Calendar
Thursday, October 24, 2024
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All day |
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3pm |
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4pm |
10/24/2024 - 4:00pm Since the work of Jensen–Kato, the analysis of the Schrodinger–Helmholtz equation at low energy has been used to study wave propagation in various settings, both relativistic and nonrelativistic. Recently, Hintz has used these methods to study wave propagation on black hole spacetimes. Part of Hintz’s result is the production of asymptotics in all possible asymptotic regimes, including all joint large-time, large-radii regimes. We carry out the analogue of this analysis for the Schrodinger equation. Based on joint work with Shi-Zhuo Looi. Location:
KT 207
10/24/2024 - 4:30pm H Verlinde suggested in 1980’s to use quantization of the Teichmüller spaces of surfaces to study the spaces of conformal blocks for the Liouville conformal field theory. This suggestion initiated and stimulated the development of quantum Teichmüller theory, and the first major steps were taken by Kashaev and by Chekhov and Fock in 1990’s, where the Chekhov-Fock quantization is generalized later by Fock and Goncharov to quantization of cluster varieties. The modular functor conjecture asserts that these quantum theories of Teichmüller spaces indeed yield a 2-dimensional modular functor, which can be viewed as one axiomatization of conformal field theory. The core part of the conjecture says that, for each punctured surface S and an essential simple loop in S, the Hilbert space associated to S by quantum Teichmüller theory should decompose into the direct integral of the Hilbert spaces associated to the surface obtained by cutting S along the loop and shrinking the holes to punctures. I will give an introduction to this story and present some recent developments, including 2405.14727.
Location:
KT 101
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