Prof. Yilin Wang
Institut des Hautes Études Scientifiques (IHES)
The Brownian loop measure on Riemann surfaces and applications to length spectra
Friday, April 11th, 2025 - 14:30
Room 1A150 Torre Archimede
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The goal of this talk is to showcase how we can use stochastic processes to study the geometry of surfaces. More precisely, I will recall the basic facts about surfaces with constant curvature and Brownian motion on them. Then, we use the Brownian loop measure to express the lengths of closed geodesics on a hyperbolic surface and zeta-regularized determinant of the Laplace-Beltrami operator. This gives a tool to study the length spectra of a hyperbolic surface and we obtain a new identity between the length spectrum of a compact surface and that of the same surface with an arbitrary number of additional cusps. This is a joint work with Yuhao Xue (IHES).
Short Bio
Prof. Yilin Wang is a rising star in mathematics, specializing in probability theory and its applications to geometry. She is currently Junior Professor and mathematician at IHES, near Paris. In July 2025, she will join ETH Zürich as an Associate Professor.
She completed her Ph.D. at ETH Zürich in 2019. Prof. Wang's groundbreaking work has earned her the 2024 Salem Prize, awarded by Institute for Advanced Study, and the 2022 Maryam Mirzakhani New Frontiers Prize. She is an ERC Starting Grant recipient for her project on random conformal geometry and Teichmüller theory. Prof. Wang is an invited speaker at both the 2024 European Congress of Mathematics and the International Congress of Mathematical Physics.
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