Mathematical Problems in General Relativity Organized by Mike Anderson, Sergiu Klainerman, Philippe LeFloch, and Jared Speck January 5 – February 6, 2015 Einsteins field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts, … Read more
Geometric Flows Organized by Simon Brendle, Xiuxiong Chen, Simon Donaldson, and Yuanqi Wang October 13 – December 19, 2014 Since its invention in 1982, Hamilton’s Ricci flow has become a central tool in global differential geometry. In particular, the Ricci flow has played a central role in Perelman’s proof of the Poincare conjecture, as well … Read more
Interactions of Homotopy Theory and Algebraic Topology with Physics through Algebra and Geometry Organized by John Morgan and Dennis Sullivan October 1, 2014 – June 30, 2015 While activities will depend on the visitors for their specific focus, we expect them to be organized around several general themes: (i) rigorous approaches to perturbative quantum field theories, and especially to gauge theories … Read more
Gauge Theory, Integrability, and Novel Symmetries of Quantum Field Theory Organized by Anton Kapustin, Nikita Nekrasov, Samson Shatashvili, Volker Schomerus, and Konstantin Zarembo September 2 – December 19, 2014 The interplay between the supersymmetric gauge theories and (non-supersymmetric) integrable theories in various dimensions is a puzzling development of several decades of research. In recent years … Read more
G2 Manifolds Organized by Mark Haskins, Dietmar Salamon, and Simon Donaldson August 18 – October 3, 2014 This program seeks to connect recent developments and open questions in the theory of compact manifolds with special or exceptional holonomy (especially G_2 manifolds) with other areas of mathematics and theoretical physics: differential topology, algebraic geometry, (non compact) Calabi-Yau … Read more
Organized by Kenji Fukaya, Dusa McDuff, and John Morgan January 2 – June 30, 2014 Gromov-Witten theory, Lagrangian-Floer homology and symplectic field theory arise from the notion of pseudo-holomorphic curves, possibly with boundary conditions, in symplectic manifolds. All these theories rely in a fundamental way on Gromov’s compactness result for moduli spaces of pseudo-holomorphic curves, … Read more
Quantum Anomalies, Topology, and Hydrodynamics Organized by Alexander Abanov, Dmitri Kharzeev, Boris Khesin, Dam Son, and Paul Wiegmann February 17-June 13, 2014 Recent developments in relativistic hydrodynamics place it at the crossroads of nuclear physics, condensed matter physics and string theory. Hydrodynamics is known to be very effective in describing the long-wavelength behavior of many … Read more
Organized by Ljudmila Kamenova, Alexander Kirillov, Jr., Nikita Nekrasov, and Olivier Schiffmann September 30 – November 8, 2013 Quivers and quiver varieties, introduced and studied in a series of papers of Nakajima, Lusztig, Ringel and others in 1990s, have since appeared in many areas of mathematics and mathematical physics, from gauge theory, string theory, … Read more
Physics and Mathematics of Scattering Amplitudes Organized by Zvi Bern, Lance Dixon, Michael Douglas, Alexander Goncharov, and Lionel Mason Fall 2013 Starting date: August 26, 2013 The study of scattering amplitudes in relativistic quantum field theory has undergone a remarkable renaissance and transformation in recent years, with the advent of new perturbative approaches such … Read more
Mock Modular Forms, Moonshine, and String Theory Organized by Miranda Cheng, Matthias Gaberdiel, and Terry Gannon August 26 – September 27, 2013 Modular functions, Jacobi forms and mock modular forms appear naturally in various contexts in string theory and conformal field theory. In particular, characters of conformal field theories (CFTs) define (vector-valued) modular functions, while … Read more
