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SUMMARY:The Brownian loop measure on Riemann surfaces and applications to 
 length spectra - Yilin Wang (IHES)
DTSTART:20241203T140000Z
DTEND:20241203T150000Z
UID:TALK224593@talks.cam.ac.uk
CONTACT:118195
DESCRIPTION:The Brownian loop measure on the Riemann sphere was introduced
  by Lawler and Werner in studying the Schramm-Loewner evolution. We consid
 er its generalization to an arbitrary Riemann surface and show that the le
 ngths of closed geodesics are encoded in the Brownian loop measure. This g
 ives a tool to study the length spectra of Riemann surfaces. In particular
 \, using properties of the Brownian loop measure\, we obtain a new identit
 y between the length spectrum of a surface and that of the same surface wi
 th an arbitrary number of additional cusps. We also express the determinan
 t of Laplacian of a compact hyperbolic surface as the total mass of Browni
 an loop measure renormalized according to the length spectrum. This is bas
 ed on a joint work with Yuhao Xue (IHES).\n
LOCATION:MR12
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