Georgia Benkart Named MAA Pólya Lecturer for 2000-01, 2001-02

Georgia Benkart

Each year the Board of Governors of the Mathematical Association of America selects a Pólya Lecturer, to serve for two academic years. Georgia Benkart has been selected to serve in 2000-01 and 2001-02. On a rotating basis, the various MAA sections around the country can invite a current Pólya Lecturer (there are two at any given time) to speak at a regional meeting.

Georgia received the PhD from Yale University in 1974 and has been a member of our Mathematics Department ever since. Her research specialities are Lie Algebras, Representation Theory, and Combinatorics. She won a University of Wisconsin Mid-Career Award in 1996 on the basis of her strong research accomplishments and continued potential. She is regarded as an inspiring and dedicated teacher, in the best traditions of George Pólya, and won a campus-wide Distinguished Teaching Award in 1987. Giving lectures around the country won't be anything new for Georgia. In the year 2000 she gave 9 invited lectures, including lectures at MSRI (Berkeley), Seoul National University (Korea), Canada (Toronto and Alberta), and Oberwolfach (Germany). In 1999 among her 11 invited lectures were the Taft Lectures at the University of Cincinnati. Professor Benkart currently serves on the editorial boards of the Journal of Algebra and the Korean Mathematical Colloquium. Fourteen graduate students have completed doctoral dissertations under her supervision.

Eleny Ionel awarded Sloan Fellowship

Eleny Ionel

An Alfred P. Sloan Fellowship has been awarded to Eleny Ionel for the years 2000-02. According to the award letter, the fellowship is ``an extraordinarily competitive award, involving nominations for most of the best scientists of your generation from around the country.'' The award, worth $40,000, recognizes past research accomplishments and future potential.

Eleny studied as an undergraduate at the University ``Al. I. Cuza'' (Romania) and received the PhD from Michigan State University in 1996 with a thesis ``From Gromov invariants to enumerative invariants'' guided by Thomas H. Parker. She was C.L.E. Moore Instructor at MIT before arriving on the Madison campus in 1999. In addition, she was a Postdoctoral Fellow at MSRI (Berkeley) in the fall of 1996.

Professor Ionel's research interests are in symplectic topology and 4-manifolds, and Gromov-Witten and Seiberg-Witten invariants. Among the highlights of her work are the computation of the number of tori in projective space with fixed j-invariants, a gluing formula for Gromov-Witten invariants, and the discovery of important new relations in the cohomology of Deligne-Mumford moduli spaces of stable Riemann surfaces. Very quickly she has become a leading member of our growing topology & geometry group.

Steffen Lempp receives Vilas Associate Award

Steffen Lempp

Steffen Lempp was named a Vilas Associate for the years 2000-02. This prestigious award provides summer salary support for two years and $10,000 each in flexible research funds for the pursuit of his scholarly activities. The Department's record in winning such awards is impressive in that there have been 8 such awards to its faculty in the first five years of the Vilas Associates Program.

Steffen studied at the Universities of Karlsruhe and Bonn (Germany) before entering the graduate school at the University of Chicago where he received the PhD in 1983. He was a Gibbs Instructor at Yale University for two years before joining our Department in 1988 as an Assistant Professor. He was promoted to Associate Professor in 1992 and Professor in 1996. Steffen was on research leave at the University of Leeds (England) in the spring of 1996 and spent the summer of 1998 at the University of Siena (Italy). Seven students have received PhDs with his guidance. He was the editor of the Journal of Symbolic Logic from 1993-98, and is currently the editor of the Lecture Notes on Logic series of the Association for Symbolic Logic.

Professor Lempp's research area is computability theory in which he is a leader. According to Steffen, computability theory is the study of the effective content of mathematics, in particular of mathematical constructions. It has strong connections with theoretical computer science since it explores the theoretical limitations of mechanical computability, that is, by idealized computers without bound on run time or memory space. Computability theory arose out of the work of Gödel in the 1930's in which it was demonstrated that Hilbert's program to axiomatize arithmetic in a finitary manner was impossible. This work led to a number of undecidability results, including the undecidability of the word problem for finitely presented groups and of Hilbert's 10th problem on diophantine equations.

Steffen has done significant and ground-breaking work in the two major aspects of computability theory, namely the study of complexity of sets of integers (regarded as coding natural mathematical problems) and applied computability (the study of the effective content of various branches of mathematics, in particular, algebra and model theory). He has been a energetic member of our logic group, organizing meetings, seminars, and other activities.

