Conference on Algebraic Geometry, Mathematical Physics, and Solitons

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This project will conduct a three day conference on the topic of "Algebraic Geometry, Mathematical Physics, and Solitons", to be hosted at Columbia University from October 7-9, 2022. This event will bring together early career researchers and world-renowned mathematicians from a variety of fields, including algebraic geometry and mathematical physics. The conference will be an opportunity for graduate students and postdoctoral fellows to interact with each other and with mathematicians from a wide range of mathematical disciplines. This broad perspective from some of the leading experts will be invaluable to early career researchers.Integrable systems were originally studied in physics in order to describe the integrals of motion arising in classical mechanics. The ideas and methods of integrable systems have since had a wide influence in many areas of mathematics. For example, the Schottky problem, a classical problem in the theory of Riemann surfaces, is deeply connected to the study of various integrable hierarchies, the Korteweg-De Vries and Kadomtsev-Petviashvili equations. The Korteweg-De Vries equation, a nonlinear partial differential equation, is notable for having soliton solutions, which are a type of nonlinear wave. More recently, the Korteweg-De Vries equation has appeared in the Witten conjectures on the enumerative geometry of the moduli space of compact Riemann surfaces of genus g. These conjectures were solved by Kontsevich, Okounkov-Pandharipande, and Mirzakhani, and led to surprising connections with dynamical systems, hyperbolic geometry, and Gromov-Witten theory. Other aspects of integrable systems connect to symmetry groups and to more general algebraic structures such as quantum groups, loop groups, and Cherednik algebras. In terms of the original physical motivation, integrable systems control the behavior of various supersymmetric quantum field theories and random matrices. The goal of the conference is to bring together these many different strands of mathematics and mathematical physics. The conference website can be found at https://math.columbia.edu/~agmps22/.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.