Schedule

• Sep 14

  Pu Yu (NYU)

  Note: Starting at 4:00 PM

  Convergence of tree-weighted maps under Riemann uniformization embedding

  Abstract: One natural way to draw a planar map is to use the Riemann uniformization embedding, where one views each face of degree p as a unit side length regular p-gon, and glue them all together to create a Riemann surface. In this talk, we show that under a conformal map, the Riemann surface encoded by spanning tree weighted maps is close to the SLE_8-decorated \sqrt{2}-Liouville quantum gravity surface encoded by Duplantier-Miller-Sheffield's mating-of-trees. Based on joint work with Nina Holden.

• Sep 21

• Sep 28

  Jeanne Boursier (MIT)

  Large deviations for the TAP landscape of Ising spin glasses

  Abstract: To understand spin glasses, physicists in the 1970s and 1980s began studying the landscape of a high-dimensional random function called the Thouless–Anderson–Palmer (TAP) free energy. Calculations imposing supersymmetry produced an elegant formula for counting critical points, but its probabilistic meaning remained unclear. I will explain how this formula governs rare events in the landscape: the probability that the maximum exceeds its typical value. The approach also provides a route to a constructive proof of Parisi’s formula for the limiting free energy of Ising spin glasses, extending ideas of Huang and Sellke for spherical models.

• Oct 5

  Sky Cao (U Penn)

  Construction of the 2D Yang-Mills-Higgs measure

  Abstract: I discuss the construction of the 2D Yang-Mills-Higgs (YMH) measure via stochastic quantization, or i.e. by Markov Chain Monte Carlo. To do so, we show global well-posedness and uniform-in-time bounds for the associated Langevin dynamics, given by the 2D stochastic YMH equations. A key component of our approach is the further development of techniques in stochastic geometric analysis, combining ideas from geometric analysis and stochastic analysis. These methods yield a manifestly gauge-covariant local existence theory, refined estimates for covariant stochastic objects, and a decay mechanism driven by unstable Yang-Mills connections. Based on joint work with B. Bringmann, M. Hairer, and W. Zhao.

• Oct 12

  Indigenous People's day

• Oct 19

  Ben Schweinhart (George Mason U)

• Oct 26

  Oanh Nguyen (Brown)

• Nov 2

  Reihaneh Malekian (Columbia)

• Nov 9

  William Da Silva (University of Vienna)

• Nov 16

  Jorge Garza Vargas (MIT)

• Nov 23

  Hang Du (MIT)

• Nov 30

  Anna Brandenberger (MIT)

• Dec 7