MIT Reports to the President 1998-99

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.

During the academic year 1998—99, there were 237 undergraduates majoring in mathematics, 204 in Course XVIII, Mathematics, and 33 in Course XVIII-C, Mathematics/Computer Science. Bachelor of Science degrees, including double majors, were awarded to 76 students, 70 in Course XVIII and 6 in Course XVIII-C. There were a total of 89 graduate students in mathematics, all in the Ph.D. program. This year 15 students received the doctoral degree.

The Mathematics Department experienced the death of two senior faculty members this year: Professor Emeritus Irving Segal and Professor Gian-Carlo Rota. Professor Segal joined the Mathematics Department in 1960 and retired in 1989. He was one of the pioneers in functional analysis and generalized harmonic analysis. Professor Gian-Carlo Rota became a senior faculty member at MIT in 1967. Regarded as the seminal figure most responsible for developing the study of discrete mathematics, combinatorics, into a high-level mathematics, he had a deep impact on the wider academic community and on students. In March 1997 Professor Rota was the James R. Killian Lecturer, and he was appointed as Norbert Wiener Professor of Mathematics in July 1997.

Associate Professors of Applied Mathematics Bonnie Berger (computational molecular biology), Alan Edelman (numerical analysis), and Michel Goemans (operations research) each will be granted tenure. Assistant Professor Michael Brenner (fluid dynamics) will be promoted to Associate Professor of Applied Mathematics.

Dr. Hubert Bray, a CLE Moore Instructor in differential geometry, will be promoted to Assistant Professor. Dr. David Ingerman will join the department as an Assistant Professor of Applied Mathematics, concentrated in bridging discrete and continuous mathematics. Currently he is an Assistant Professor at the Courant Institute of Mathematical Sciences, New York University. András Vasy, Morrey Assistant Professor at University of California, Berkeley, will be appointed Assistant Professor of Mathematics. His specialization is in analysis.

Professor Alexander Beilinson resigned from MIT for a faculty position at the University of Chicago.

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

Gang Tian has constructed quantum cohomology for several symplectic manifolds, deepening the connections between the tools of topology and the classical counting problems of algebraic geometry. Victor Guillemin, in collaboration with his students Tara Holm and Catalin Zara, is developing graph-theoretic techniques to study the geometry of a manifold with a group action. Hubert Bray has proved the Penrose Conjecture, which concerns the possible structures of asymptotically flat space-times containing black holes.

Michel Goemans is working on improved bounds on error-correcting codes, and on connections between cooperative game theory and combinatorial optimization. Santosh Vempala has found the first polynomial-time algorithm for detecting genetic linkage. Sara Billey has found deep connections between the combinatorics of permutations and the singularities of some associated algebraic varieties.

Six MIT undergraduates participated with five mathematics graduate-student mentors in the Department's second 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 1998 was the sixth 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 thirteen high-school students from the US and abroad for a five-week period.

Professor David Jerison was elected to the American Academy of Arts and Sciences.

Professor George Lusztig was selected by the department faculty to be the next Norbert Wiener Professor of Mathematics through June 2004. He also received the Brouwer Medal by the Dutch Mathematical Society and the Dutch Academy, a medal awarded every three years for a different area of mathematics, this year for algebra, including algebraic K-theory.

Professor Gilbert Strang was elected to an Honorary Fellowship at Balliol College, Oxford.

Associate Professor Michel Goemans (with David Williamson, IBM) was awarded his second Prize of the Society for Industrial & Applied Mathematics Activity Group on Optimization.

Assistant Professor John Bush was selected for the School of Science Ferry Fund award for his proposal "Experimental Fluid Dynamics." Assistant Professor Maurice Van Putten was awarded the School of Science Reed Fund for his proposal "Structure from Gravitational-Magnetic Stability in Saturn's Rings."

Assistant Professor Santosh Vempala received the Career Award of the National Science Foundation for the research project entitled "Geometric Tools for Algorithms."

Concerning the graduate students: Bojko Bakalov, Alexander Perlin, and Catalin Zara each received the Alfred P. Sloan Doctoral Dissertation Fellowship. Peter Dodds and Dana Pascovici were selected for the Housman Graduate Student Teaching Award, given to graduate students in mathematics who have demonstrated exceptional skill and dedication to teaching. Catalin Zara received 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 MIT Mathematics team, comprised of Seniors Amit Khetan, Eric Kuo and Edward Lee, finished second in the 1998 William Lowell Putnam Intercollegiate Mathematical Competition. This was MIT's best finish in this competition in more than twenty years. Seniors Amit Khetan, Eric Kuo, and Vivek Mohta were awarded the Jon A. Bucsela Prize in Mathematics in recognition of distinguished scholastic achievement. Among those seniors awarded degrees in mathematics, four were elected to Phi Beta Kappa.

Professor David A. Vogan, Jr. succeeds Professor David J. Benney as Head of the Mathematics Department.

Professor Richard Melrose will be Chairman of the Pure Mathematics Committee following David Vogan, and Professor Tomasz Mrowka succeeds Richard Melrose as Chairman of the Graduate Student Committee. Professor Richard Stanley follows Professor Michael Artin as Chairman of the Undergraduate Committee. Professor James Munkres continues as Chairman of the Committee of Advisors, and Professor Michael Sipser as Chairman of the Applied Mathematics Committee.

The Undergraduate Mathematics Committee, led by Michael Artin (the Undergraduate Chair) and James Munkres (Chair of Mathematics Advisors) has carried out a careful review of the structure of our calculus offerings for freshmen. One small but helpful change is that the numbering of these courses is now parallel to that of the freshmen physics courses. A second consequence will be a change (beginning in 2000) in how we assign advanced standing for Advanced Placement (AP) exam scores. Because the AB Calculus syllabus lacks a number of important topics covered in 18.01 Calculus, we will no longer offer 18.01 credit for the AB Advanced Placement Calculus exam. It will still be possible to receive this credit on the basis of an advanced standing exam taken at MIT.

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

David A. Vogan, Jr.

MIT Reports to the President 1998-99