP Calculus I and II, respectively. ITCEP, together with the new Mathematics Education faculty, Professor Jeremy Kahn, continues working with pre-service and in-service teacher training in mathematics. Carraig Hegi, another Master's program graduate, gave a presentation to in-service teachers on "Issues involved with teaching mathematics concepts to diverse groups of students" as part of his professional development work with ITCEP this summer.

Note: The Newsletter editors are grateful to Alexandra Janosek, ITCEP Communication and Public Relations Coordinator, for providing the information on which this note is based.

## Contact Us

School of Mathematics

University of Minnesota

127 Vincent Hall

206 Church Street S.E.

Minneapolis, MN 55455

Ph: 612-625-5591, Fax: 612- 626-2017

dept@math.umn.edu

www.math.umn.edu

Department Head: Naresh Jain, Ph: (612) 625-5591, jain@math.umn.edu

Undergraduate Studies: Lawrence Gray, Ph: (612) 625-4848, undergradinfo@math.umn.edu

Graduate Studies: Paul Garrett, Ph: (612) 625-1306, gradprog@math.umn.edu

ASSOCIATED PROGRAMS

MINNESOTA CENTER FOR INDUSTRIAL MATHEMATICS

Avner Friedman, Director (on leave)

Fadil Santosa, Acting Director

Rachel Kuske, Associate Director

537 Vincent Hall, 206 Church St. SE

Minneapolis, MN 55455-0463

Ph: 612-625-3377, Fax: 612-624-2333

mcim@math.umn.edu

www.math.umn.edu/mcim

IT CENTER FOR ECUCATIONAL PROGRAMS (ITCEP)

Harvey Keynes, Director

4 Vincent Hall, 206 Church St. SE

Ph: 612-625-2861, Fax: 612-626-2017

www.math.umn.edu/itcep

INSTITUTE FOR MATHEMATICS & ITS APPLICATIONS (IMA)

Douglas Arnold, Director

Fadil Santosa, Deputy Director

Robert Gulliver, Associate Director

400 Lind Hall, 207 Church St. SE

Minneapolis, MN 55455a

www.ima.umn.edu

Ftp: ftp.ima.uma.edu