# Department of Mathematics

The Department of Mathematics at MIT seeks to improve upon its top ranking in both research and teaching by aggressively hiring the very best faculty, with special attention to the recruitment of top women and under-represented minority candidates, and by continuing to serve the broad and varied educational needs of its graduate students, the mathematics majors, and all undergraduates of the Institute.

### Students

During the academic year 2001–2002, there were 294 undergraduates majoring in mathematics: 247 in Course XVIII, Mathematics, and 47 in Course XVIII-C, Mathematics/Computer Science. Bachelor of Science degrees, including double majors, were awarded to 84 students: 75 in Course XVIII and nine in Course XVIII–C. There were a total of 120 graduate students in mathematics, all in the PhD program. This year 21 students received the doctoral degree.

### Faculty Changes

Associate Professor Gigliola Staffilani joins the department as associate professor with tenure from Stanford University. She is an analyst specialized in dispersive nonlinear partial differential equations.

Associate Professors Bonnie Berger (computational molecular biology), Alan Edelman (numerical analysis) and Michel Goemans (operations research) were promoted to professor.

Assistant Professors Sara Billey (algebraic combinatorics), John Bush (fluid dynamics), and Daniel Spielman (theoretical computer science) were promoted to associate professor.

CLE Moore Instructors Denis Auroux (symplectic geometry) and Jeff Viaclovsky (geometric pde's) were promoted to assistant professor, and Dmitriy Panchenko will join the department as assistant professor. His specialization is in probability theory and mathematical statistics, and he is a graduate of Novosibirsk State University and the University of New Mexico.

Professor Harvey Greenspan retired from MIT in January 2002 after 40 years of distinguished service.

Assistant Professor Lucia Caporaso resigned from MIT for a faculty position at the University of Rome "Roma Tre."

Assistant professor Andras Szenes also resigned from MIT for a faculty position at the Institute of Mathematics, Budapest University of Technology and Economics.

### Administration

Professor Michael Artin will continue as chair of the Undergraduate Committee and Professor Michael Sipser as chair of the Committee of Advisors. Associate Professor Pavel Etingof will follow Professor Tomasz Mrowka as chair of the Graduate Student Committee; Professor David Jerison will succeed Professor Richard Melrose as chair of the Pure Mathematics Committee, and Professor Ruben Rosales will follow Professor Daniel Kleitman as chair of the Applied Mathematics Committee.

### Research

Here are a few snippets from the great range of research underway in the department.

Daniel Freedman has begun to study string theory in a PP-wave geometry. Stimulated by recent work by J.M. Maldacena and others postulating a new and direct connection between gauge field theory and string theory, Professor Freedman with collaborators has proposed a specific identification in field theory of the basic 3-string interaction and has obtained a non-trivial consistency check of this proposal.

Steven Kleiman, with Eduardo Esteves, proved a new upper bound on the arithmetic genus of a closed algebraic leaf of a foliation.

Pavel Etingof and CLE Moore Instructor Victor Ostrik, jointly with Dmitry Nikshych, developed a general theory of fusion categories and the theory of Frobenius-Perron dimensions of such categories.

Martin Bazant is publishing a series of articles on "the stochastic renormalization group," which is a broad generalization of usual renormalization group to describe probability distributions of various quantities in phase transitions.

András Vasy is investigating connections between his prior work in quantum many-body scattering (an inherently analytic field) and scattering theory on symmetric spaces (a field with a rich algebraic structure).

Six MIT undergraduates participated with four mathematics graduate-student mentors in the department's fifth Summer Program in Undergraduate Research (SPUR), which offers a six-week program of full-time research experience culminating in written papers and lectures to faculty.

Summer 2001 was the ninth year of the Mathematics Department's participation in the Research Science Institute program (RSI) for gifted high school students, in which fourteen mathematics graduate students mentored 22 high school students from the US and abroad for a five week period. The mentored students included two of the top ten finishers in the Intel Science Talent Search for 2001, and one of the six winners of the National Siemens Westinghouse Science and Technology Competition.

### Honors and Awards

#### Faculty

Michael Artin received the Leroy P. Steele prize for lifetime
achievement of the American Mathematical Society for
"contributions to commutative and non-commutative algebra and
ring theory as well as to modern algebraic geometry." Daniel
Freedman has been selected to give the Andrejewski lectures in Leipzig
and Berlin in summer 2003. Michael Hopkins was elected fellow of the
American Academy of Arts and Sciences and foreign member of the Royal
Netherlands Academy of Arts and Sciences. Steven Kleiman was elected
foreign member of the Norwegian Academy of Science and Letters, which
also hosted a conference on the occasion of his 60^{th}
birthday. Haynes Miller was awarded a Cambridge-MIT fellowship for
AY2003. Daniel Stroock was named the first holder of the second Simons
professorship of mathematics. Martin Bazant was awarded the Paris
Science Chair, a visiting professorship at École Superieure de
Physique et Chimie Industrielles, for the fall 2002 term. John Bush
received an NSF career award for fluid dynamics. András Vasy and
Santosh Vempala received an Alfred P. Sloan research fellowship.

Seven of our faculty are invited speakers at the 2002 International Congress of Mathematicians this summer in Beijing, China: plenary lectures to be given by Michael Hopkins, Victor Kac and Gang Tian; invited lectures to be given by Hubert Bray, Pavel Etingof, Lars Hesselholt, and Daniel Spielman.

#### Students

The Housman graduate student teaching award was presented to John
Dunagan, and a second shared by Baochi Nguyen and Igor Pavlovsky, for
their exceptional skill and dedication to teaching. Ryan
O'Donnell and Donald Yau were awarded the Charles W. and Jennifer
C. Johnson prize for an outstanding research paper accepted in a major
journal by a graduate student in mathematics. The Clay Mathematics
Institute selected Tara Holm, Kevin McGerty, and Aleksey Zinger for its
*Liftoff* postdoctoral research program for summer 2002.
Jing-Rebecca Li, a 2001 doctoral graduate, received the Householder
prize for the best dissertation in numerical algebra between January
1999 and December 2001.

Senior Abhinav Kumar was awarded the Jon A. Bucsela prize in mathematics in recognition of distinguished scholastic achievement. Among those seniors awarded degrees in mathematics, 15 were elected to Phi Beta Kappa.

The MIT Mathematics team, comprised of Freshman Reid Barton, Senior Abhinav Kumar, and Junior Pavlo Pylyavskyy, finished second in the 2001 William Lowell Putnam Intercollegiate Mathematical Competition. Reid Barton was among the five highest ranking individuals and was therefore designated a Putnam fellow. MIT had seven other individual scores in the top 26, and another four individuals were given honorable mention for finishing in the top 61.

### Education

The project, "Computer Aided Teaching of Mathematics," developed by Professors David Jerison, Haynes Miller, and Gilbert Strang with the support of the D'Arbeloff grant, is making considerable progress and setting a high standard for mathematics courseware design. The goals are two-fold: to broaden the active learning experiences of the classroom through visualization tools which can be student-manipulated, and to design tools to interact closely with other MIT courses, such that students can use them throughout their MIT educational careers.

Through the generous sponsorship of the Akamai Educational Foundation and the Mathematical Association of America, the mathematics department hosted 200 high school students competing for positions on the US team for the International Mathematical Olympiad. The students were introduced to MIT through tours arranged by the admissions office and a picnic luncheon arranged by the mathematics department.

More information about the Mathematics Department can be found on the web at http://www-math.mit.edu/.