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. To apply to the School of Mathematics, please go to https://www.mathjobs.org/jobs. The deadline for School applications, as well as for the supporting letters of recommendation, is December 1, 2016.

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 2016-2017, 2017-2018 and 2018-2019 years are as follows: 2016-2017 - term I, Monday September 19 to Friday, December 16, term II, Monday, January 16 to Friday, April 14, 2017; 2017-2018 - term I, Monday September 25 to Friday, December 22, term II, Monday, January 15 to Friday, April 13, 2018. 2018-2019 - term I, Monday September 24 to Friday, December 21, term II, Monday, January 14 to Friday, April 12, 2018.

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 2016-17 academic year, the School will have a special program on Homological Mirror Symmetry. Paul Seidel of MIT will be the Distinguished Visiting Professor. Maxim Kontsevich, IHES, will be attending the program for one month during each of the fall and spring terms (from mid-October to mid-November, and for the month of February). Denis Auroux, UC Berkeley, will be attending for the spring term.

Homological Mirror Symmetry (HMS) was initiated by Kontsevich. It benefits from a close relationship with string theory, and has developed into a powerful and versatile idea. During the program, we will consider the core conjectures of HMS, and its role as a framework within which wider questions from mirror symmetry and other parts of mathematics can be studied. This is still a developing subject, and the program is open to a variety of approaches and viewpoints.

The intention is that the fall term will have a greater focus on the core building blocks of HMS as currently understood: the A-model theory (Lagrangian submanifolds, holomorphic curves and their generalizations), the B-model theory (derived categories in algebraic geometry), and mathematical interpretations of the Strominger-Yau-Zaslow approach, including the Gross-Siebert program. Specific questions of interest include: the role of singular Lagrangian submanifolds (such as Lagrangian skeleta); the effect of instanton corrections on the construction of mirror manifolds; and the structure of wrapped Fukaya categories. We will also consider the interplay between the various algebraic notions that appear in HMS.

The spring term would widen the focus, allowing space for emerging interactions between HMS and other areas. Examples are the theory of Special Lagrangian submanifolds, tropical geometry, and non-archimedean analytic geometry, as well as sheaf-theoretic methods. We also intend to look at applications of ideas from homological mirror symmetry to specific classes of manifolds, such as complex symplectic manifolds and cluster varieties.

There will be two workshops during the special program. The term I workshop, "homological mirror symmetry: methods and structures", will be held November 7-11, 2016. The term II workshop, "homological mirror symmetry: emerging developments and applications", will be held March 13-17, 2017.

For the 2017-2018 academic year, the School will have a special program on Locally Symmetric Spaces: Analytical and Topological Aspects. Akshay Venkatesh of Stanford University will be the Distinguished Visiting Professor. Alexander Goncharov, Laurent Clozel and Joseph Bernstein will be Members during term I, and Wei Zhang will be with us for both terms.

The topology of locally symmetric spaces interacts richly with number theory via the theory of automorphic forms (Langlands Program). Many new phenomena seem to appear in the non-Hermitian case (e.g., torsion cohomology classes, relations with mixed motives and algebraic K-theory, derived nature of deformation rings). One focus of the program will be to try to better understand some of these phenomena.

During the 2018-19 academic year, the School will have a special program on Variational Methods in Geometry. Fernando Codá Marques of Princeton University will be the Distinguished Visiting Professor.

Geometric variational problems have been studied by mathematicians for more than two centuries. The theory of minimal submanifolds, for instance, was initiated by Lagrange in 1760. Minimization principles have been extremely useful in the solution of various questions in geometry and topology. Most recently, and remarkably, minimax principles and unstable critical points have given us new tools and played a key role in the solution of old problems.

Many basic questions about existence and regularity remain to be solved. Recent advances suggest this is an exciting time for the field. This program will cover a variety of topics, including minimal submanifolds, harmonic maps, Willmore and constant mean curvature surfaces, eigenvalue extremal problems, systolic inequalities, connections with phase transition partial differential equations and others. The goal of the program is to develop further the variational theory of these objects and to find new connections between the themes.

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.

To apply to the School of Mathematics, please go to https://www.mathjobs.org/jobs

The deadline for School applications, as well as for the supporting letters of recommendation, is December 1, 2016.