Mini courses:
Dmitry Chelkak: TBA
Jorg Teschner: TBA
Marta Mazzocco: Confluencing moduli spaces
Anton Zorich: Random square-tiled surfaces, and random flat and hyperbolic surfaces of large complexity
Talks:
Cedric Boutillier, The dimer model with Fock's weights on the Aztec diamond and related graphs
Abstract: In a joint work with Béatrice de Tilière, we construct an explicit expression for the inverse Kasteleyn matrix of the dimer model on the Aztec diamond of size n, for a particular choice of weights, due to Vladimir Fock, defined in terms of theta functions on a maximal Riemann surface (any weight function is gauge equivalent to such a particular Fock weight function). We explain some consequences of this formula to understand limit shape for the Aztec diamond, beyond the arctic circle theorem. We also present a work in progress with Bishal Deb and Béatrice de Tilière to extend this construction to a much larger family of graphs, considered by David Speyer.
Oleg Lisovyi, TBA
Jiasheng Lin, Twist Operators from Entanglement and Related Questions (informal but with slides)
Abstract: I'll explain a setting in quantum information where twist Operators of a CFT naturally shows up (originally due to Cardy and Calabrese). Then I'll raise some questions towards possible rigorous construction and analysis of these objects: their relation to magnetic operators, flat bundles, and zeta determinant of self-adjoint Laplacians with twist boundary conditions, ... and much more! (Tentative)
Niklas Affolter, Dimers, Ising and Discrete Geometry
Shinji Koshida, TBA
Sid Maibach, TBA
Tianyue Liu, Asymptotics of $b$-6j symbols from $U_q\mathfrak{sl}(2; R)$
Abstract: In this talk I will present recent results on various classical limits of the b-6j symbol and relate them to the geometry of hyperideal tetrahedrons. We will discuss two regimes: In the first we obtain the volume of hyperbolic tetrahedrons, which has been used to show that a Turaev-Viro type invariant recovers the hyperbolic volumes for certain three manifolds. In the second we obtain the volume of AdS tetrahedrons, which are related to the generating function between Fenchel-Nielson coordinates on a four-hole sphere. This talk is based on joint work with Shuang Ming, Xin Sun, Baojun Wu and Tian Yang.
Duong Dinh, Fourier transforms for integrable systems
Abstract: Let C be a Riemann surface, possibly with punctures, of negative Euler characteristic. The geometric (analytic) Langlands correspondence is a spectral decomposition for sheaves (square-integrable functions) on the moduli of bundles on C in terms of local systems (real opers) on C, and can be regarded as some sort of non-abelian Fourier transforms for quantum integrable systems. I will discuss how one can realize these transforms, as well as their classical limits and quantization. This talk is from works with Joerg Teschner and ongoing works with Dima Arinkin.