# Plenary Talks

Schedule:

- Monday, Jul 23 [symposia auditorium]
- 11:00 Gilles Brassard (Université de Montréal),
*No presentation title available* - 14:00 Subir Sachdev (Harvard University),
*No presentation title available* - Tuesday, Jul 24 [symposia auditorium]
- 09:00 Thibault Damour (Institut des Hautes Études Scientifiques),
*No presentation title available* - 10:30 Lai-Sang Young (New York University),
*No presentation title available* - Wednesday, Jul 25 [symposia auditorium]
- 09:00 Duncan Haldane (Princeton University),
*No presentation title available* - 10:30 Anne-Laure Dalibard (Université Pierre et Marie Curie),
*No presentation title available* - 11:30 Alessandro Giuliani (Università di Roma Tre), Universal fluctuations in interacting dimers
- Thursday, Jul 26 [symposia auditorium]
- 09:00 John Cardy (University of California), The $T\overline T$ deformation of quantum field theory
- 10:30 Slava Rychkov (The Institut des Hautes Études Scientifiques), Conformal Field Theory and Critical Phenomena in $d=3$
- 11:30 Rupert Frank (LMH Műnich),
*No presentation title available* - Friday, Jul 27 [symposia auditorium]
- 09:00 Masatoshi Noumi (Kobe University), Elliptic hypergeometric functions and elliptic difference Painlevé equation
- 10:30 Jean-Christophe Mourrat (École Normale Supérieure Paris), Quantitative stochastic homogenization
- 11:30 Fabio Toninelli (Université Claude Bernard Lyon 1), (2+1)-dimensional Stochastic Interface Dynamics
- Saturday, Jul 28 [symposia auditorium]
- 09:00 Edward Witten (Institute for Advanced Study), Open and Closed Topological Strings In Two Dimensions
- 10:30 Richard Kenyon (Brown University), Analytic limit shapes for the 5 vertex model
- 11:30 Lisa Jeffrey (University of Toronto),
*No presentation title available*

- Universal fluctuations in interacting dimersIn the last few years, the methods of constructive Fermionic Renormalization Group have successfully been applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including: weakly non-planar 2D Ising models, Ashkin-Teller, 8-Vertex, and close-packed interacting dimer models. In this talk, I will focus on the illustrative example of the interacting dimer model and review some of the universality results derived in this context. In particular, I will discuss a proof of the massless Gaussian free field (GFF) behavior of the height fluctuations. It turns out that GFF behavior is connected with a remarkable identity (`Haldane relation') between an amplitude and an anomalous critical exponent, characterizing the large distance behavior of the dimer-dimer correlations. Based on joint works with V. Mastropietro and F. Toninelli.
- The $T\overline T$ deformation of quantum field theoryThe $T\overline T$ deformation is a modification of local 2d QFT at short distances which is in some sense solvable. I argue that this is because it corresponds to coupling the theory to a random metric whose action is topological. Under the deformation, partition functions satisfy linear diffusion-type equations which describe a kind of Brownian motion in the moduli space of the world sheet manifold.
- Elliptic hypergeometric functions and elliptic difference Painlevé equationElliptic hypergeometric functions are a new class of special functions that have been developed during these two decades. In this talk I will give an overview of various aspects of elliptic hypergeometric series and integrals with emphasis on connections with integrable systems including the elliptic difference Painlevé equation.
- Quantitative stochastic homogenizationOver large scales, many disordered systems behave similarly to an equivalent "homogenized" system of simpler nature. A fundamental example of this phenomenon is that of reversible diffusion operators with random coefficients. The homogenization of these operators has been well-known since the late 70's. I will present recent results that go much beyond this qualitative statement, reaching optimal rates of convergence and a precise description of the next-order fluctuations. The approach is based on a rigorous renormalization argument and the idea of linearizing around the homogenized limit.
- (2+1)-dimensional Stochastic Interface DynamicsThe goal of this talk is to discuss large-scale dynamical behavior of discrete interfaces. These stochastic processes model diverse statistical physics phenomena, such as interface growth by random deposition or the motion, due to thermal fluctuations, of the boundary between coexisting thermodynamic phases. While most known rigorous results concern (1+1)-dimensional models, I will present some recent ones in dimension (2+1). On the basis of a few concrete models, I will discuss both: (1) two-dimensional interface growth and the so-called Anisotropic KPZ universality class; and (2) reversible interface dynamics and the emergence of hydrodynamic limits, in the form of non-linear parabolic PDEs.
- Open and Closed Topological Strings In Two DimensionsSeveral decades ago, three parallel theories of two-dimensional quantum gravity were developed, involving random matrices; Liouville theory coupled to matter; and topological field theory. The first two approaches have fairly straightforward extensions to the case of quantum gravity on a two-manifold with boundary, but the third does not. However, an extension of the third approach was discovered relatively recently by Pandharipande, Solomon, and Tessler, with later work by Buryak and Tessler. In this talk (based on work with R. Dijkgraaf), I will explain their construction in a more physical language.
- Analytic limit shapes for the 5 vertex modelThis is joint work with Jan de Gier and Sam Watson. The Bethe Ansatz is a very old technique but using some new tools inspired by conformal invariance we can make progress on both the limit shape phenomenon and fluctuations for models beyond free fermionic models. In particular using the Bethe Ansatz we find an explicit expression for the free energy of the five vertex model. The resulting Euler-Lagrange equation can be reduced to an equation generalizing the complex Burgers' equation. We show how to solve this equation, giving analytic parameterizations for limit shapes.