# School of Mathematics Newsletter - Volume 6 - 1999

## In This Issue...

## From the Department Head

The past academic year 1998-99 was one of challenge, change and renewal—more so than some of the past years. This was the last year under the quarter system. It was a major undertaking to prepare for the semester system start-ing with 1999-2000. The School faculty saw this as an opportunity to revise and reorganize the graduate and un-dergraduate cur-ricula and took full advantage of it. Our con-tinuing efforts toward improv-ing undergraduate education in mathematics culminated in the expansion of our reformed calculus (Calculus Initiative) program to cover all students (about 680) in the Institute of Technology. A new calculus course for biological sciences was offered for the first time to some eighty students with excellent results. Several innovative courses for juniors and seniors such as "Dynamical Systems and Chaos" and "Cryptology and Number Theory" are flourishing. Our new curriculum for elementary school teachers has been attract-ing larger numbers of students. Among some remarkable happenings, I would like to single out two items. Our applied mathematics program was ranked fourth in the latest U.S. News and World Report survey of academic programs nationwide—one place higher than last year. Only programs at MIT, Princeton and New York Uni-versity are ranked ahead of us, and it will be a real challenge

Our applied mathematics program was ranked fourth in the latest...survey of aca-demic programs nationwide.

in the years ahead to keep and improve that ranking above top programs such as Berkeley, Stanford and Caltech. Our strength in applied mathematics undoubtedly played a sig-nificant role in the successful recompetition for the Institute for Mathematics and Its Applications (IMA), the second item I wished to mention. The IMA was established in 1982 with support from the National Science Foundation and has now been renewed for another five years until 2005. This insti-tute has established an enviable track record for leadership in innovative research in mathematics related to science, engineering and industry under the successive direction of our faculty members, Professor Hans Weinberger (1982-87), Professor Avner Friedman (1987-1997) and Professor Willard Miller, Jr. (1997- ). Another focus of our activity is the Minnesota Center for Industrial Mathematics, which the School established in 1994 with Professor Avner Friedman as Director and Professor Fadil Santosa as Associate Director. In addition to its other research and teaching programs, the center matches Master's and Ph.D. students with industrial internships in our indus-trial program. This year three students received their Ph.D.'s under the program and found excellent positions.

It is also a matter of great satisfaction for us that even in a tight job market our Ph.D.'s and postdocs in fields such as automorphic forms, commutative algebra, algebraic geom-etry, partial differential equations, differential geometry, numerical analysis, mathematical physics and probability have continued to find excellent academic positions. Thanks to a senior position acquired through the newly es-tablished Digital Technology Center, we were able to attract Professor Hans Othmer, a world-renowned mathematical biologist, to join our faculty. The University has made a major commitment to improving its programs in the bio-logical sciences and Professor Othmer's addition to the School gives us a major presence in the area of mathemati-cal biology. We expect a significant increase in interaction between the School of Mathematics faculty, some medical school faculty and other faculty from biological sciences, in terms of course offerings, joint seminars and research. Other new hires this year were Assistant Professor Igor Rodniansky (currently on leave at Princeton) in analysis and Assistant Professor Jiaping Wang in differential geometry. I would like to welcome them all on behalf of the School. As always, I feel surrounded by people who are doing work which is both exciting and useful, and this is a very good feeling. I hope the rest of the items in this newsletter convey both these qualities.

-Naresh C. Jain, Head

## Incoming Faculty and New Postdoctoral Appointees

We welcome the new members of the School of Mathemat-ics—Professor Hans G. Othmer, and Assistant Professors Igor Rodnianski and Jiaping Wang. We also welcome the new postdoctoral appointees Assistant Professors Douglas A. Hanes, Guido Kanschat, Henri U. Schurz, Soogil Seo, Stephen B. Tanner, and Linghai Zhang, and Postdoctoral Associates Kevin J. Painter and Nianquing Wang.

Professor Hans G. Othmer received his Ph.D. in Chemical Engineering from the University of Minnesota in 1969. He worked in industry until 1973, at which time he joined the Mathematics Department of Rutgers University. Since 1979 he has been Professor of Mathematics at the Univer-sity of Utah and has served as Director of the Utah Supercomputing Institute. Professor Othmer is one of the major leaders and innovators in the field of mathematical biology. He has made major contributions to the following areas of research: chemical oscillators, dynamics of bio-chemical networks within biological cells, pattern forma-tion in reaction-diffusion systems, modeling the life cycle of Dictyostelium discoideum, calcium dynamics, and elec-trophysiology of the heart.

Assistant Professor Igor Rodnianski received his Ph.D. in 1999 from the University of Kansas, Manhattan. He is currently on leave at Princeton University. His research ar-eas are partial diffential equations, geometric analysis and calculus of variations.

Assistant Professor Jiaping Wang received his Ph.D. from the University of California, Irvine, in 1994. His previous positions include Szegii Assistant Professorship at Stanford University, 1994-96; AMS Centennial Research Fellowship, visiting MIT, 1996-97; and H.C. Wang Assistant Professor-ship at Cornell University, 1997-99. His research areas are geometric analysis and partial differential equations.

