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Geometric Action-Angle Coordinates for Calogero-Moser type systems

Algebraic Geometry

Speaker: Matej Penciak, Northeastern University
Related Webpage: https://cos.northeastern.edu/people/matej-penciak/
Location: 2112 MSB
Start time: Wed, Mar 4 2020, 12:10PM

For completely integrable systems, finding the coordinates on the phase space in which the flows are particularly simple is a basic problem to solve. A moduli-theoretic description of the phase space of an integrable system in terms of spectral curves and line bundles serves as a way to tackle this problem. After reviewing the old work of David Ben-Zvi and Tom Nevins on the Calogero-Moser system, I will consider the analogous results for a closely related relativistic analogue of the CM system: the Ruijsenaars-Schneider system.

Finally, if time permits I will introduce a pair of problems that benefit from this perspective on the RS system: proving the 2D Toda-RS correspondence, and a new way of understanding the quantization of the RS system in terms of MacDonald difference operators