# School of Mathematics Newsletter - Volume 7 - 2001

## In This Issue...

## School of Math Welcomes Incoming Faculty and Postdocs

It is a pleasure to welcome the new members of the School of Mathematics - Professor Sergey G. Bobkov, and Assistant Professors Ionut Ciocan-Fontanine and Jackie Shen. We also welcome the new Dunham Jackson Assistant Professors Mark de Longueville, Luca Rondi, and Dominik M. Schoetzau, as well as visiting Assistant Professor Pavel Belik and Professor Sergey G. Bobkov, and Postdoctoral Associates Vittorio Cristini, Nikolaos Mantzaris and Steven D. Webb.

Professor Sergey G. Bobkov received his doctorate in 1988 from the University of St. Petersburg. Since then he has been on the faculty of Syktyvkar University where he attained the rank ofAssistant Professor Ionut Ciocan-Fontanine Professor in 1998. He has been a frequent research visitor to leading institutions in western Europe and the U.S. His research area is in isoperimetric problems in multidimensional spaces.

Assistant Professor Ionut Ciocan-Fontanine received his Ph.D. in 1996 from the University of Utah. He held a postdoctoral fellowship at the Mittag-Leffler Institute (1996-97), followed by a Visiting Assistant Professorship at Oklahoma State University (1997-98), and Ralph P. Boas Assistant Professorship at Northwestern University (1998-2000). His research area is algebraic geometry.

Assistant Professor Jackie Shen received his Ph.D. in 1998 from MIT. For the past two years he held a Computational and Applied Mathematics Assistant Professor Jackie Shen. Assistant Professorship at UCLA. His research area is applied mathematics.

Dunham Jackson Assistant Professor Mark de Longueville received his Ph.D. in 2000 from Berlin Technical University. His research area is combinatorics.

Dunham Jackson Assistant Professor Luca Rondi received his Ph.D. in 1999 from the International School for Advanced Studies in Trieste. He spent the 1999-2000 academic year as a postdoctoral researcher at Johannes Kepler University in Linz. His research area is applied mathematics.

Dunham Jackson Assistant Professor Dominik M. Schoetzau received his Ph.D. in 1999 from ETH Zurich and spent the past academic year as a postdoctoral researcher in our department. His research area is numerical analysis.

Assistant Professor Pavel Belik received his Ph.D. in 2000 from our department. His research area is numerical analysis.

Postdoctoral Associate Vittorio Cristini received his Ph.D. in chemical engineering from Yale University in 2000. His research area is microstructure and dynamics of multiphase fluids.

Postdoctoral Associate Nikolaos Mantzaris received his Ph.D. in chemical engineering from the University of Minnesota in 2000. His research area is mathematical biology.

Postdoctoral Associate Steven D. Webb received his Ph.D. from the Heriot-Watt University in 2000. His research area is mathematical modelling in biology and medicine.

## From the Department Head

We are going through a very challenging period of change. Professors John W. Eagon, Gebhard Fuhrken, Laurence Harper, Johannes Nitsche, Marian Pour-El and Edgar Reich retired last June after long years of distinguished service to the School and the profession. Professor Yasutaka Sibuya will retire at the end of this academic year. Professors Bennett Chow and Paul Edelman resigned their positions and moved to other schools. Other retirements are coming. The challenge we face is to bring in top quality mathematicians dedicated to teaching and research, to replace our losses and, whenever possible, to enhance the overall quality of the School. My colleagues recognize this challenge and they are working hard to meet it. I would like to take this opportunity to thank the many friends and well wishers of the School for giving us advice and good suggestions in these matters.

We can never forget that graduate and undergraduate teaching are major components of our profession. Our faculty have been putting extraordinary efforts into undergraduate, graduate and cross-disciplinarycurriculum development, mentoring of the graduate and undergraduate students, research and career training for graduate students, and as a result the improvements in these programs and services have been substantial and very noticeable.

We look forward to the recognition dinner in honor of Professor Sibuya on the occasion of his retirement and two forthcoming milestone conferences to celebrate the 60th birthday of Professor Krylov and 75th birthday of Professor Serrin. Such occasions remind us that we make our contributions as a community of scholars and researchers, within a continuing tradition of commitment to excellence.

## Promotions

*Professor Claudia Neuhauser* was promoted to the rank of Full Professor effective September 2000. Claudia's research area is probability theory and mathematical biology.

P*rofessor Rachel Kuske* was promoted to the rank of Associate Professor with tenure effective September 2000. Rachel's research area is applied mathematics.

*Professor Conan Leung* was promoted to the rank of Associate Professor with tenure effective September 2000. Conan's research area is differential geometry.

## Awards and Recognitions

*Professor Paul Garrett* was selected to receive the Purdue University School of Science Distinguished Alumnus Award for 2001. The award recognizes graduates who have achieved particular distinction in professional and related fields. Paul is currently Professor of Mathematics and Director of Graduate Studies.

