Organized by Lara Anderson and Laura Schaposnik Hitchin systems have found remarkable applications in many different areas of mathematics and physics. In particular, Hausel and Thaddeus related Higgs bundles to mirror symmetry, and in the work of Kapustin and Witten, Higgs bundles were used to give a physical derivation of the geometric Langlands correspondence. Moreover, … Read more
Organized by Daniel Persson, Terry Gannon, David Ginzburg, Axel Kleinschmidt, Stephen D. Miller, Boris Pioline The purpose of this interdisciplinary program is to investigate connections between string theory, automorphic forms, mock modular forms and beyond. Automorphic representations form a cornerstone of the Langlands program, while at the same time playing a crucial role in understanding the … Read more
Organized by: Stefan Hollands, Vaughan Jones, Gandalf Lechner, Roberto Longo Since Heisenberg’s and Jordan’s “matrix formulation” of quantum mechanics about one hundred years ago, theoretical quantum physics has been a major incentive for mathematical research into operator algebras. The stimulus from physics has helped the development of this field, founded by von Neumann with the … Read more
Organized by: Nathan Haouzi, Vladimir E. Korepin, Sergei L. Lukyanov, Nikita A. Nekrasov, Samson Shatashvili, and Alexander B. Zamolodchikov Weekly program seminars are held on Mondays at 11:30am and Fridays at 11:00am. For the full upcoming schedule please visit our calendar: https://scgp.stonybrook.edu/calendar/full-calendar Integrability is a traditional area of mathematical physics. For 1+1 dimensional field theory the … Read more
Organized by: Vasily Pestun and Maxime Zabzine The program will be focusing on the development of localization techniques in quantum field theories and its applications. In particular we want to concentrate on the developments in the field since 2007. The main idea of different localization formulas is that the specific finite dimensional integral can be … Read more
Organized by: Anton Alexeev and Samson Shatashvili The proposed program will touch upon two topics in Mathematics: Poisson geometry of moduli spaces and the theory of associators, and some of the mathematical aspects of quantum field theory. Both the moduli space theory and the associator theory are intimately related to quantum field theory. In particular, … Read more
Organized by: Uriel Frisch, Konstantin Khanin and Rahul Pandit Some of the most basic questions relating to the Euler and Navier-Stokes equations for the motion of a 3D incompressible fluid are still open. There is a strong belief that answers to these questions cannot be obtained without creative use of geometric/Lagrangian and measure-theoretic/probabilistic tools. This … Read more
Organized by: Alexander Abanov, Kristan Jensen, and Vadim Oganesyan Scientific advisors: Igor Aleiner, David Huse, Anatoli Polkovnikov, Steven Shenker The program aims to highlight and explore recent progress in understanding the emergence of macroscopic dynamical laws in many-body systems. Traditionally, the challenge of connecting macroscopic and microscopic many-body dynamics was addressed by computing hydrodynamic parameters, … Read more
Organized by: Lukasz Fidkowski, Dan Freed, and Anton Kapustin May 1 – June 23, 2017 Over the last decade there has been a lot of progress in understanding gapped quantum phases of matter. To a large extent this progress has been achieved by exploiting connections to seemingly unrelated areas of mathematical physics, such as Topological … Read more
Organized by: Gregory Falkovich and Alexander Zamolodchikov Fluid mechanics in two dimensions has wide range of applications and possesses unique mathematical properties which are far from being fully explored and used. A landmark feature of turbulence in two dimensions is an inverse cascade, that is an appearance of large vortices and jets out of multi-scale … Read more