Assistant Professor Douglas A. Hanes received his Ph.D. from the University of Michigan, Ann Arbor, in 1999. His research area is commutative algebra.

Assistant Professors Guido Kanschat received his Ph.D. in 1996 from the University of Heidelberg, where he has been working since. His research area is numerical analysis.

Postdoctoral Associate Kevin J. Painter received his Ph.D. from Oxford University in 1998. His research area is mathematical biology.

Assistant Professor Henri U. Schurz received his Ph.D. from Humboldt University, Berlin, in 1997 and taught the past two years at La Universidad de Los Andes, Bogota, Co-lombia. His research areas are stochastic analysis and sto-chastic differential equations.

Assistant Professor Soogil Seo received his Ph.D. from University of California, Berkeley, in 1999. His research areas are number theory and arithmetic algebraic geometry.

Assistant Professor Stephen B. Tanner received his Ph.D. from University of Washington, Seattle in 1999. His research area is probability theory.

Postdoctoral Associate Nianquing Wang received his Ph.D. from University of Michigan, Arm Arbor, in 1999. His research area is mathematical biology.

Assistant Professor Linghai Zhang received his Ph.D. from Ohio State University, Columbus, in 1999. His research area is partial differential equations.

## Promotions

Professor Bennett Chow was promoted to the rank of Full Professor effective September 1999. Ben's area is differential geometry and nonlinear partial differential equa-tions, especially geometric evolution equations.

Professor John Lowengrub was promoted to the rank of Full Professor effective September 1999. John's area is numerical analysis and computational mathematics, especially applications to fluid dynamics and materials science. He is spending the 1999-2000 academic year visiting the University of North Carolina, Chapel Hill.

## Visitors

Continuing Postdocs and Visiting Faculty Assistant Professors: •Santiago Betelu (University of Buenos Aires, fluid dynamics, nonlinear diffusions), *Cynthia Kaus (Ph.D. Brandeis, education, applied math-ematics), *Matthew Killough (Ph.D. New York University, scientific computing, materials science), .Hyeong-Gi Lee (Ph.D. New York University, computational fluid dynamics), •Vladimir Markovic (Ph.D. Belgrad Univer-sity, complex analysis),..David Nicholls (Ph.D. Brown Uni-versity, fluid dynamics, numerical methods), and *Moxun Tang (Ph.D. University of Alberta, differential equations). Associate Professors: *Jaeduck Jong (Hankuk University, partial differential equations), and *Grozdena Todorova (Bulgarian Academy of Sciences, ordinary differential equations, hyperbolic partial differential equations). Professors: *Lawrence Breen (University of Paris 13, al-gebraic geometry), *Blaise Morton (Honeywell, MCIM), *Hal Smith (Arizona State University, Tempe, dynamical systems and mathematical biology), and .Songmu Zheng (Fudan University, nonlinear partial differential equations and applications).

### Distinguished Ordway Visitors

The Ordway Visitors Program of the School brings highly distinguished mathematicians to Minneapolis for one month, or longer, to lecture and interact with faculty and students. The Samuel G. Ordway Endowment was established through the generosity of Katharine Ordway in memory of her husband.

The Ordway visitors during the 1998-1999 academic year were Professors *Michel Broue (University of Paris 7, group representations), *Albrecht Dold (University of Heidelberg, algebraic topology), *Fang-Hua Lin (Courant Institute of Mathematical Sciences, partial differential equations), •Philip Rosenau (Tel Aviv University, partial differential equations), .Lee Segel (Weizmann Institute, mathematical biology), *Michael Vogelius (Rutgers, applied mathematics), and .Thomas Zink (University of Bielefeld, algebraic geometry). These visitors are outstanding research-ers in their fields and made a very valuable contribution to the creative environment of the School. Each visitor gave several public lectures while visiting, usually in the form of a colloquium lecture and several seminars. The visitors exchanged ideas with faculty and graduate students, and a num-ber of research collaborations took place both with our own faculty and with members of other departments in cross-disciplinary research. In addition, Professor Segel was one of the organizers of the IMA 1998 Fall program, entitled Theoretical Problems in Developmental Biology and Immunology. The 1999-2000 academic year visitors will be Professors *Lawrence Breen (University of Paris 13, algebraic geometry), *Haim Brezis (University Pierre et Marie Curie, Paris, partial differential equations), .Carlos Kenig (University of Chicago, harmonic analysis), *Rafael Khasminskii (Wayne State University, probability), *David Levermore (University of Arizona, partial differ-ential equations), *Stefan Muller (Max Planck Institute, Leipzig, partial differential equations, calculus of variations), and .William Symes (Rice University, inverse problems).

### Other Visitors Professors

Jeongwook Chang (Seoul National University, differential geometry), Kazuhiro Ishige (Nagoya Univer-sity, partial differential equations, nonlinear analysis), Jinho Lee (Sookmyung Women's University, Seoul, partial differ-ential equations), Boris Levitan (Minneapolis, functional analysis, differential equations), Debra Lewis (University of California-Santa Cruz, mathematical physics), Ilaria Perugia (University of Pavia, numerical analysis), Enrique Reyes (McGill University, Montreal, mathematical physics), Dominik Schoetzau (ETH-Zikich, numerical analysis), and Mingxin Wang (Southeast University, Nanjing, par-tial differential equations).

