Mission

Fifty to sixty mathematicians are invited to the School each year to study with the Faculty and to pursue research projects of their own. A small number of memberships for a longer period of time are also available. Funding for candidates comes from a variety of sources. Some mathematicians are funded by the Institute, others receive financial aid from their home institutions, and a portion receive grants from governments or foundations.

The School frequently sponsors special programs. However, these programs comprise no more than one-third of the membership so that each year a wide range of mathematics is supported.

Recently the School has established the von Neumann Fellowships. Six of these fellowships will be available for the 2008-09 academic year. To be eligible for the von Neumann Fellowships, applicants should be at least five years following the receipt of their Ph.D. but not yet eligible to receive their first paid sabbatical.

The Veblen Research Instructorship is a three-year position which was established in partnership with the Department of Mathematics at Princeton University in 1998. Three-year instructorships will be offered each year to candidates in pure and applied mathematics who have received their Ph.D. within the last three years. The first and third year of the instructorship will be spent at Princeton University and will carry regular teaching responsibilities. The second year will be spent at the Institute and dedicated to independent research of the instructor's choice.

During the academic year 2006-07, the School of Mathematics will have a special program on algebraic geometry. We don't want to focus on any single aspect, but rather aim to have many flavors of algebraic geometry and its applications represented, including (not exhaustive list) cohomology theories, motives, moduli spaces, Shimura varieties, complex or p-adic analytic methods and singularities. During term II there will be a seminar and two workshops on homological mirror symmetry. The first workshop, “Mathematical Foundations of Homological Mirror Symmetry”, will take place during the period January 22-27, 2007; the second, “Applications of Homological Mirror Symmetry” from March 25 to March 31. For a list of 2006-2007 members and visitors, click here.

During term I of the 2007-08 academic year, School faculty member Jean Bourgain and Van Vu of Rutgers University will lead a program on arithmetic combinatorics. Additive combinatorics deal with problems in number theory with combinatorial flavor. While this theory has been developing for many decades, the field has seen exciting developments and dramatic changes in direction in recent years (a well known example is Green-Tao theorem about the existence of arithmetic progressions in primes). In this focus program, we will bring together active researchers in this field and many related areas such as number theory, combinatorics and theoretical computer science.

During both terms of the 2007-08 academic year, Roman Bezrukavnikov of MIT will lead a special program on New Connections of Representation Theory to Algebraic Geometry and Physics.

In the first term the emphasis will be on mathematics connected to quantum field theory, in particular the new differential geometric approach to the geometric Langlands program. A part of the second term will be devoted to absorbing the emerging new homotopy foundations of algebraic geometry, with a view towards applications.

One common feature of recent trends is “categorification”, often synonymous with “geometrization”. Categorification stands for the passage from a traditional mathematical object to its higher categorical analogue, and, more loosely, for the emphasis on categories instead of particular objects. The categories involved are typically of geometric nature (categories of sheaves of certain kind) and are constructed in a homological framework, i.e., they are triangulated categories, or refinements of these. Examples in representation theory include geometric Langlands duality (a categorification of the theory of automorphic forms); character sheaves (a categorification of representation theory of finite Chevalley groups); localization techniques for modular representations; Nakajima’s geometric construction of Kac-Moody Lie algebra representations etc. However, there are many examples in other fields which are relevant for representation theory: categories of D-branes in string theory; Fukaya categories (a categorical version of symplectic geometry); homological mirror symmetry and, more generally, focus on derived categories of coherent sheaves in algebraic geometry, which is a categorification of standard cohomology theories. The goal of the year is to explore these subjects and establish bridges to representation theory.

The following mathematicians have agreed to participate in the program for at least a semester: A. Braverman, M. Finkelberg, H. Nakajima, I. Mirković, D. Orlov.

Alice Chang of Princeton University will lead a special program on geometric partial differential equations during the 2008-09 academic year. The emphasis will be on non-linear partial differential equations with applications to problems in differential, conformal and convex geometry. Topics covered will include Yamabe type equations, Q-curvature equations, fully non-linear equations in conformal and convex geometry, construction of conformal invariants and operators, problems in conformally compact Einstein manifolds, measure and probability theory approaches to the Ricci Tebnsor. Partial differential equations continue to be one of the central tools for studying geometric and even topological questions, and one goal of this program will be to bring researchers in geometry and PDE together to study problems of common interest in areas such as those mentioned above.

During the 2009-10 academic year, Enrico Bombieri of the School and Peter Sarnak of Princeton University will lead a program on analytic number theory. (Preliminary information - more to come.)

The Institute for Advanced Study is committed to diversity and strongly encourages applications from women and minorities.

The School is grateful for the continued support of its programs by the National Science Foundation, the State of New Jersey, The Ambrose Monell Foundation and The Starr Foundation.

APPLICATION PROCEDURE: Apply Online

APPLICATION DEADLINE: December 1.