*Professor Dihua Jiang* was awarded the McKnight Land-Grant Professorship for 2000-2002. These Professorships are awarded to tenure track faculty following a university-wide competition and provide substantial research support for a two year period. The award enabled Professor Jiang to spend the Fall Semester 2000 as a member at the Institute for Advanced Study at Princeton where he participated in the Special Year on Automorphic Forms. Professor Jiang's area is number theory.

*Professor Harvey Keynes* won the University of Minnesota President's Award for Outstanding Service in the areas of outreach and K-12 teacher preservice and inservice activities. Professor Keynes is the Director of the Institute of Technology Center for Educational Programs (ITCEP). This Center runs the nationally known University of Minnesota Talented Youth Mathematics Program(UMTYMP), and Professor Keynes has dedicated a good part of his academic life to the development of this program. He also actively participates in the School of Mathematics Math/Ed Masters' program for the training of future K-12 teachers as well as in many inservice programs and projects for K-12 mathematics teachers. He is often asked to serve on national committees for the improvement of K-12 education.

*Regents' Professor Emeritus Lawrence Markus* was elected to Honorary Fellowship of the Royal Society of Edinburgh. We congratulate Professor Markus on this great honor.

In recognition of his outstanding contributions to the area of non-linear partial differential equations, *Professor Vladimir Sverak* has been named a Distinguished McKnight University Professor by the University of Minnesota. According to the Graduate School, which initiated the program of these professorships, the award is "to honor and reward our most distinguished and highest achieving mid-career faculty who have recently attained full professor status - especially those who have made signicant advances in their careers at the University, whose work and reputation are identified with the University of Minnesota, and whose work has brought great renown and prestige to Minnesota." The grant associated with the Professorship consists of $100,000 over five years to be used, in accordance with University policy, for research, scholarly, or artistic activities, and expended at the recipient's discretion.

*Professor Jiaping Wang* has been awarded the McKnight Land-Grant Professorship for 2001-2003. Professor Wang's research is in differential geometry.

*Professor David Cooke*, currently Professor of Mathematics at Hastings College, Nebraska, was one of the Mathematical Association of America Award Winners for Distinguished Teaching in the year 2000. He received his doctorate in 1989 under the supervision of Professor Peter Olver and is currently Professor of Mathematics at Hastings College, Nebraska.

## Academic Visitors

*CONTINUING PROFESSORS AND VISITING FACULTY**Assistant Professors:* Shaun Cooper (Massey University, New Zealand, combinatorics), Liliana Forzani (INTEC Guemes, Argentina, harmonic analysis), Douglas Hanes (Ph.D. University of Michigan, commutative algebra), Cynthia Kaus (Ph.D. Brandeis, education, applied mathematics), Vladimir Markovic (Ph.D. Belgrad University, complex analysis), David Nicholls (Ph.D. Brown University, fluid dynamics, numerical methods), Ilaria Perugia (University of Pavia, Italy, numerical analysis), Henri Schurz (Ph.D. Humboldt University, Berlin, stochastic analysis), Soogil Seo (Ph.D. UC Berkeley, number theory), Stephen Tanner (Ph.D. University of Washington, probability theory), and Linghai Zhang (Ph.D. Ohio State University, partial differential equations).

*Associate Professors:* Tatsuhiko Tabara (Golden Gate University, San Francisco, ordinary differential equations), Stephen Taylor (University of Auckland, New Zealand, partial differential equations and control theory), Grozdena Todorova (Bulgarian Academy of Sciences, ordinary differential equations, hyperbolic partial differential equations).

*Professors: *Borys Bazalyi (Institute of Applied Mathematics, Donetsk, Ukraine, fluid dynamics), Shouchuan Hu (Southwestern Missouri State University, nonlinear functional analysis, multivalued analysis), Elisabeth Logak (University of Cergy-Pontoise, France, nonlinear partial differential equations, bio mathematics)

*Postdoctoral Associates,* including IMA Postdoctoral Associates who participated in the teaching activities: Yalchin Efendiev (Ph.D. Caltech, numerical methods, scientific computation), Takumi Hawa (Ph.D. Rensselear Polytechnic Institute, theoretical and computational fluid dynamics), Yong Jung Kim (Ph.D. University of Wisconsin, applied mathematics, partial differential equations), Alexei Novikov (Ph.D. Stanford, partial differential equations and numerical methods), Moxun Tang (Ph.D. University of Alberta, differential equations, dynamical systems, mathematical biology), and Nianqing Wang (Ph.D. University of Michigan, mathematical biology).

*DISTINGUISHED ONE-MONTH ORDWAY VISITORS (2000-2001)*

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

Professors: Mariano Giaquinta (Scuola Normale Superiore, Pisa, calculus of variations, nonlinear partial differential equations), Nicholas Katz (Princeton, number theory, arithmetic algebraic geometry), John Mallet-Paret (Brown University, dynamical systems), Howard Masur (University of Illinois Chicago, geometry and dynamics), Michael Rapoport (University of Cologne, arithmetic algebraic geometry), James Sethian (UC Berkeley, applied mathematics, numerical analysis), and Neil Trudinger (Australian National University Canberra, analysis, partial differential equations).