## Retirements, Resignations

Professor John A. Eagon will retire at the end of the Spring Semester 2000, after 33 years of service. Jack's research area is commutative algebra, especially free resolutions. He received his doctorate in 1961 from the University of Chi-cago under Irving Kaplansky. He held an NSF NATO Postdoctoral Fellowship, 1961-63, and an Assistant Profes-sorship at the University of Illinois, Urbana, 1963-67, before joining the University of Minnesota in 1967 as an Associate Professor. He was promoted to Full Professor in 1975. He spent the 1972-73 academic year as a Visiting Fellow at Sheffield University, England, and the 1997-98 academic year on sabbatical leave at Northeastern Univer-sity, Brandeis University, and the University of Colorado, Boulder. Seven doctoral students completed their theses under his guidance; six of these were at the University of Minnesota.

Jack has also made major contributions in administration. He was the Director of Undergraduate Studies, 1983-84, and again 1998-99, the last year of the quarter system. He thus played a key role in the conversion process to semesters and his energy and wisdom were invaluable during this critical period. He also served as Associate Head, 1984-86. We are sure Jack will continue to provide his valuable advice to the Department in future years and wish him well in retirement.

Professor E. Gebhard Fuhrken will retire at the end of Spring Semester 2000, after 38 years of service. Gebhard received his doctorate from the University of California, Berkeley, in 1962. His advisor was R.L. Vaught. Gebhard's specialty is mathematical logic, in particular model theory. He joined the University of Minnesota in 1962 as an Assis-tant Professor and was promoted to Associate Professor in 1971. He spent the 1969-70 academic year on sabbatical leave at the University of Colorado, Boulder. Gebhard is a dedicated teacher. Over the years he has taught a wide array of courses in mathematical logic (computabil-ity theory, set theory, model theory, nonstandard analysis), always preparing extensive lecture notes for his students and presenting each topic with his customary clarity and preci-sion. He has also run the Logic Seminar for many years. We wish Gebhard well in retirement and hope that he will continue to participate in Department activities.

Professor David H. Sattinger has accepted the chairman-ship of the Mathematics Department at Utah State Univer-sity, Logan, effective September, 1999. David has enjoyed many fruitful years at Minnesota but looks forward to the opportunities and challenges of this new stage in his career, as well as to living near the mountains. David received his doctorate from MIT in 1965 under the direction of Norman Levinson. His first position was at UCLA. He joined the University of Minnesota in 1971 as an Associate Professor and was promoted to Full Professor in 1976. David is a highly respected mathematical physicist. His work in symmetry and bifurcation theory is well known. Recently, he has worked in integrable systems and inverse scattering as well as nonlinear waves and numerical methods. He has published some seventy research papers, several monographs as well as a graduate level textbook. He has been very ac-tive in mentoring postdocs. We are sorry to lose Dave and his wife Irene but our loss is Utah State's gain and we wish them happiness in their new location.

## Conferences Organized Under the Auspices of the School

### Riviere-Fabes Memorial Symposium

The Second Riviere-Fabes Symposium on Analysis and Partial Differential Equations, in memory of Nestor Riviere and Gene Fabes, was held April 17 and 18, 1999. The speakers were Patricia Bauman, of Purdue University, Jean Bourgain, of the Institute for Advanced Study, Carlos Kenig, from the University of Chicago, and Wolodymyr Madych, from the University of Connecticut. Professor Bourgain gave two lectures, "On the nonlinear Schrodinger equation with critical nonlinearity", and "On Ginzburg-Landau functionals and minimizers in 3D". Pro-fessor Kenig also gave two lectures, "Well-posedness for KdV: positive results and counterexamples", and "Free boundary regularity for Poisson kernels". Professor Bauman spoke on "Analysis of solutions to a coupled Ginzburg-Landau system for layered superconductors", and Professor Madych spoke on "Three approximation theoretic vignettes". There was some exciting interplay amongst the talks, as shown by their titles! Thanks to the efforts of the organizing committee consist-ing of Professors Max Jodeit, Nikolai Krylov, Walter Littman, and Wei-Ming Ni (Chair), the Symposium was a great suc-cess. The lectures and the Symposium dinner Saturday evening were very well attended. Jeremy Pagel and Joyce O'Connell did an excellent job in providing hospital-ity for the visitors. Special thanks go to Monika Stumpf and Kathy Sweden for their help before and through the dura-tion of the Symposium. The Third Riviere-Fabes Symposium will be held April 28-30, 2000. The organizing committee consists of Professors Max Jodeit, Nikolai Krylov, Walter Littman, Fernando Reitich and Mikhail Safonov (Chair) from the School of Mathematics and Carlos Kenig of the University of Chicago. For information (as it develops) please visit the School of Mathematics web page, http://www.math.umn.edu and follow the link there to the page for the Symposium.

