# 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 2000-2001, there were 273 undergraduates majoring in mathematics, 230 in Course XVIII, Mathematics, and 43 in Course XVIII-C, Mathematics/Computer Science. Bachelor of Science degrees, including double majors, were awarded to 93 students, 79 in Course XVIII and 14 in Course XVIII-C. There were a total of 109 graduate students in mathematics, all in the Ph.D. program. This year 15 students received the doctoral degree.

### Faculty Changes

The Mathematics Department experienced the death of two senior faculty members this year: Professor Franklin Paul Peterson and Professor Emeritus Dirk Struik. Professor Peterson joined the MIT faculty in 1958 and was an internationally respected algebraic topologist specialized in the study of cohomology operations. He chaired the Pure Mathematics Committee during the periods 1972-75, 1979-82, and 1984-87, and served as Treasurer of the American Mathematical Society from 1974-1998. Professor Emeritus Dirk Struik was a member of the MIT faculty from 1928-1960, a highly respected analyst and geometer and an internationally acclaimed historian of

Mathematics, beginning with his book, Concise History of Mathematics, in 1948. Professor Struik maintained a life-long interest in social justice and Marxist Socialism; which, during the McCarthy period in 1951, led to an indictment "to overthrow the governments of the United States and Massachusetts." The indictment was dropped five years later, during which period Professor Struik was on paid-leave from MIT; he was reinstated to the faculty by President James R. Killian, Jr. in 1956.

Assistant Professors Pavel Etingof (representation theory, quantum groups) and Lars Hesselholt (algebraic topology) were promoted to Associate Professor (Professor Etingof with tenure). Dr. Alexander Postnikov will join the department as Assistant Professor of Applied Mathematics. Specialized in algebraic combinatorics, he is currently a Miller Research Fellow at the University of California, Berkeley.

Associate Professor Michael Brenner resigned from MIT for a faculty position at Harvard University, and Assistant Professor Karen Smith resigned for a faculty position at the University of Michigan.

Professor Michael Artin will continue as chair of the Undergraduate Committee, Professor Daniel Kleitman

as chair the Applied Mathematics Committee, Professor Richard Melrose as chair of the Pure Mathematics Committee, Professor Tomasz Mrowka as Chair of the Graduate Student Committee, and Professor Michael Sipser as chair of the Committee of Advisors.

### Research

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

Sigurdur Helgason has proven a certain refinement of the Huygens Principle, and obtained a stronger form of the support theory for the Radon transform on a symmetric space G/K. With Alexey Rudakov, Victor Kac conjectured a new generation of quarks on the basis of representation theory of E(3,6).

Bonnie Berger, with Visiting Professor Lenore Cohen, MIT Professor Jonathan King, graduate student Philip Bradley, and undergraduate Matthew Menke, developed a mathematical method, codified in the BetaWrap program, which can predict in nanoseconds whether a protein folds into a structure called a beta helix.

Hubert Bray is generalizing his three-dimensional theorem on the mass of black holes to the case of higher dimensional black holes. David Ingerman is working on a new representation of matrices as Dirichlet-to-Neumann maps based on a theory of planar graphs and continued fractions, among other applied mathematical studies. Byunghan Kim, a mathematical logician, has begun to develop a "geometric simplicity theory," combining ideas from his own simplicity theory with Rota's combinatorial geometry. Santosh Vempala has developed a simple new algorithm for solving linear and convex programs in polynomial time.

Nine MIT undergraduates participated with five mathematics graduate-student mentors in the department's fourth 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 2000 was the eighth year of the Mathematics Department's participation in the Research Science Institute program (RSI) for gifted high school students, in which eleven mathematics graduate students mentored seventeen high school students from the U.S. and abroad for a five-week period.

### Honors, Prizes and Awards

Professor Michael Hopkins received the Oswald Veblen Prize in Geometry for his work on homotopy theory.

Professor Victor Kac was invited as Plenary Speaker at the International Congress of Mathematicians 2002.

