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 2013-14, 2014-15 and 2015-16 years are as follows: **2013-14** - term I, Monday, September 23 to Friday, December 20, term II, Monday, January 13 to Friday, April 11, 2014; ** 2014-15** - term I, Monday, September 22 to Friday, December 19, term II, Monday, January 12 to Friday, April 10, 2015; **2015-16** - term I, Monday September 21 to Friday, December 18, term II, Monday, January 11 to Friday, April 8, 2016.

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.

**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 will be the School's Distinguished Visiting Professor and together with Tom Spencer will lead the program. Jürg Fröhlich, Joel Lebowitz 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.

During the **2015-16** academic year, the School will have a special program on **Geometric Structures on ****3-manifolds**, and Ian Agol of the University of California, Berkeley, will be the Distinguished Visiting Professor.

Thurston proposed the classification of geometric structures on n-manfolds. While the spectacular Geometrization Theorem classified the geometric structures on 3- manifolds with compact isotropy group, i.e. locally homogeneous Riemannian metrics, there is a cornucopia of other fascinating structures such as contact structures, foliations, conformally flat metrics and locally homogeneous (pseudo-) Riemannian metrics.

The goal of this program is to investigate these other geometric structures on 3-manifolds and to discover connections between them. Additionally, it is important to forge connections between geometric structures on 3-manifolds and other geometric constructs, such as gauge theory, PD(3) groups, minimal surfaces, cube complexes, geometric structures on bundles over 3-manifolds, and strengthened structures such as taut foliations, tight contact structures, pA flows, convex projective structures and quasi-geodesic foliations. Many of these do not even have a conjectural classification (in terms of topological restrictions and moduli), and specific examples are still being constructed.

The focus of the special program during **2016-17** will be **Mirror Symmetry**. Paul Seidel of MIT will be the Distinguished Visiting Professor.

>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.