### Yamabe Memorial Lecture

Professor Jeff Cheeger of the Courant Institute (NYU) will deliver the twelfth annual Yamabe Memorial Lecture here on March 16, 2000. The title will be announced on the de-partment web page: http:/vvww.math.umn.edu. Cheeger is an eminent differential geometer, having been editor in chief of the "Journal of Differential Geometry" for a number of years. This lecture series, which alternates between Northwestern University and the University of Minnesota has been established to honor the memory of Hidehiko Yamabe (1923-1960) whose work on topological groups and geometry was an outstanding contribution to modern mathematics. Previous speakers were Professors: Neil Trudinger, Eugenio Calabi, Richard Schoen, Shizuo Kakutani, Craig Evans, Walter Rudin, Robert Hardt, Katsumi Nomizu, Fred Gehring, Richard Hamilton, and Peter Sarnak.

### McKnight Seminar in the Mathematical Biosciences

This seminar is a joint project of the Graduate School, the Departments of Chemical Engineering and Materials Sci-ence, Mathematics, Neuroscience, the Biological Process Technology Institute, and the Institute for Mathematics and its Applications. It continues in expanded form the highly successful joint Mathematics/Physiology Seminar began in the Fall 1998. The seminar presentations are intended to fos-ter ongoing collaborations between biologists and physical sciences and mathematics faculty and to stimulate new in-teractions that can serve to advance the emerging discipline of computational biology. The seminar, coordinated by Pro-fessor Claudia Neuhauser of the School of Mathematics, will feature invited guest speakers, as well as local speakers.

Joint School of Mathematics and IMA Seminars This year members of the School of Mathematics have organized three weekly seminars which are making an important contribution to the interaction between our faculty and visiting researchers at the IMA. The Dynamical Systems Seminar, organized by Professor George Sell, is strongly related to the 1999-2000 1MA pro-gram on "Reactive Flow and Transport Phenomena", since dynamical systems play a key role in modeling the processes which are studied in this program. In preparation for the 2000-01 IMA program "Mathematics in Multimedia", Professors Peter Olver of the School of Mathematics and Guillermo Sapiro of the Department of Electrical and Computer Engineering are organizing a Mul-timedia Seminar. The topics include computer vision and image processing, speech processing and language model-ing, medical applications and digital libraries. Professors Bernardo Cockburn, Mitchell Luskin and Fernando Reitich have set up a Numerical Analysis Seminar to promote the interchange of ideas among experts in nu-merical analysis and applied mathematics. In addition to our regular faculty a number of visitors at the School of Math-ematics and the IMA are participating.

### IMA Workshop on Local Interaction and Global Phenomena in Vegetation Systems

This workshop, held at the Institute of Mathematics and its Applications April 19-23, 1999, was organized by Profes-sors Simon A. Levin of Princeton University and Claudia Neuhauser of the School of Mathematics and brought to-gether mathematicians with theoretical and experimental ecologists. For the list of speakers and abstracts of the talks see the IMA website at http://www.ima.umn.edu/biology/ fall/bio10.html

### Workshop on Partial Differential Equations and Materials

Professors Robert Gulliver and Fernando Reitich organized a conference April 30 to May 2, 1999 at the University of Minnesota on the topic, "Nonlinear Partial Differential Equa-tions and Applications to Materials". The workshop was supported by the Participating Institutions of the 1MA, by the Midwest Partial Differential Equations Seminar and by the National Science Foundation, as well as the School of Mathematics. Funds were provided to support participation by 20 well-qualified graduate students from across the U.S. The workshop brought together researchers in materials sci-ence, applications of partial differential equations, analysis of partial differential equations and numerics in a setting which allowed informal interaction as well as a selection of hour talks by leaders in the respective fields. In this man-ner, issues of intense interest in materials science were brought to the attention of modelers, theoretical analysts and numerical analysts for discussion. At the same time, new concepts and methods currently being brought to bear on the fundamental issues in the analysis of partial differential equations (numerical and theoretical) were presented in a way which is expected to open new paths of inquiry for modelers and for materials scientists.

Topics which were discussed include level-set methods, non-linear homogenization, multiple time scales, widely varying length scales, fast numerical methods, rapid solidi-fication, nanoscale machines, laminated microstructure, and shape-deforming phase transitions. A distinguished list of scientists gave plenary talks: Oscar Bruno, Avner Friedman, Richard James, Robert Kohn, John Lowengrub, Mitchell Luskin, Geoff McFadden, Graeme Milton, George Papanicolaou, Stanley Osher, Mete Soner and Vladimir Sverak.

The success of the workshop was indicated by the lively dis-cussions among the 91 participants. Abstracts of the talks and a full list of participants may be found at http://www./ ima.umn.edu/—gulliver/confs/pdemat.html2

## Additional Conferences Organized by Our Faculty

### NATO Advanced Studies Institute on Math-ematical Problems Arising from Biology

Professors Richard Durrett of Cornell University and Claudia Nenhauser of the School of Mathematics were coorganizers of this workshop held June 14-24, 1999 at the Fields Insti-tute for Research in Mathematical Sciences in Toronto. The workshop was a part of a year long program in Probability and its Applications. Further details can be found at the Fields Institute web s ite hftp ://www. fi el ds .utoronto c a/ biol.html

### International Symposium on Discontinuous Galerkin Methods

Professor Bernardo Cockburn, of the School of Mathematics, with Professors George Kamiadakis and Chi-Wang Shu, both of Brown University, have organized the First International Symposium on Discontinuous Galerkin Methods. Discon-tinuous Galerkin Methods have been developed only recently but have quickly found extensive applications in diverse ar-eas of engineering. The meeting was funded by the National Science Foundation, Department of Energy andAir Force Research Office and took place at Salve Regina University, Newport, RI, from May 24 to May 26, 1999. The proceedings will be published this Fall in the Lecture Notes of Computational Science and Engineering series of Springer Verlag.

