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
Geometric representation theory Organized by: David Ben-Zvi, Roman Bezrukavnikov and Alexander Braverman January 4-29th, 2016 The program will focus on emerging trends in representation theory and their relation to the more traditional ideas of the subject. The celebrated success of the perverse sheaves methods in 1980’s has led to development of a direction which may … Read more
Moduli spaces and singularities in algebraic and Riemannian geometry Organized by Simon Donaldson (SCGP), Hans-Joachim Hein (Maryland), Henry Guenancia (Stony Brook), Radu Laza (Stony Brook), Yuji Odaka (Kyoto), Song Sun (Stony Brook),Valentino Tosatti (Northwestern) August 17-November 20th, 2015 Weekly Talks are held in SCGP Rm 313. The theme of this program is the interaction between … Read more
Foundations and Applications of Random Matrix Theory in Mathematics and Physics Organized by Alexei Borodin,Peter Forrester, Yan Fyodorov, Alice Guionnet, Jon Keating, Mario Kieburg, and Jacobus Verbaarschot August 24 – December 18, 2015 Weekly Talks are held in SCGP Room 313 at 11:00 am. Random Matrix theory has been applied to many areas in pure … Read more
Organized by Robert Berman, Semyon Klevtsov, Paul Wiegmann, and Steve Zelditch April 20 – June 19, 2015 This program centers on the use of holomorphic sections of high powers of positive Hermitian holomorphic line bundles over a Kahler manifold to construct projective embeddings, Bergman Kahler metrics, and Gaussian random fields. The main tool is the … Read more
Organized by Sergei Gukov, Mikhail Khovanov, and Piotr Sulkowski March 16 – June 12, 2015 The aim of this program is to understand new relations between knot theory, supersymmetric field theories, and string theory. Tremendous development in knot theory in recent decades led to the formulation of polynomial knot invariants, such as the Jones polynomial … Read more
