Thematic Semester on Probabilistic Methods in Geometry, Topology, and Mathematical Physics

Temple University, Philadelphia PA

Investigators

Abstract

The Centre de Recherches Mathematiques (CRM) will organize a Thematic Program on Probabilistic Methods in Geometry, Topology, and Mathematical Physics, held in Montreal, Canada, during the period of August to December, 2016. The Program, which will be the principal activity of the CRM in this period, is comprised of five intensive week-long workshops. In addition, there will be lecture series by three leading mathematicians: Nalini Anantharaman (Univ. Strasbourg), Yuval Peres (Microsoft Research), and Scott Sheffield (MIT). The workshops will be preceded by preparatory lectures for advanced graduate students. Numerous long-term visitors and postdoctoral researchers will be hosted at CRM throughout the seminar; this award provides support for junior US researchers to participate in the program. Probabilistic methods have played an increasingly important role in many areas of mathematics. The CRM Thematic Program will cover a broad range of such topics, including: geometric analysis on manifolds of metrics and applications to spectral theory and quantum chaos; geometry of random metrics and related problems in quantum gravity; applications of probabilistic techniques in partial differential equations; eigenstate localization in random domains; probabilistic results in number theory; random simplicial complexes and geometry of spaces of triangulations and connections to geometric group theory, manifold learning, topological statistics, and geometric probability; probabilistic methods in 3-manifold theory; random growth problems and random matrices, and their connections to stochastic partial differential equations (such as the Kardar-Parisi-Zhang equation) and to integrable discrete models. The program is naturally interdisciplinary, with an emphasis on interconnections and cross fertilization of ideas between researchers working in probability, geometric analysis, spectral theory, group theory, topology, geometry, and mathematical physics. Young researchers will be provided with an excellent opportunity to learn from and interact with experts in these fields. http://www.crm.umontreal.ca/en/index.shtml