### Differential Geometric Methods in the Control of Partial Differential Equations

Boundary control and stabilization of partial differential equations has been a very active area of research during the last two decades, dealing with problems originating in sub-jects such as elasticity, acoustics and fluid dynamics. On the other hand, it has stimulated many new developments in the theory of partial diffential equations itself. Very recent research supports the expectation that differential geomet-ric techniques when brought to bear on certain partial differential equation modeling and control problems would yield significant mathematical advances. To enhance that goal, Professors Robert Gulliver and Walter Littman of the School of Mathematics, and Professor Roberto Triggiani (University of Virginia) organized a conference on "Differential Geometric Methods in the Control of Par-tial Differential Equations" at the University of Colorado, Boulder, June 27 - July 1, 1999. This was one of the seven "Joint Summer Research Conferences in the Mathematical

Sciences" chosen competitively from a large number of pro-posals by a committee representing the AMS, The Institute of Mathematical Sciences and SIAM.

There were sixteen main speakers interspersed with several shorter talks and "working seminars". The main speakers, in addition to the organizers, were:Sagun Chanillo (Rutgers), Jean-Michel Coron (Paris-Sud), Michel Delfour (Montreal), Jose Escobar (Cornell), Victor Isakov (Wichita State), Markus Keel (Caltech), Irena Lasiecka (University of Vir-ginia), John Lee (University ofWashington), Jan Sokolowski (Nancy, France), Giuseppe Tomassini (Scuola Normale Pisa), Francois Treves (Rutgers), Masahiro Yamamoto (University ofTokyo), and Peng-Fei Yao (Beijing University). The con-ference ended with a very stimulating session on "future problems", led by Markus Keel, Jean-Michel Coron and Roberto Triggiani. For further details see http//www.ima.umn.eduk-gulliver/ confs/control.himl

### Workshop on Local Cohomology and its Applications

Professor Gennady Lyubeznik of the School of Mathemat-ics is a coorganizer, with Professor Xavier Gomez-Mont of Centro de Investigacion en Matematicas (CIMAT), Guanajuato, Mexico, of a workshop on Local Cohomology and its Applications. The workshop will be held at CIMAT, Nov. 29 - Dec. 3, 1999 and is sponsored by the National Council of Science and Technology of Mexico and by the National Science Foundation. The focus of the conference will be to discuss some of the exciting recent developments and promote cooperation between US and Latin American mathematicians in this field. Some of the topics to be dis-cussed, from a local cohomology viewpoint, are: recent work on Fujita's freeness conjecture; applications of D-modules; effective Nullstellensatz; Greenlees-May duality; F-modules; and finiteness properties of local cohomology modules. The participants will include: I. Aberbach (University of Missouri), R. Belshoff (Southwest Missouri State Univer-sity), M. Brodmann (Zurich, Switzerland), J. Vassilev (Virginia Commonwealth University), J. Greenlees (Sheffield, UK), J. Lipman (Purdue), T. Marley (University of Nebraska), Z. Mebkhout (Paris, France), LA. Montaner (Nice, France), R. Sharp (Sheffield, UK), A. Singh (Univer-sity of Utah), I. Swanson (New Mexico State University), H.U. Walther (MSRI, Berkeley), C. Wickham (Southwest Missouri State University), K. Yanagawa (Osaka, Japan), and S. Zarzuela (Barcelona, Spain). Several advanced graduate students will also take part.

### Computability and Complexity in Analysis (CCA 2000)

This symposium is organized by Professors Ker-I Ko of SUNY at Stony Brook, Marian Pour-El of the School of Mathematics and Klaus Weihrauch of Fernuniversitat-GH-Hagen, and will be held in Swansea, Wales, September 17-19, 2000. This is the fourth international meeting of CCA.

## Other Notable Activities

Professor Bernardo Cockburn gave an invited lecture on "A new a posteriori error estimate for Hamilton-Jacobi equa-tions" at the Foundations of Computational Mathematics Conference held at Oxford University during July 18-28, 1999. Regents' Professor Avner Friedman gave a plenary lecture titled "Propagation of cracks in elastic media" at the Inter-national Conference of Industrial and Applied Mathemat-ics, Edinburgh, Scotland, July 5-9, 1999, and a plenary lecture titled "Free Boundary Problems in Mathematical Biology" at the International Conference on Applied Partial Differential Equations, Tongji University, Shanghai, China, July 13-16, 1999. He also gave an invited lecture at "Braude College Days of Differential Equations and Applied Analy-sis," Karmiel, Israel, May 18-20, 1999. Among other activi-ties, Professor Friedman has begun a three-year term on the Science Advisory Board of Carnegie Mellon University.

