Three MIT faculty are among 21 mathematicians, theoretical physicists and theoretical computer scientists who have been selected by the Simons Foundation as Simons Investigators.
The MIT recipients are Shafi Goldwasser, professor of computer science and engineering; Alice Guionnet, who will join MIT in September as a professor of mathematics; and Paul Seidel, professor of mathematics.
Simons Investigators receive $100,000 annually to support their research. The support is for an initial period of five years, with the possibility of renewal for an additional five years. The goal of the program is to provide a stable base of support for outstanding scientists in their most productive years, enabling them to undertake long-term study of fundamental questions.
Goldwasser has had tremendous impact on the development of cryptography and complexity theory. She has created rigorous definitions and constructions of well-known primitives such as encryption schemes (both public- and private-key versions) and digital signatures, as well as brand-new ones that she invented: zero-knowledge interactive proof systems. Goldwasser suggested efficient probabilistic primality testers as a means of recognizing (and generating) prime numbers, addressing an algorithmic problem of great significance; these output short proofs of primality, based on the theory of elliptic curves. Continuing her work on interactive proofs, she suggested the notion of two-prover systems, which have turned out to be important in complexity theory. In recent work, Goldwasser has adapted ideas from interactive proofs to show how a client can delegate computation to a not-so-trusted server and verify that the computation of the server is correct. She showed that this technique is applicable to a rich class of computational problems.
Guionnet’s work on large deviations for spectra of random matrices has extended the large deviation principle to the context of Dan-Virgil Voiculescu’s free probability theory. In a series of works with Thierry Cabanal-Duvillard, Mireille Capitaine and Philippe Biane, she proved various large-deviation bounds in this more general setting. These bounds enabled her to prove an inequality between the two notions of free entropy given by Voiculescu, settling half of the most important question in the field. With her former students Mylène Maïda and Édouard Maurel-Segala, and more recently with Vaughan Jones and Dimitri Shlyakhtenko, Guionnet has studied statistical mechanics on random graphs through multi-matrix models. This work on the general Potts models on random graphs branches out in promising directions of operator algebra theory. Guionnet has also done work on statistical mechanics of disordered systems (and in particular the dynamics and aging of spin glasses), random matrices (with an emphasis on the combinatorics of maps) and operator algebra.
Seidel has done major work on the border of symplectic and algebraic geometry. His work is distinguished by an understanding of very abstract algebraic constructs (such as derived twisted categories) in sufficiently concrete terms to derive results about the analytic/geometric objects at the basis of symplectic geometry. In this way Seidel has made substantial advances towards proving Maxim Kontsevich’s homological mirror symmetry conjecture, actually proving the conjecture in several special cases. Jointly with Ivan Smith, Seidel constructed the first deformationally non-standard examples of Stein complex structures on a Euclidean space. With his former student Mohammed Abouzaid, he has developed this into a powerful technique to construct infinitely many examples of non-symplectomorphic Stein structures on a any smooth manifold of dimension greater than four.