*OTHER VISITORS* *Professors:* Santiago Betelu (University of Buenos Aires, fluid dynamics, nonlinear diffusions), Jeongwook Chang (Seoul National University, differential geometry), Roger Chen (National Cheng Kung University, Taiwan, geometric analysis), Tatsuo Itoh (Tokai University, Japan, partial differential equations), Yukio Kan-on (Ehime University, Japan, partial differential equations and applications), Hobum Kim (Yonsei University, S. Korea, differential geometry, foliations, dynamical systems), Yonghoi Koo (University of Connecticut, differential geometry, parabolic partial differential equations),Hyeong-Gi Lee (Ph.D. New York University, computational fluid dynamics), Boris Levitan (Minneapolis, functional analysis, differential equations), Robert Liptser (Tel-Aviv University, probability), and Thomas Schwartzbauer (Minneapolis, probability).

## Retirements and Resignations

Professors John Eagon, Gebhard Fuhrken, Laurence Harper, Johannes Nitsche, Marian Pour-El and Edgar Reich retired during 1999-2000. A dinner in their honor, attended by faculty and staff of the School of Mathematics and many friends, was held on April 12, 2000 at the campus Radisson Hotel. The Head of the School, Professor Naresh Jain, several colleagues and friends paid tribute to the honorees for their accomplishments and contributions to teaching, research and service to the University and the community. The faculty and staff of the School wish them many more productive and fruitful years. Short summaries highlighting their careers and accomplishments are contained in the next paragraphs.

*Professor Laurence Harper* received his Ph.D. in Algebra from the University of Chicago in 1959 and became a member of the Minnesota faculty that same year as an Assistant Professor. He was promoted to Associate Professor in 1984. His research was published in such prestigious journals as the Proceedings of the National Academy of Sciences and the Transactions of the American Mathematical Society. In later years he concentrated his efforts on teaching. He was a very conscientious teacher and was regarded highly by his sutdents.

*Professor Johannes Nitsche* did his graduate work at the University of Goettingen and received his Ph.D. from Leipzig University in 1951. He held several visiting positions, including one at Stanford University before he joined the Minnesota faculty in 1957 as an Associate Professor. He was promoted to Full Professor in 1960. Johannes has made outstanding contributions to the theory of minimal surfaces. He obtained an important uniqueness theorem for such surfaces. The proof uses what is now known as the Nitsche-Sasaki-Gauss-Bonnet inequality. Another of his notable results is a simple proof, published in the Annals of Mathematics, of a celebrated theorem of Bernstein. His monograph "Lectures on Minimal Surfaces" is an indispensable reference for researchers in this area. Professor Nitsche gave invited addresses at many conferences and symposia all over the world, often as a principal speaker, and served on the editorial borards of many leading journals. The prestigious awards he has won include the Humboldt Prize from the Alexander Humboldt Foundation and the Lester Ford Award from the Mathematical Association of America for outstanding expository writing. He was also the recipient of the George C. Taylor Service Award of the Institute of Technology Alumni Association for distinguished service.

Professor Nitsche played a major role in the department. He served as Head of the School from 1971 through 1978. He spent a lot of time reorganizing the office of the Head. The flawless filing system that he introduced has been working very efficiently. The following mathematicians were hired during his tenure as Head: Karel Prikry and Joel Roberts (1972), Robert Gulliver, Max Jodeit and Dennis White (1973), Morton Harris in 1974, Luis Caffarelli and David Frank in 1975, Lawrence Gray and Steven Sperber in 1977 and Dennis Hejhal in 1978.

Students found Johannes' teaching very inspiring and he always put his best effort into it. He will always be regarded as one of the finest teachers of the School.

*Professor Marian Pour-El* received her Ph.D. in Mathematical Logic from Harvard University in 1958. She was on the faculty of Penn State University from 1958 to 1964. There she was promoted to Associate Professor in 1962 and spent the years 1962-1964 at the Institute for Advanced Studies at Princeton. She joined the School in 1964 as an Associate Professor and was promoted to Full Professor in 1968. Her interests in research expanded into computability and functional analysis, and applications to physical theory.

Marian has been a leader in her field. She was invited to address many international symposia and conferences in Logic. She gave one-hour addresses at the American Mathematical Society meeting and meetings of Mathematical Association of America. A symposium was held in her honor in Kyoto, Japan, in April 1993.

Her service on American Math Society Committees, University Senate and its Committees and departmental committees has a very long record. In spite of all these time consuming commitments, which involved a considerable amount of travel, Marian played a unique and admirable role in mentoring female graduate students. Her impact on the School and the matheamtical community will always be remembered.

*Professor Edgar Reich* received his Ph.D. from UCLA in 1954. After visiting the Institute for Advanced Study at Princeton, he joined the department in the Institute of Technology in 1956. He became an associate Professor in 1958 and was promoted to Full Professor in 1961. Professor Reich's earlier research interests were in the area of numerical analysis and probability theory, but he has been a leading figure in complex analysis for a long time.