Professor Robert Gulliver has been invited to give a plenary lecture at the Annual Meeting of the Australian Mathemati-cal Society in Brisbane, July 2-5, 2000.

Professor Dihua Jiang gave invited lectures at an Interna-tional Conference on Modular Forms held at Oberwolfach, Germany, December 6-12, 1998 and at an International Con-ference on Automorphic Forms and L-Functions at Luminy, France, May 9-16, 1999.

Professor Mitchell Luskin gave a plenary lecture on "The Stability and Uniqueness of Crystal Microstructure" at the 1999 Annual Meeting of the Deutsche Mathematiker-Vereinigung (German Mathematical Society) held in Mainz, Germany during September 6-9, 1999.

Professor Mikhail Safonov gave a plenary lecture "On Schauder type estimates for solutions of elliptic and para-bolic partial differential equations" at the International Con-ference on Nonlinear Partial Differential Equations held August 23-29, 1999, in Lvov, Ukraine. The Conference was dedicated to the one-hundredth anniversary of the birth of the famous Polish mathematician Juliusz Schauder.

## Undergraduate Program

### From quarters to semesters

The long-anticipated switch to the semester system has finally arrived, and thanks to a great deal of work by several of our faculty and staff, the School of Mathematics has got-ten off to a good start. Furthermore, the changeover seems beneficial to our teaching effort in most respects. The "over-head" associated with registration, record-keeping, final exams, assignment of instructors, etc., is signficantly reduced. And many of our courses can now be given at a more comfortable pace. For example, Math 1031 (College Algebra) has become a 3-credit semester course, covering the same material as the old 4-credit quarter course. And second year calculus now divides up into 4-credit courses as follows: one semester of multivariable calculus (Math 2263 or 2373) and one semester of linear algebra and differential equations (Math 2243 or 2374). Formerly, these topics were crammed into two quarters of 5 credits each. In addition, students desiring a strong mathematics emphasis will take Math 2283, "Sequences, Series, and Foundations", during the second semester of their second year. For a limited time, we are offering a few transitional courses to help students who are caught by the quarter-to-semester conversion. One example is Math 1257, which bridges the gap between the old first quarter of calculus, and the new second semester calculus.

### IT Calculus

The "Calculus Initiative" project, which originated four years ago in the ITCEP office, under the direction of Harvey Keynes, has now matured to become the default calculus sequence for IT students, and all administrative aspects of it have now been assumed by the School of Mathematics. To mark the change, the new name of the sequence is officially "IT Calculus".

There are two main differences between the IT Calculus, Math 1371-1372-2373-2374, and the more traditional cal-culus sequence, Math 1271-1272-2243-2263. The first is that graphing calculators (in the first year) and the Mathematica and Matlab computer packages (in the second year) are an integral part of the course. The second is that there are two lectures and three section meetings per week, as opposed to three lectures and two section meetings. The extra time in section meetings is used for group learning and computer lab time. Course instructors assist the TA's during section meetings, so student-instructor contact is increased. This year, we are teaching 680 students in the first and sec-ond years combined of the IT Calculus. Because of the change in how the course is administered by the department, and also because of the switch to semesters, we expect to do a lot of fine-tuning before we can consider the sequence to be fully established in our curriculum.

### Scholarships

The School of Mathematics uses several funds, given to us by generous donors, to provide scholarships and awards for our most promising undergraduates. Funds have been es-tablished in memory of Halbert C. Christofferson, Hans H. Dalaker, William B. Hart, Ian Richards and Ella Thorp. In addition, some awards are made by the School itself, and others are made by the Institute of Technology Honors Pro-gram. During the 1998-99 academic year a total of $42,427 was awarded for scholarships in the School of Mathematics. These scholarships play an important role in fostering the mathematical studies of many of our best students. We feel that this is one of the most productive uses for contributions to the School.

### Writing Intensive Courses

The University's new writing requirements include at least one writing intensive course in each student's major. We have one such course which has been approved by the Writ-ing Center. It is Professor Wayne Richter's course "Sequences, Series and Foundations," Math 2283/3283. If a student takes 2283 there is no writing required other than the usual homework. A student taking 3283 (for one more credit) will be expected to carefully write proofs of theorems and expositions of the subject matter. Work remains to be done on writing in the mathematics ma-jor. Transfer students who have taken the equivalent of 2283 will not take 3283, and a writing situation must be created for them. The College of Liberal Arts now requires a "Ma-jor Project" from each of its students. The form that this project will take in mathematics remains to be determined. The Curriculum Committee will include these questions in its deliberations this year. -Larry Gray, Director of Undergraduate Studies

### Actuarial Program News

In reporting on the progress of the Actuarial Program at this time last year I noted that 1998 had been a big year for place-ments, the total then standing at 18. The final total was closer to 21, a record for any single year. The pressure con-tinues into 1999, with 14 already hired and several more

anticipated. This number includes recent PhD Chengwei Lee, who has taken a position with Wm. Mercer (Twin Cities office of a national consulting firm). "Internship" is something of a buzzword, really meaning "summer job" or "part-time job". Our students have been unusually successful at finding these opportunities as well, with 15 documented "interns" out there this very summer. Ten would be well above average. This group includes gradu-ate student Wen-Hong Wang, whose sister Doris Chiang made the move into the actuarial profession following her graduation (with PhD) a year ago. The transition to semesters has not greatly impacted the pro-gram. Rather than beef up the course and possibly drive out some marginally qualified students, we made Theory of In-terest into a 3-semester-credit course with no new/additional content. The extra time will be good for working problems in class. We thank Tom Schwartzbauer (recently retired from OSU) for teaching the final quarter-version of the course.

