Research in Mathematics

Institute For Advanced Study, Princeton NJ

Investigators

Abstract

The School of Mathematics (SoM) at the Institute for Advanced Study (IAS) has two primary goals. First, it supports fundamental research in mathematics, encourages original thinking, and produces significant advances in knowledge. Second, it invests in the development of a diverse pool of mathematical talent. The School strongly encourages the participation of women and members of other groups underrepresented in mathematics, and is dedicated to furthering the education and careers of all of its postdoctoral fellows. Junior mathematicians benefit from both their interactions with senior scholars and the mentoring they receive from faculty members. Mid-career and senior mathematicians consolidate their research projects and explore new research directions. The School's emphasis on a unified, interdisciplinary mathematical perspective and its work in bringing together a diverse group of mathematicians has led to numerous unanticipated mathematical developments. The School is in a strong position to identify, at an early stage, subject areas with the potential for important new developments. The School is led by eight permanent faculty members whose expertise span a wide spectrum of mathematics. As a center for new collaborations and new lines of research, the School hosts approximately 75 visiting mathematicians annually whose collaborative research visits typically last 4-10 months. This grant supports 23 of these scholars (17 postdoctoral fellows and 6 mid-career mathematicians), who join approximately 50 other mathematicians supported by funds from other sources. It also provides funds to host small groups of collaborators during the summer. The School of Mathematics provides this diverse community of scholars with an interactive environment, rich in mathematical content and conducive to collaboration. Each year SoM conducts a special program focused on a particularly exciting field of mathematics. The programs for the next three years will be "Locally Symmetric Spaces: Analytical and Topological Aspects" in 2017-2018; "Variational Methods in Geometry" in 2018-2019; and "Optimization, Statistics, and Theoretical Machine Learning" in 2019-2020. Each semester SoM facilitates a week-long workshop associated with the special topical program, as well as a separate week-long working group. The "Emerging Topics Working Group" is a group of researchers selected to work on a topic which seems ripe for significant progress. Other programs include "Mathematical Conversations," an informal discussion group that meets once a week, and "Summer Collaborators," small groups of invited researchers who collaborate on special research projects during the summer months. In addition to these workshops and programs, the SoM offers regular seminars, lecture series, and reading groups. All IAS lectures are videotaped and are available to the public. Visiting mathematicians supported by the grant receive individual and group mentoring from the permanent faculty members. Their individual research projects dive into one or more of the following fields of study: Analysis, Partial Differential Equations of Applied Mathematics, Probability, Algebra, Algebraic Geometry, Lie Groups, Representation Theory, Differential Geometry, Topology, Mathematical Physics, Dynamical Systems, Computer Science, Discrete Mathematics, Theoretical Machine Learning, and Number Theory.