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)

  A Cellular Representation of Potts Lattice Gauge Theory

  Abstract: Graphical representations are a powerful tool in the study of lattice spin models. We will present an extension of this idea to higher dimensions wherein Potts lattice gauge theory --- which assigns spins to edges rather than vertices --- is coupled with a dependent plaquette percolation called the plaquette random cluster model. We show that Wilson loop expectations in Potts lattice gauge theory equal the probability of a topological event in the plaquette random cluster model. Applications include a proofs that Wilson loop expectations in three dimensions undergo a sharp phase transition from area law to perimeter law behavior, and that the self-dual point in four dimensions is the threshold for the existence of giant plaquette surfaces in the sense of homological percolation. Based on joint work with Paul Duncan. If time permits, I will discuss recent work with Summer Eldridge and Malin Forsström on an extension of this representation to the Potts lattice Higgs model.

• 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

  Seoyeon Yang (Princeton University)

• Nov 30

  Anna Brandenberger (MIT)

• Dec 7

  Hang Du (MIT)