-Steve Agard, Acturial Program Coordinator

### Elementary Partial Differential Equations Course for IT

We have recently revised and upgraded this two-semester course to meet the need of providing science and engineer-ing graduate students with a modern and practical toolbox for analysis of physical problems that they encounter in their research. In making the revision, we cooperated with the Directors of Graduate Studies and professors in several Institute of Technology (IT) departments and discussed with them our plan to make this course serve as a gateway to more rigorous analytical research that students typically encounter in their graduate studies and in the workplace. The revised course covers mathematical theory and meth-ods for the solution of partial differential equations which model physical problems in many areas of applications. The mathematical content is balanced with physical interpreta-tion of the equations and their solutions, the goal being to teach the students how to apply these techniques in a wide range of settings. The methods range from transform tech-niques and fundamental solutions to asymptotic methods and introductory bifurcation theory. Numerical treatment is also introduced, with hands-on experience provided in the newly developed computer laboratory in Vincent Hall. In order to make the course as useful as possible we have organized it so that the second semester can be taken with-out the first, given some minimal background work. The new course is finding increasing popularity with the gradu-ate students in IT; the Fall Semester enrollment is a healthy 35 students.

We continue to make improvements and hope that the course will become a recommended elective for all first and sec-ond year graduate students in IT outside of Mathematics.

-Rachel Kuske and Fadil Santosa

### Mathematician Finds Future is Fractal

Although this news is over 100 years old, it has only recently found its way into the mathematics curriculum. One of the main goals of Math 5535, entitled "Dynamical Sys-tems and Chaos", is to spread the word to the next genera-tion of scientists and engineers. Over the past several years this course has been very successful with students from a wide range of fields, reflecting the fact that dynamical sys-tems occur in most areas where mathematics is applied. Since the time of Newton, a fundamental premise of science has been that it is possible to predict the future states of physical systems by mathematically analyzing their laws of motion. For example, the planets in the solar system move in such a way that if you know their positions and velocities at a certain moment, you can compute their positions and velocities at any other time, at least in theory. Around the turn of the century, the French mathematician Henri Poincare realized that things were not so simple in practice. In fact it turns out that the detailed positions of some of the planets cannot be predicted for more than a few million years (a rather small time by cosmic standards). The reason, in a word, is "chaos". One of the great lessons of twentieth century mathematics is that even very simple laws of motion can lead to extremely complicated behavior. As the system evolves, small uncer-tainties about the present state of the system can grow rapidly to produce large uncertainties about the future. The problem arises from the laws of motion themselves, not from the methods we use to solve them. This realization has profound implications for our whole approach to scientific problems. After all, there is not much point in working harder and harder to produce accurate planetary predictions if a tiny difference in the initial conditions leads to a completely different answer!

But the news is not all bad. Over the years, mathematicians have devised new methods for understanding chaotic dy-namical systems. Often it is possible to say something about the future, even if the detailed behavior is unpredictable. For example, the picture below shows the "attractor" for the fa-mous Lorenz dynamical system. For this system we can be sure that the future states of the system will be represented by some points on this complicated fractal set, but it is im-possible to say. exactly where. In the course, students are introduced to these new, geometri-cal ways of thinking. Computer graphics provide motiva-

tion and inspiration, but to really understand what is going on in a chaotic system, the students have to learn some math-ematics. And that, of course, is the real goal of the course.

-Rick Moeckel

## Graduate Program

Overall, our graduate program is growing somewhat, due to the success of the program in applied mathematics in attracting students of good quality and to students who are coming to the joint program with Education Department that provides a MS in mathematics along with state Secondary Education certification. There has been no diminution of our traditional academic programs. We continue to receive a substantial number of very well prepared students from many countries abroad. During the period September 1998-August1999, ten students earned the Ph.D. In the list following, the dissertation advisor is noted in parentheses, % denotes the Applied and Industrial Mathematics option, and their present position is noted. Yi-Ju Chao (Nicolai Krylov)% Motorola Kendra Killpatrick (Dennis White) Colorado State Yonghoi Koo (Robert Gulliver) Max Plank Institute Chengwei Lee (Naresh Jain) Mercer, Inc. Namyong Lee (Yasutaka Sibuya) Gerald Naughton (Max Jodeit) St. Thomas Svetlana Rudnaya (Fadil Santosa)% Avanti Corporation Scott Shald (Avner Friedman)% Lincoln Labs, MIT Uli Walther (Gennady Lyubeznik) MSRI, Berkeley HyekYoo (Nicolai Krylov)

Uli Walther received the Eugene B. Fabes award for an out-standing thesis. Awards for outstanding teaching were made to: Kyle Calderhead, Chengwei Lee, Salome Martinez, Irina Mitrea, Huiyan Qiu, Seung Suk Seo, Cetin Urtis, and Tamas Wiandt. These awards are made on the basis of classroom observa-tions by faculty, confirmed by student evaluation reports. Irina Mitrea was awarded an Alfred P. Sloan Doctoral Dissertation Fellowship. Irina is one of only twenty-five persons nationally who received such a grant. The Director of Graduate Studies position rotates among the faculty. In July, Donald Kahn completed his term and since then Charles McCarthy has occupied the DGS posi-tion.

