Mission

The School of Mathematics is an international center of research and postdoctoral training in many diverse aspects of mathematics including pure mathematics, theoretical computer science, mathematical physics and applied mathematics.

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.

Term dates for the 2011-12 and 2012-13 years are as follows:  2011-12 - term I, Monday, September 19 to Friday, December 16, 2011, term II, Monday, January 16 to Friday, April 13, 2012.  2012-13 - term I, Monday, September 24 to Friday, December 21, 2012 and Monday, January 14 to Friday, April 12, 2013.  Please note that the School's term II begins and ends one week later than the rest of the Institute.

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.

Several years ago the School established the von Neumann Fellowships. Up to eight of these fellowships will be available for each academic year. To be eligible for the von Neumann Fellowships, applicants should be at least five but no more than fifteen years following the receipt of their Ph.D.

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 2011-2012 academic year, Helmut Hofer, Institute for Advanced Study, and John Mather, Princeton University, will lead a program on symplectic dynamics.

The mathematical theory of dynamical systems provides tools to understand the complex behavior of many important physical systems.  Of particular interest are Hamiltonian systems.  Since Poincaré's fundamental contributions, many mathematical tools have been developed to understand such systems.  Surprisingly these developments led to the creation of two seemingly unrelated mathematical disciplines: the field of dynamical systems and the field of symplectic geometry.  In view of the significant advances in both fields, it seems timely to have a program that aims at the development of the common core, which potentially should lead to a new field with highly integrated ideas from both disciplines.  Of particular interest will be the study of the dynamics of area-preserving disk maps, the ramifications of new symplectic techniques in three-dimensional hydrodynamics, as well as questions about the utility of the symplectic pseudoholomorphic curve techniques in questions related to KAM and Aubry-Mather theory.

There will be weekly seminars and several workshops.

The special program for the 2012-2013 year will focus on Univalent Foundations of Mathematics.  The program will be organized by Steve Awodey of the Carnegie Mellon University, Thierry Coquand of the University of Gothenburg and Vladimir Voevodsky of the Institute for Advanced Study.  The main goal of the program will be to make available to a wider mathematical audience the recent advances which may finally make it practical for pure mathematicians to use "proof assistants" in their work.

Non-equilibrium dynamics and random matrices will be the topic of the special program during the 2013-14 academic year.  Horng-Tzer Yau of Harvard and Tom Spencer of the Institute will lead the program. Jürg  Fröhlich and Herbert Spohn will be among the senior participants attending.

Over the past few decades there has been considerable progress in the mathematical analysis of equilibrium statistical mechanics.  However, non-equilibrium dynamics is still in the early stages of its development.  Recent developments suggest that this is a good time for the proposed program.  Dynamics related to Dyson's Brownian motion have played a key role in the recent proof of the universality of the local eigenvalue spacing statistics for Wigner matrices.  Also there have been recent advances in the fluctuations of stochastically-driven equations such as KPZ and dynamics of glassy models.

Claire Voisin, Institut de Mathématiques de Jussieu, will be the School's Distinguished Visiting Professor during the 2014-15 academic year. Professor Voisin will lead a special program on "The Topology of Algebraic Varieties".

The topology of algebraic varieties is traditionally understood in two different senses: either one considers real or complex algebraic varieties, and then one studies (mostly via Hodge theory) the topology of (the set of real or complex points of) this algebraic variety, endowed with the Euclidean topology, or one studies this algebraic variety endowed with the Zariski or étale topology with the help of various cohomology theories (étale, de Rham...)

The second viewpoint is closer in spirit to the theory of motives, as it includes the various comparison isomorphisms, and because it does not use non-algebraic data. The complex point of view is, in fact, also very well-adapted to the study of algebraic cycles, in view of the Bloch-Beilinson conjectures.

This program intends to bring a mix of people interested in various aspects of the subject: Motives, K-theory, Chow groups, periods, fundamental groups.

>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 and The Ambrose Monell Foundation.

APPLICATION PROCEDURE: Apply Online

APPLICATION DEADLINE: December 1.