MIT Reports to the President 1999–2000

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.

During the academic year 1999—2000, there were 278 undergraduates majoring in mathematics, 239 in Course XVIII, Mathematics, and 39 in Course XVIII-C, Mathematics/Computer Science. Bachelor of Science degrees, including double majors, were awarded to 94 students, 85 in Course XVIII and 9 in Course XVIII—C. There were a total of 100 graduate students in mathematics, all in the Ph.D. program. This year 17 students received the doctoral degree, and 3 the Master’s degree.

Professor James Munkres retired from MIT after 40 years of distinguished service on the Mathematics Faculty.

Assistant Professor of Applied Mathematics Martin Bazant (computational fluid dynamics) was promoted from an Applied Mathematics Instructorship appointment in January. Assistant Professor Byunghan Kim (mathematical logic) was also promoted from the CLE. Moore Instructorship in January. Dr. Igor Pak will join the department as Assistant Professor of Applied Mathematics. Specialized in algebraic combinatorics, he is currently a J. W. Gibbs Instructor of Mathematics at Yale University.

Associate Professor Sergey Fomin resigned from MIT for a faculty position at the University of Michigan.

Professor Michael Artin will follow Professor Richard Stanley as Chairman of the Undergraduate Committee.

Professor Daniel Kleitman will chair the Applied Mathematics Committee following Professor Michael Sipser, who will succeed Professor James Munkres as Chairman of the Committee of Advisors. Professor Richard Melrose will continue as Chairman of the Pure Mathematics Committee, and Professor Tomasz Mrowka as Chairman of the Graduate Student Committee.

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

Sigurdur Helgason is working on problems concerning the Radon transform corresponding to the double fibration relative to two symmetric subgroups of a semisimple Lie group. Steven Kleiman, in collaboration with Eduardo Esteves and Mathieu Gagne, proved an autoduality theorem for the relative compactified Jacobian and a family of curves with arbitrary double points. With W. Wakimoto, Victor Kac developed representation theory of affine superalgebras and discovered its connection to the theory of elliptic functions. Gerald Sacks is currently working on the invariant Post problem and the minimal upper bound problem for hyperdegrees in recursion theory; and, with Jessica Young, on the Vaught conjecture in model theory.

Byunghan Kim is investigating the relationship between stable structures and simple structures in model theory. Santosh Vempala formulated an algorithmic theory explaining how the brain can effectively learn concepts from a small number of examples. He also developed a rigorous analysis for the heuristic known as spectral clustering, and proved that the traveling salesman problem cannot be approximated to within 2% of the optimum. (This proof is novel in that it uses a probabilistic analysis to obtain the deterministic lower bound.)

Six MIT undergraduates participated with five mathematics graduate-student mentors in the department’s third 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 1999 was the seventh year of the Mathematics department’s participation in the Research Science Institute program for gifted high school students, in which seven mathematics graduate students mentored twelve high school students from the US and abroad for a five-week period.

Professor Aise Johan de Jong received the Frank Nelson Cole Prize in Algebra of the American Mathematical Society (shared with Andrei Suslin) "for important work on the resolution of singularities by generically finite maps."

Professor Isadore Singer received the Leroy P. Steele Prize for Lifetime Achievement of the American Mathematical Society for his series of five papers with Michael P. Atiyah on the Index Theorem for elliptic operators (which appeared in 1968—71) and for his three papers with Atiyah and V. K. Patodi on the Index Theorem for manifolds (which appeared in 1975—76) which are among the great classics of global analysis.

Professor Richard Stanley was selected to be the initial Norman Levinson Professor of Applied Mathematics through June 2005.

Associate Professor Bonnie Berger received the TR100 Award of *Technology
Review* for 100 top young innovators for the 21^{st} century.

Associate Professor Michel Goemans received an IBM Faculty Partnership Award.

Concerning the graduate students: Ioana Dumitriu received the Provost’s
Women/Minority Graduate Fellowship for 2000—2001. The Housman Graduate
Student Teaching Award was given to Alexander Perlin and Catalin Zara for their
exceptional skill and dedication to teaching. Bojko Bakalov and Kiran Kedlaya
were each 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 Bojko Bakalov, Kiran Kedlaya, and Catalin
Zara for its initial *Liftoff* postdoctoral research program for summer
2000.

Senior Benjamin Wieland was awarded the Jon A. Bucsela Prize in Mathematics in recognition of distinguished scholastic achievement. Among those seniors awarded degrees in mathematics, six were elected to Phi Beta Kappa.

The MIT Mathematics team, comprised of Sophomores Kai Huang, Abhinav Kumar, and Hoe Teck Wee, finished sixth in the 1999 William Lowell Putnam Intercollegiate Mathematical Competition. Abhinav Kumar was among the six highest ranking individuals and was therefore designated a Putnam Fellow. MIT had three other individual scores in the top fourteen, and another six individuals were given Honorable Mention for finishing in the top 60. A total of 2900 students from 431 colleges and universities in Canada and the US participated in the competition. MIT had the largest number of individuals (10) in the top 60.

The Undergraduate Mathematics Committee, led by Richard Stanley (the Undergraduate Chair) added two new courses to the calculus options required of all MIT students. They are 18.013A and 18.023A Calculus with Applications, which are accelerated versions of the applied options 18.013 and 18.023. These new courses supply an applied analogue of the accelerated versions 18.01A and 18.02A Calculus of the standard calculus courses 18.01 and 18.02. There were significant changes this year regarding mathematics majors. For academic year 2000—01 the number of freshmen who chose mathematics as their major is 72, up from 49 for 1999—00, and the highest number since 1973. There is a trend for more students, especially from course 6 to earn a second degree in mathematics. Over the last three years, the percentage among junior and senior mathematics majors in this category increased from approximately 25% to 50%.

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

David A. Vogan, Jr.