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Lie Group Quantum Mathematics Seminar

General Relativity and Integrability

Robert Penna, Institute for Advanced Study, School of Natural Sciences

Location:  Zoom
Date & time: Friday, 01 April 2022 at 12:10PM - 1:10PM

Abstract: A remarkable fact about general relativity is that it admits many exact solutions.  This fact can be explained (at least in many cases) by the fact that the dimensional reduction of general relativity to two spacetime dimensions is an integrable system.   The 2d theory has an infinite dimensional hidden symmetry called the Geroch group that underlies its integrability.  I will review this story and then describe a new exact solution for gravitational pulse wave scattering.  The pulses maintain their shapes after scattering, as in ordinary soliton scattering.  In the last part of the talk, I will describe evidence for a further symmetry enhancement in one dimension.   This enhanced symmetry is apparently a hyperbolic Kac-Moody algebra, which is an interesting and mysterious mathematical object in its own right.

Zoom link
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module

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