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
Organized by: Simon Donaldson, Kenji Fukaya, and John Morgan The program will focus on various mathematical aspects of gauge theory, including applications to topology and geometry. This area of study began when Donaldson showed how to use the moduli space of ASD connections on auxiliary SU(2)-bundles of charge one on a Riemannian 4-manifold to study … Read more
Organized By: Chris Herzog, Vladimir Korepin and Bruno Nachtergaele. Entanglement is the property of quantum states that most clearly distinguishes them from classical states. Entanglement is responsible for the fascinating effects in the low-temperature states of matter and the phase transitions between them that are the subject of much research in experimental and theoretical … Read more
Geometry of Quantum Hall States Organized by Sasha Abanov, Tankut Can, Anton Kapustin, and Paul Wiegmann April 18, 2016 – June 17, 2016 The quantum Hall effect (QHE) is a fascinating and important phenomenon. Since its experimental discovery in the early 80’s the QHE continues to fuel work in experimental physics, metrology, fundamental theoretical physics … Read more
Complex, p-adic, and logarithmic Hodge theory and their applications Organized by Mark de Cataldo, Radu Laza, Christian Schnell March 7, 2016 – April 29, 2016 Hodge theory is a very powerful tool for understanding the geometry of complex algebraic varieties and it has a wide range of applications in complex and algebraic geometry, mirror symmetry, … Read more
Statistical mechanics and combinatorics Organized by Pavel Bleher, Vladimir Korepin, and Bernard Nienhuis February 15 – April 15, 2016 The purpose of the program is to relate physics and mathematics, and more specifically, statistical mechanics, algebraic combinatorics, and random matrices. The program will focus on the six-vertex model of statistical mechanics and related models, such … Read more