Edgar received many honors and awards. He gave a one-hour address at a meeting of the American Mathematical Society. He was the recipient of a Guggenheim Fellowship and was elected to the Finnish Academy of Sciences in 1980. He addressed many international symposia and conferences in complex analysis and has been a regular visitor to the Eidgenossische Technische Hochschule (ETH) in Zurich.

Edgar was Head of the School from 1969 to 1971. During his headship Professors Jay Goldman, Richard McGehee and David Sattinger were hired in the School.

Professor Reich has been known as an excellent lecturer. His contributions to research and teaching will be a model for many.

Please consult last year's newsletter for a description of the contributions of Professors Eagon and Fuhrken.

*Professor Yasuka Sibuya *has decided to retire at the end of this academic year after 38 years of service to the School of Mathematics. A dinner will be given in his honor on Thursday, April 10, 2001. Those interested in attending this important event may contact Monika Stumpf at (612) 625-5591,
, for further details.

*Professors Bennett Chow and Paul Edelman* have resigned their positions effective September 2000. Professor Chow, whose area is differential geometry, joined the Mathematics Department of the University of California in San Diego. Professor Edelman's area is combinatorics and he joined the Mathematics Department of Vanderbilt University in Nashville. We wish them both continued success.

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

A "Symposium on Partial Differential Equations" will be held under the auspices of the School of Mathematics and the IMA to celebrate the 75th birthday of Regents' Professor Emeritus James Serrin on November 8-11, 2001. The tentative list of invited speakers consists of Haim Brezis (University of Paris VI), Constantine M. Dafermos (Brown University), Emmanuele DiBenedetto (University of Genoa, Italy), Avner Friedman (University of Minnesota), Jack Hale (Georgia Institute of Technology), Olga Ladyzhenskaya (Steklov Institute, St. Petersburg), Howard Levine (Iowa State University), L.A. Peletier (Leiden University), Patrizia Pucci (University of Perugia, Italy), Paul Rabinowitz (University of Wisconsin, Madison), Hans Weinberger (University of Minnesota), William Ziemer (Indiana University) and Henghui Zou (Northwestern University).

The Organizing Committee consists of Antonio Ambrosetti (University of Trieste), Haim Brezis (University of Paris VI), Walter Littman (University o f Minnesota), Norman Meyers (University of Minnesota), and Patrizia Pucci (University of Perugia, Italy). For further information please contact Professor Patrizia Pucci (pucci@dipmat.unipg.it) or visit the school of Mathematics web page.

## Speaking Invitations & Other Notable Activities

*Regents' Professor Avner Friedman* was an invited plenary speaker at the International Conference on Nonlinear Parabolic Equations, Tel Aviv, Israel, June 2000, and participated in the program on "Free Boundary Problems in Industry" held at the Isaac Newton Institute in Cambridge, England, July 30 to August 5. He also served as a member of the organizing committee for the conference "Homogenization and Materials Science" held at the University of Akron, Ohio, September 15-17, 2000, as well as moderator for the panel discussion, "The Future of Homogenization", at this conference. Professor Friedman also gave an invited lecture entitled "Free Boundary Problems in Mathematical Biology" at the Conference on Singularities Arising in Nonlinear Problems in Kyoto, Japan, December 4-6, 2000, and accepted an invitation to serve on the Scientific Advisory Board of the Institute for Mathematical Sciences at the University of Singapore.

*Professor Paul Garrett *will be an invited speaker at the annual meeting of the Minnesota Mathematical Association of Two-Year Colleges and the Minnesota Council of Teachers of Mathematics to be held in April 2001 in Duluth. He will give presentations about his innovative courses on Cryptology and Coding Theory, and about the on-line calculus exercises he developed for our first-semester calculus, and which have now been in use for one-and-half years.

*Professor Dihua Jiang* was an invited participant and speaker at the Automorphic Forms Semester held at the Institut Henri Poincare, Paris, during May-June 2000. He will also be an invited speaker at a conference on automorphic forms and number theory to be held in March 2001 at Hebrew University, Jerusalem.

*Professor Willard Miller * has been appointed to the Organizing Committee for the 2001 Annual Meeting of the Society for Industrial and Applied Mathematics (SIAM), to be held in San Diego, July 9-13. Willard is organizing plenary talks and special minisymposia on networks, including wired networks (such as most of the internet) and wireless networks. These sessions will be coordinated with two workshops to be held in Minnesota at the IMA in early August 2001: "Mathematical Opportunities in Network Dynamics" and "Wireless Networks."

*Professor Peter Olver* is a member of the organizing committee for the Year on Multimedia taking place during the current academic year at the Institute for Mathematics and its Applications (IMA) (for more information on IMA activities see the IMA update near the end of this Newsletter). He was also a member of the organizing committee for Special Session on Integrable Systems, at the First Joint International Meeting of the AMS and the Hong Kong Mathematical Society, Hong Kong, December 13 - 17, 2000. He will be an invited speaker at the international conference "Differential Equations and Related Topics" dedicated to 100th anniversary of birthday of the prominent Russian mathematician I.G.Petrovskii (1901-1973). The conference will be held in Moscow, May 22-27, 2001.