-Charles McCarthy, Director of Graduate Studies

### MCIM

The Minnesota Center for Industrial Mathematics is pleased to announce that its National Science Foundation Group Infrastructure Grant has been renewed for two years. This brings the total funding to $1 Million over the five-year period starting in 1996. The renewal came after a site visit by NSF which took place in February 1999. We have had a number of students earning PhD degrees. In February, Scott Shald fmished his PhD and has since worked at MIT Lincoln Laboratories. Yi-Ju Chao, who fmished in May, is now working at Motorola. Svetlana Rudnaya, having defended inAugust, is presently at Avanti Corporation. Dur-ing their search for employment, we were pleased to find out that our Mathematics PhD's are competing successfully with students with engineering background, and that their starting salaries are at the level of engineering PhD's. Two MS students finished during the past academic year. One of them, Todd Wittman, will join the faculty of Univer-sity of South Carolina in Aiken as an instructor, while the other, Nicolas Vera, plans to move to California and seek employment there. A total of nine students were sent on internships. One of the students is performing his internship in Germany at Siemens. While companies such as Medtronic, Guidant, MTS, Seagate, continue to take our students, we also have interac-tion with two unusual companies. One of our student is working in a small local startup, Pointcloud Inc, working on an e-business project. Another student is working on a project with Algorithmics Inc, a major risk management company based in Toronto. The Applied Mathematics program, of which MCIM is a part, was ranked fourth in the last "education" issue of US News and World Report. This helps explain our success in attracting top graduate students into our program. We are pleased to announce that two of our entering graduate stu-dents in the Fall of 1999 hold prestigious NSF Fellowships.

-Fadil Santosa, Associate Director, MCIM

## Mathematics Library

The Mathematics Library is in reasonably good shape in the near future, not only because of the paint job it received during last spring break, but because looming journal cuts were forestalled, and because some resources were funded by alternate mechanisms due to negotiated deals concern-ing combinations ofpaper and electronic resources. In fact, we have managed to add five new journal subscriptions. However, given the boom in scientific publication, we must concede that we are falling behind. And it is unclear what will happen even in the short-term future because of the volatile situation of both paper and electronic publications: some news this summer indicates that funding will not im-prove in the next biennium. (Donations to Friends of the Library can be earmarked for a specific library within the system, such as the Mathemat-ics Library!) Thanks go to our library staff, Librarian Kristine Fowler and Library Assistant Lynn Tran, for keeping things running smoothly!

-Paul Garrett, Chairman of the Library Committee

## Recent Developments at the IMA

The National Science Foundation last spring awarded $ 2.2 million to the Institute for Mathematics and Its Applications in annual base funding for five years starting in 2000. This award follows the first open national competition for fund-ing of mathematics institutes since the establishment of the IMA in 1982. It is a major recognition of the leading role played by this Institute, affiliated with the School of Math-ematics, in fostering collaboration between mathematicians and other scientists, and academic institutions and industry, as well as in mentoring young researchers in applied math-ematics. Over the years, the IMA programs, focusing on large areas where mathematical tools play a crucial and in-creasingly prominent role, have demonstrated the power of sophisticated mathematics in solving problems that arise in other sciences, engineering and industry. In 1998-99 IMA researchers focused on "Mathematics in Biology", including the modeling of the spread of AIDS in the human body and the impact of vaccines onAIDS-infected cells, as well as hormone activity, cancer growth, animal aggregation, patterns of vegetation, and the spread of infec-tious diseases. The 1999 summer program on "Codes, Sys-tems and Graphical Models" (August 2-13) was a great suc-cess, with attendance at the talks averaging over 100. Part of the reason for the interest was that breakthroughs are occuring in coding theory, with development of codes that have the capability of approaching the Shannon limit—a theoretical limit on the capacity of a communication chan-nel found by the mathematician Claude Shannon in the late 1940's. Researchers in several areas of mathematics—graph theory, combinatorics, algebraic geometry, dynamical sys-tems, and symbolic dynamics—as well as in artificial intel-ligence, who are contributing to the breakthroughs, were participating in the program. The IMA annual program for the academic year 1999-2000, "Reactive Flow and Transport Phenomena", is divided into three components: "Combustion" (September-December 1999); "Natural Resources and Environment" (January-March 2000); and "Multiscale and Transition Re-gimes" (April-June 2000), devoted to mathematical prob-lems in developing adequate models for fluid flow and chemi-cal reactions under a broad range of conditions. The next year program will be "Mathematics in Multimedia".

Details about all of the IMA programs can be found on the IMA website: -www.ima.umn.edu.