# Applications

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, 2017**.

Approximately 75 mathematicians and computer scientists are invited to the School each year to work on their individual research projects and / or collaborations. A small number of memberships for a longer period of time (two years) are also available. Some mathematicians are supported by the Institute, while others receive financial aid from their home institutions, foundations or governments. While many members are at the postdoctoral level, the School hosts mathematicians at all stages of their careers. Special fellowships and joint programs with neighboring institutions are described below.

For information about special programs, see http://www.math.ias.edu/special-years.

Up to eight von Neumann Fellowships will be awarded each year. The fellowship supports a one-year membership, and interested applicants should be at least 5, but no more than 15, years past 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. **Applicants wishing to be considered for a Veblen Research Instructorship must also submit an application to the Princeton University Mathematics Department.**

Postdoctoral computer science and discrete mathematics applicants may be interested in applying for a joint (2-year) IAS position with one of the following: the Department of Computer Science at Princeton University, DIMACS at Rutgers, The State University of New Jersey, or the Simons Foundation Collaboration on Algorithms and Geometry. For a joint appointment, applicants should apply to the School as well as to the above, noting their interest in a joint appointment.

Term dates for the 2017-2018, 2018-2019 and 2019-2020 years are as follows: **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, 2019. **2019-2020 **- term I, Monday September 23 to Friday, December 20, term II, Monday, January 13 to Friday, April 10, 2020.

Please note that the School's term II begins and ends one week later than the rest of the Institute.

Each year the School's Special-Year program focuses on one area of mathematics. Typically these programs comprise up to one-third of the memberships.

For the **2017-2018** academic year, the School will have a special-year 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 **2018-2019** academic year, the School will have a special-year 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.

During the **2019-2020** academic year, the School will have a special-year program on Optimization, Statistics, and Theoretical Machine Learning. Sanjeev Arora of Princeton University will be the Distinguished Visiting Professor.

Design of algorithms and machines capable of “intelligent” comprehension and decision making is one of the major scientific and technological challenges of this century, calling for new models, new modes of analysis, and new algorithms. This Special Year will focus on developing the mathematical underpinnings of this field, including machine learning theory, optimization (convex and nonconvex), statistics, graph theoretic algorithms, etc. It will build upon the extensive frameworks that already exist and create new avenues of research. Connections will be explored to neighboring fields such as big data algorithms, computer vision, natural language processing, neuroscience and biology.

Applications for the visiting positions will be accepted in fall 2018, but expressions of interest as well as any inquiries for further information can be sent at any time to MLIASyear@gmail.com

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.

Again **deadline** for School **applications**, as well as for the supporting **letters** of recommendation, is **December 1, 2017**. To __ apply__ to the School of Mathematics, please go to

**https://www.mathjobs.org/jobs**