*Professor Hans Othmer* is the principal organizer of a semester long program titled "From Individual to Collective Behaviour in Biological Systems". The program will take place at the Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K., September-December, 2001. Incorporating individual aspects of behaviour into macroscopic descriptions of population behaviour poses challenging mathematical problems, requiring methods from a wide range of areas. Four major biological areas to be studied are (1) Physiology, (2) Developmental Biology, (3) Stochastic Spatial Ecology, and (4) Theoretical Immunology. In addition to mathematicians, leading biologists will also take part in the program.

*Regents' Professor Emeritus James Serrin* was a keynote speaker at the Third World Congress of Nonlinear Analysts in Catania, July 22-28. In addition, he was an invited speaker at other meetings at Bologna, Perugia, Rome and Pisa. He also contributed a paper on Jean Leray's work on differential equations to a special volume of the Gazette des Mathématiciens of the Société Mathématique de France, dedicated to the life and work of Leray. In the forthcoming months he will give the Hubbard Invited Lecture at the University of North Texas; a keynote address at the conference on Dynamics of Continuous, Discrete and Impulsive Systems in London, Canada; and he is an invited speaker at seventieth birthday conferences for Donald Aronson and for J. Bryce McLeod; finally he is an invited speaker for EQUADIFF 2001 in Prague and for the conference on Quasilinear Elliptic and Parabolic Systems and Equations in Luminy (Marseilles).

## A Conference to Celebrate the 60th Birthday of Professor Nicolai Krylov

A conference on "Perspectives in Partial Differential Equations and Probability" will be held on Friday, Saturday and Sunday, May 25-27, 2001 to celebrate the 60th birthday of Ordway Professor Nicolai Krylov. As a Participating Institutions Conference, it is partially supported by the IMA, the NSF, and the School of Mathematics. The invited speakers are Luis Caffarelli (University of Texas, Austin), Eugene Dynkin (Cornell University), Wendell Fleming (Brown University), Rafail Khasminski (Wayne State University), Paul Malliavin (University of Paris VI), Anatoly Skorokhod (Michigan State University), Nina Uraltseva (St Petersburg State University) and S.R.S. Varadhan (Courant Institute). The Organizing Committee consists of John Baxter and Mikhail Safonov (chair) from the University of Minnesota, and Boris Rozovsky from the University of Southern California. For more information please contact safonov@math.umn.edu and visit the School's web page.

## A Conference to Celebrate the 70th Birthday of Professor Don Aronson

A conference, titled "Nonlinear Phenomena in Science", will be held at the Free University of Amsterdam, June 6-8, 2001 to honor Don Aronson on the occasion of his 70th birthday. Organizing Committee: C.J. van Duijn (Eindhoven University of Technology), J. Hulshof (Free University of Amsterdam), D.H. Terman (Ohio State University). Scientific committee: L.A. Caffarelli (University of Texas, A&M), E.J. Doedel (Concordia University, Montreal), L.A. Peletier (Leiden University) (Chair), J.L. Vazquez (Universidad Autonoma Madrid).

## Rivière-Fabes Symposium

The fourth annual Rivière-Fabes Symposium on Analysis and PDE will be held here on April 20 - 22, 2001. Professors Daniel Stroock (MIT) and Robert Fefferman (Chicago) will give two lectures each. The other main speakers are Professors P. Daskalopoulos (UC Irvine), Steve Hoffman (University of Missouri, Columbia, Marius Mitrea (University of Missouri, Columbia), and Terence Tao (UCLA). The lectures will be held Friday afternoon, Saturday, and Sunday morning. A dinner for the participants is scheduled for Saturday evening. The organizing committee consists of Professor C. Kenig (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 http://www.math.umn.edu/arb/RiviereFabes.html.

## Actuarial Program

The School of Mathematics achieved strong placement counts for 1998 (21) and 1999 (14-16). At this point in time we have 11 known placements for 2000. These include graduate students Wen-Hong Wang (Allianz Life, Minneapolis) and Glenn Almelor (Buck Consultants, Seacaucus, NJ). The current enrollment in Actuarial Mathematics is a strong 25, up from recent years.

Following a specially convened meeting of our Advisory Committee on October 5, we have formalized new program requirements in response to substantial changes in the curriculum of the Society of Actuaries. The most significant change for our students will be an increased exposure to Economics, where we have added Intermediate Micro (3101) and Financial Economics (4751) to the Introductory Macro and Micro (110X-110Y) which have always been required. The new courses can be used as the so-called "Technical Elective" which is one of the requirements for the Math major in IT. Actuarial students will be encouraged to take Math 5652 (Introduction to Stochastic Processes) in preference to Stat 5102 (standard topics such as hypothesis testing and estimation of parameters). Our actuarial consultants reviewed all our courses and concluded that 5711 (Optimization) should be recommended in fulfillment of our algebra requirement, and that 5075-76 (Options, Futures, and Derivatives) would be a valuable elective.