Yong-Geun Oh receives Korean Young Scientist Prize

Yong-Geun Oh

Associate Professor Yong-Geun Oh has just been notified that he will be awarded the ``Korean Young Scientist Prize." The award will be presented to Yong-Geun by Korean President Kim Dae Jung at a ceremony in Korea in February. The award includes a 5-year research grant worth over $100,000.

Yong-Geun received the PhD from UC-Berkeley in 1988 under A. Weinstein. He spent postdoctoral years at MSRI (Berkeley) in 1988-89, at the Courant Institute of NYU in 1989-1991, and the Institute for Advanced Study (Princeton) in 1991-92. He came to Madison in 1992 and was promoted to Associate Professor in 1997. The academic years 1998-2000 were spent at the Korean Institute for Advanced Study and Kyoto University.

Since receiving the PhD, Yong-Geun has concentrated his research on developing and enhancing the so-called Floer homology theory in symplectic geometry and its application to various problems in symplectic geometry and topology.

Ken Ono is PECASE Recipient

Ken Ono

Associate Professor Ken Ono, who joined the Department of Mathematics in 1999, was named in April, 2000 as recipient of the 1999 Presidential Early Career Awards for Scientists and Engineers (PECASE). Ken was one of 20 recipients and the only mathematician in the bunch. The awards were presented at the White House Old Executive Building by President Clinton's science advisor, Neal Lane. According to an NSF news release, the PECASE award is the highest honor bestowed by the U.S. government on outstanding scientists and engineers who are in the early stages of establishing their research careers. These awards were established in 1996 in order to recognize some of the nation's finest scientists and engineers and to maintain U.S. leadership across the frontiers of scientific research. Each awardee receives $500,000 over a five-year period to further their research and educational efforts.

As PECASE recipient, Ken participated in the NSF's 50th Anniversary Celebration and its yearlong initiative Scientists and Engineers in the School. Along with Nobel Laureates Leon Lederman (1988, physics) and Russell Alan Hulse (1993, physics), Ken visited with high school students in the Midland, Michigan area in order to share science, experiential learning, and personal experiences with innovation and discovery. As part of this celebration, Ken and his PECASE Postdoctoral Fellow, Gwynneth Coogan, gave a presentation to students at Cherokee Heights Middle School in Madison in September, 2000. Coogan received the PhD from the University of Colorado in 1999 and is Assistant Professor at Hood College in Frederick, Maryland. She is spending the 2000-01 academic year in Madison teaching and doing research. In addition to her academic abilities, Gwynneth was a member of the 1992 USA Olympic Track and Field Team, competing in the 10,000-meter event. She was also an alternate member for the 1996 Team in the marathon.

One of Professor Ono's research interests is the partition function p(n). Ramanujan discovered congruences for the partition function involving the numbers 5, 7, and 11. For instance,

p(5n+4) º 0 mod 5, p(7n+5) º 0 mod 7, p(11n+6) º 0 mod 11.

Similar relationships hold when 5, 7, and 11 are replaced by their powers, or for a product of these powers. Since Ramanujan, only a few isolated examples of similar congruences had been found, and it was generally thought that there were no other families of congruences of this type. Now Ken Ono has shown that there are infinitely many such congruences. Ono's work was described in an article in Science News in Volume 157, No. 25, June 17, 2000. In that article, Bruce Berndt (PhD 1966, J. R. Smart) of the University of Illinois was quoted as saying Öno's work is really spectacular. This certainly must rank as the most important work on partition congruences since the epic work of Ramanujan."

Ken used the theory of modular forms and discovered a connection between p(n) and a specific modular form. This led him to establish the existence of the congruences modulo a prime number for p(n). But he provided only one specific example:

p(594·13n+111,247) º 0 mod 13.

An undergraduate, Rhiannon L. Weaver, working with Ken at his former institution, Penn State, found thousands of congruences for primes from 13 to 31. Both Ono and Scott Ahlgren of Colgate University have now shown the existence of congruences for p(n) for every modulus coprime to 6. In a recent joint paper with VIGRE Postdoctoral Fellow, Jeremy Lovejoy, Ken and Jeremy examine the optimality of the moduli in the family of congruences found by Ramanujan. In that paper they remark that to their knowledge, no explicit congruences for p(n) are known for any prime modulus greater than 31.

This past summer, Professor Ono was one of the instructors at the National Youth Science Camp in West Virginia. At this Camp, near Bartow, West Virginia in the Monongahela National Forest, were two graduating seniors from every state in the union. The Camp was established in 1964, in the post-Sputnik era, as a gift to the nation on West Virginia's 100th birthday.

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