Professor Thomson Leighton received the IEEE Babbage Award for outstanding research in parallel and distributed computing. U.S. News and World Report also named him one of ten Innovators of the Year.

Professor Richard Stanley received the Leroy P. Steele Prize for Mathematical Exposition of the American Mathematical Society for his two-volume work, Enumerative Combinatorics.

Associate Professor Alan Edelman (together with Olga Holtz, Erik Elmroth and Bo Kagstrom) received the Society for Industrial and Applied Mathematics (SIAM) Activity Group on Linear Algebra Prize for the most outstanding paper in English on applicable linear algebra. Professor Edelman was also awarded the SIAM Outstanding Paper Prize for a separate article.

Associate Professor Michel Goemans (together with David Williamson, Michele Conforti, Gerald Cornuejols, and M.R. Rao) received the eighth Delbert Ray Fulkerson Prize, awarded every three years for a paper in discrete mathematics.

Assistant Professor Sara Billey received a Presidential Early Career Award for Scientists and Engineers, established by President Clinton in 1996. She was also selected for the MIT Class of 1922 Career Development Professorship.

Assistant Professor Hubert Bray received an Alfred P. Sloan Research Fellowship.

Assistant Professor Lucia Caporaso was among the first recipients of the Medaglia di Le Scienze by Le Scienze.

CLE Moore Instructor Ravi Vakil was awarded the G de B Robinson Award of the Canadian Mathematical Society for an outstanding paper in the Canadian Journal of Mathematics.

Graduate students received several awards. The Housman Graduate Student Teaching Award was given to Federico Ardila and Donald Yau for their exceptional skill and dedication to teaching. Adam Klivans was 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 Philip Bradley, Edward Goldstein, and Jesper Grodal for its Liftoff postdoctoral research program for summer 2001.

Seniors Ethan G. Cotterill and Joshua Sussan were awarded the Jon A. Bucsela Prize in Mathematics in recognition of distinguished scholastic achievement. Among those seniors awarded degrees in mathematics, eight were elected to Phi Beta Kappa.

The MIT Mathematics team, comprised of Sophomore Ivan Petrakiev, Junior Abhinav Kumar, and Senior Aram Harrow, finished second in the 2000 William Lowell Putnam Intercollegiate Mathematical Competition. Abhinav Kumar and Sophomore Pavlo Pylyavskyy were among the five highest ranking individuals and was therefore designated Putnam Fellows. MIT had three other individual scores in the top twenty-five, and another ten individuals were given Honorable Mention for finishing in the top sixty. These included Junior Marketa Havlickova who was the highest ranking of all female competitors. A total of 2800 students from 434 collages and universities in Canada and the US participated in the competition. MIT had the largest number of individuals (15) in the top 60.

### Educational

Enrollments in the Mathematics Department's service courses have been steady. The number of mathematics majors in each class seem to be rising, having jumped from the 70s to the 90s two years ago. A total of 93 majors graduated in 2001, of which 50 took their first degree in mathematics. This year 63 sophomores chose to major in mathematics.

As is shown by the results of the last Putnam exam, in which 15 of the 60 students who received special recognition were MIT undergraduates, our top mathematics students seem to be doing better than ever. No doubt thanks are due in part to the excellent problem-solving seminar run by Professor Hartley Rogers and Richard Stanley.

The Mathematics Department was short of teaching staff during the year. There was a drop in available teaching hours in every faculty category, so the reasons for this are diffuse. But the shortage was substantial. It was met by increasing recitation size slightly and by using essentially all of our teaching assistants in the classroom. Other jobs for teaching assistants, such as grading papers, suffered accordingly. To continue this overuse of teaching assistants would seriously affect the department's undergraduate and graduate programs in the long run.

With the assistance of the d'Arbeloff Grant on a project developed by Professors David Jerison, Haynes Miller, and Gilbert Strang, the Mathematics Department is engaged in revising its service courses.

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