Steve Agard, Program Coordinator

Actuarial Program web site

## Research Experiences for Undergrads (REU)

In summer 2000 the School of Mathematics offered for the first time a Research Experiences for Undergraduates (REU) program. Seven faculty volunteered to mentor 16 undergraduate students from all around the U.S. The program was promoted nationally, in print, on our web pages, and by word of mouth. From the many applicants the participating faculty jointly chose the most promising applicants whose interests best meshed with our strengths. The students were in residence here for about 8 weeks. The summer 2000 program was the first year of our ongoing REU program intended to introduce undergraduates to genuine research environments and to put them in close contact with research mathematicians. Working in teams or individually, students carried out their own projects and wrote reports on their findings. We do hope to continue this program with NSF support. Details on how to apply for being accepted to the program for the Summer 2001 can be found on the department website.

Below are the project titles, the mentors and the student participants on each project:

*T*he Use of Symmetries in Euclidean and Non-Euclidean Mechanics.* Mentor: Professor Scot Adams. Students: Pritam Dalal, UC Berkeley, and Shawn Hermans, St. John's University.

**A Design for Magnetic Heads. * Mentor: Professor Avner Friedman. Student: Phil Mendelsohn, University of Minnesota, Twin Cities.

**Traffic Simulation.* Mentor: Professor Lawrence Gray. Students: Steve Formaneck, University of Minnesota, Morris and Joel Rice, Colorado College.

**Stochastic Simulation of Exotic Options*. Mentor: Professor Rachel Kuske. Student: Nick Stadtmiller, Northwestern.

**Randomness in Physics and Chemistry.* Mentor: Profes sor Rachel Kuske. Student:Laura Chasman, California Institute of Technology.

**Tree groups of shifted graphs.* Mentor: Professor Victor Reiner. Students:Paul Bendich, Grinnell College and Tristram Bogart, Oberlin College.

**One-parameter families of algebraic curves.* Mentors: Professors Victor Reiner and Joel Roberts. Student: Rory Mulvaney, University of Minnesota, Twin Cities.

**Cryptology, Coding, and Number Theory.* Mentor: Professor Paul Garrett, Students: Geoff Anderson, Harvard, Dan Biebighauser, Concordia College, Erin Casey, St. Benedict, Andrew Crabbe, Trinity University, Chris Davis, Stanford University, and Kaisa Taipale, California Institute of Technology.

Professor Victor Reiner wrote as follows about the two projects he mentored: "This past summer I mentored two projects, one jointly with Joel Roberts, titled 'One-parameter families of algebraic curves' involving a single U of M undergrad named Rory Mulvaney. Rory's goal was to assimilate some basic material from elementary algebraic geometry, and then create some graphics macros usable in MATLAB that do such things as plot implicitly defined curves in the real plane, compute multiple tangent lines to an algebraic curve at its singular points, and superimpose these on a plot of the curve, compute the equation for the envelope of a 1-parameter family of algebraic curves, and superimpose a plot of the envelope on the plot of the family."

"Rory did a wonderful job, and his software is being used in the labs associated with MATH 5385 Introduction to computaalgebraic geometry, which was taught by Joel Roberts this Fall."

"Another project, titled 'Tree groups of shifted graphs', involved two undergraduates: Paul Bendich from Grinnell College and Tristram Bogart from Oberlin College. Paul and Tristram read up on the background for what I was calling the "tree group" of a graph (network): a subtle and fairly mysterious isomorphism invariant of a graph, which is a finitely generated abelian group of order equal to the number of spanning trees in the graph. For a particularly nice class of graphs (threshold graphs), where we know a simple product formula for the number of trees, I had them perform experiments in Maple computing the structure of this tree group via a Smith normal form computation on the Laplacian matrix of the graph. They then formulated a conjecture as to what the structure for general shifted graphs should be, and proved some special cases. I'm hoping that some future REU students will resolve this conjecture!"

For more information on both of these projects, see the students' reports at the math REU web page: www.math.umn.edu/arb/reu/.

## School of Math Fall Picnic, September 2000

The School of Mathematics annual fall picnic was held at Hidden Falls Park on Saturday, September 22nd, 2000. Hidden Falls Park is in South St. Paul and features, fishing, boating and hiking trails. The students, staff and faculty who attended braved the early winter temperatures for the sake of free food and games, including volleyball, soccer, badminton and football.

## School of Math Holiday Party, December 2000

The School of Mathematics held its annual Holiday party in the main lounge of Vincent Hall on December 14, 2000. For the most part, the Holiday party was served as a potluck, with graduate students, staff and faculty bringing their favorite dishes and desserts (the salmon is always a hit!). Main topics of conversation: the presidential election, the brutally cold winter and, of course, mathematics.

## NCS-MAA Team Math Contest, November 11, 200

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. This year, there were 54 teams from 17 schools located in Minnesota, the Dakotas, Alberta, and Manitoba. The University of Minnesota (Twin Cities) sponsored five teams for the contest this year. The results are summarized below. The problems were scored at ten points for each, so that a perfect set of solutions gave a score of 100. The actual scores ranged from 12 to 99.

Top 10 teams: Rank; School; Team name; Score

1. University of Minnesota (TC); Gold; 99 Team members: Brian Jacobson, Derek Larson, Jon Moon

2. Carelton; 88

3. Macalester; 84

4. U. Manitoba; Geeks&Nerds; 81

5. Carleton; 75

6. Macalester; 72

7. University of Minnesota (TC); Kestrel; 69

Team members: Michel D. Sa, Timothy Lee

8. Carleton; 68

9. St. Olaf; 65

10. U. Manitoba; Crablegs; 62

Our additional teams:

21. University of Minnesota (TC); Raptor; 43

22. University of Minnesota (TC); Gopher; 41

35.5 University of Minnesota (TC); Maroon; 30

On behalf of the School of Mathematics, I would like to extend our congratulations to the team members who did so well. Thanks and appreciation go to all who helped make this a successful event: the team members, and Professors Warren S. Loud and Bert Fristedt.

Charles A. McCarthy

University of Minnesota contest coordinator.

## Graduate Program

In July and August we welcomed 37 new TAs, from all around the world. As usual, the international TAs arrived first, and had a special program conducted by the English as Second Language Department that helped orient them in the ambient language and culture. The ESL people also assess international TAs' communication skills (more than just English fluency itself) and make recommendations about their readiness to work in a classroom.

After the ESL orientation was completed, 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 a few videotaped practice sessions in which they practiced presenting material as a TA would. Several senior TAs (M. Boutin, M. Galbraith, T. Garrett, N. Reading, C. Rios, S. Seo, T. Wiandt, N. Wodarz) assisted, lending their insights and perspectives. As is traditional, some mildly farcical play-acting scripted and acted by the grad students made it all more memorable.

The Written Preliminary Ph.D. exams were given about the second week of 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 modest pay raise for completion of this requirement.

We are continuing to refine our special Master's degree with emphasis on Math Education, in addition to our Actuarial Master's and Applied/Industrial Master's degrees. In these and possibly other directions there are opportunities for us to find people interested in studying higher mathematics.

*Diane Trager*, our new graduate secretary, did an excellent job of organizing things for the School of Mathematics picnic. She's also learning the myriad details and undocumented conventions that play a role in running the graduate program. If a few things seem to slip by our office down here, please do be indulgent, and just remind us of what you need.

*Outstanding Thesis Prizes *After a great deal of discussion, the Graduate Studies Committee decided to award Outstanding Thesis prizes 1999-2000 to five alumni:

*Pavel Belik, Irina (Berchenko) Kogan, Salome Martinez, Irina Mitrea, and Yi Ouyang*. Though in the past we have never awarded so many prizes in one year, all these candidates' theses were exceptionally good. Congratulations to them all! The titles of the theses, as well as the names of the Ph.D. advisors are given below:

*Pavel Belik, 'Computational Methods for Martensitic Thin Films' (Advisor: Professor Mitch Luskin)

*Irina (Berchenko) Kogan, 'Inductive Approach to Cartan's Moving Frame Method with Applications to Classical Invanant Theory' (Advisor: Professor Peter Olver)

*Salome Martinez, 'Diffusion and Cross-Diffusion in the Multi-Species Lotka-Volterra Competitive System' (Advisor: Professor Wei-Ming Ni)

*Irina Mitrea, 'Spectral Properties of Elliptic Layer Potentials on Nonsmooth Domains' (Advisors: Professors Mikhail Safonov and Carlos Kenig (Chicago))

*Yi Ouyang, 'Group Cohomology of the Universal Ordinary Distribution and its Application' (Advisor: Professor Greg Anderson)

Paul Garrett, Professor of Mathematics

Director of Graduate Studies in Mathematics

Ph: (612) 625-1306

gradprog@math.umn.edu

http://www.math.umn.edu/grad/

## Minnesota Center for Industrial Mathematics

The Minnesota Center for Industrial Mathematics (MCIM), a graduate program within the School of Math, continues to provide industry training for its students in the form of industrial internships. In the summer of 2000, 8 mathematics graduate students performed internships at leading industry research laboratories. While some local companies such as 3M have accepted our students for several years now, there were also several new local companies working with Center students and staff for the first time. In addition, several companies from out-of-state participated in our internship program for the first time. Kimberly Clark in Wisconsin, IBM in New York, Agilent Technology in California and Ford Motor Co. in Michigan all supported MCIM interns in the summer of 2000. Moreover, four of the students are continuing the research they did during the summer into the academic year, collaborating with their industry mentors.

Sam Albert, working under Bernardo Cockburn, finished his Ph.D. in August, and is now working for Interactive Data, a company that provides valuation products. Jinzhu Yu graduated with an M.S. degree and is working for Minnesota Public Radio.

We have been actively recruiting and the program has grown to over 20 graduate students. Two of our students, Thomas Hoft and Paul Macklin, hold NSF Graduate Fellowships.

The Center now enjoys a well deserved reputation for the ability of its students and faculty to solve problems originating in industry. It receives inquiries from companies who are interested in finding students for internships and employment, as well as requests to provide research support on specific company projects. We are presently working with several companies on projects of different scales that are long-term in nature. The Center is directed by Avner Friedman, with Fadil Santosa as Associate Director.

For more information, including past internship projects, industry partnerships and program requirements, please see our website at www.math.umn.edu/mcim or contact us at mcim@math.umn.edu.

Fadil Santosa, Professor of Mathematics

Associate Director, MN Center for Industrial Math (MCIM)

mcim@math.umn.edu

## IMA Math Modeling Workshop

## INSTITUTE FOR MATHEMATICS & ITS APPLICATIONS

*IMA MATH MODELING WORKSHOP*

If you visited the fifth floor at the end of July, you might have noticed increased activity in rooms 502 and 570. These rooms were occupied by two of the six graduate student teams participating in the IMA Mathematical Modeling in Industry Workshop, held July 19-28 (Rachel Kuske and Fernando Reitich, organizers). During this bi-annual 10 day workshop, six industry mentors supervised projects teams of six students each. The purpose of the workshop was to expose students to the types of mathematical problems which arise in industry, thus providing an educational experience complementary to the usual academic program. The topics were Network Analysis (NSA), Speech Recognition (Lingustic Technologies), Computed Tomography (GE), RF Communication Circuits (Lucent), Surface Intersection Problem of Optimal Design (Boeing), Dynamics of Microactuators (Kodak). The student teams developed models and algorithms for analyzing the problems which had been presented by the industry mentors on the first day of the workshop. The groups used mathematical techniques from a wide range of areas, including numerical linear algebra, optimization, combinatorics, probability, statistics, differential equations, Fourier analysis, and geometry. The students worked intensely for the whole workshop, causing one mentor to comment, "I can't figure out when they're eating and sleeping." They did take some time out for a picnic on the River Flats, an impropmtu soccer game, and a look around downtown Minneapolis. Two of the mentors, being puzzle enthusiasts, entertained the participants with some mind-twisters. By the end of the workshop, everyone appeared to be exhausted (even one of the mentors pulled an "all-nighter" on the last day) but pleased with their results. Each team gave a presentation of their results, with several of the groups providing valuable new insight into the industry problems. The final reports and presentations are available from the IMA web page.

Rachel Kuske

Associate Professor of Mathematics

*IMA UPDATE*

The IMA annual program for the academic year 2000-2001, "Mathematics in Multimedia", is divided into three components: "Vision, Speech and Language" (September-December, 2000), "Digital Libraries" (January-March, 2001), and "Geometric Design and Computer Graphics" (April-June, 2001). Professor Peter Olver of the School of Mathematics is one of the members of the organizing committee. A large variety of mathematical tools and theories are relevant to multimedia, and thus the program is exposing mathematicians to a new range of challenging and timely problems and applications, and, hopefully, helping to lay foundations for a genuinely mathematical discipline that will become known as "multimedia".

The 2001 Summer Program (July 16-27, 2001) is "Geometric Methods in Inverse Problems and PDE Control". Next year's program will be "Mathematics in Geosciences". A preparatory seminar is being run during the current academic year; Professor George Sell of the School of Mathematics is the organizer. Details about all of the IMA programs can be found on the IMA website: www.ima.umn.edu.

*David C. Dobson* (a 1990-92 IMA Industrial Postdoc) received the Felix Klein Prize at the 3rd (2000) European Congress of Mathematics in Barcelona. The Felix Klein prize "is awarded to a young scientist or a small group of scientists for using sophisticated methods to give an outstanding solution, which meets with the complete satisfaction of industry, to a concrete and difficult industrial problem." The program award states "David C. Dobson started his work on the diffraction of electromagnetic waves from periodic structures, when he was a postdoc at the famous Institute of Mathematics and Its Applications of Professor Avner Friedman. The Honeywell Technology Center had posed the problem to model and analyze the diffraction and to develop appropriate numerical algorithms. In a next step an optimal shape design problem for phase lenses was solved. The fact, that he used a "Fraunhofer approximation" was not (!) the reason to give him a prize endowed by the Fraunhofer Institute for Mathematics, what convinced the committee, that he should be the first prize winner, was, that he used rigorous and sound mathematical methods in a quite tricky way for the problem, which Honeywell states to be of very high industrial importance."

## Contact Us

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

University of Minnesota Graduate Studies: Paul Garrett; 612-625-1306, gradprog@math.umn.edu

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

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

Email:

Web Page: http://www.math.umn.edu

ASSOCIATED PROGRAMS

MINNESOTA CENTER FOR INDUSTRIAL MATHEMATICS

Avner Friedman, Director

Fadil Santosa, Assoc. Director

537 Vincent Hall, 206 Church St. SE

Minneapolis, MN 55455-0463

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

Email:

http://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

Email:

http://www.math.umn.edu/itcep

INSTITUTE FOR MATHEMATICS & ITS APPLICATIONS (IMA)

Willard Miller, Director

Fadil Santosa, Assoc. Dir. for Industrial Programs

Frederic Dulles, Assoc. Program Director

400 Lind Hall, 207 Church St. SE

Minneapolis, MN 55455a

http://www.ima.umn.edu

Ftp: ftp.ima.uma.edu