Schedule

• Sep 8

  Pu Yu (NYU)
  3:15pm

  Convergence of circle packing for the mated-CRT map and triangulation from UST weighted maps

  Abstract: Liouville quantum gravity (LQG) is conjectured to describe scaling limits of random planar maps. One way to phrase the convergence of random planar maps is through conformal embeddings. This has been done by Holden and Sun (2019) for the uniform triangulation under Cardy embedding, and by Gwynne, Miller and Sheffield (2017) as well as Bertacco, Gwynne and Sheffield (2023) for the mated-CRT map under Tutte and Smith embedding. In this talk, I will discuss the convergence of the mated-CRT map to LQG and the triangulation from uniform spanning tree weighted maps through Mullin bijection to \sqrt{2}-LQG under circle packing. Based on joint work with Nina Holden.

• Sep 15

  Andres Contreras Hip (University of Chicago)

  Gaussian curvature for Liouville Quantum Gravity and random planar maps

  Abstract: Liouville quantum gravity is a canonical model for random surfaces conjectured to be the scaling limit of various planar maps. Since curvature is a central concept in Riemannian geometry, it is natural to ask whether this can be extended to LQG surfaces. In this talk, we introduce a notion of Gaussian curvature for LQG surfaces, despite their low regularity, and study the relations with its discrete counterparts. We conjecture that this definition of Gaussian curvature is the scaling limit of the discrete curvature. In support of this conjecture, we prove that the discrete curvature on the $\epsilon$-CRT map with a Poisson vertex set integrated with a smooth test function is of order $\epsilon^{o(1)},$ and show the convergence of the total discrete curvature on a CRT map cell when scaled by $\epsilon^{1/4}.$ Joint work with E. Gwynne.

• Sep 22

  Gabriel Raposo (UC Berkeley)

  Fluctuations for standard Young Tableaux

  Abstract: We will introduce the Young generating function and use it to characterize the law of large numbers and the central limit theorem behaviors for random partitions. As an application of these results, we present a framework to obtain conditional Gaussian Free Field fluctuations for height functions associated with random standard Young tableau. To prove these results we develop algebraic formulas for operators on the Gelfand–Tsetlin algebra of the symmetric group.

• Sep 29

  Eilon Solan (Tel-Aviv University)

  Equilibrium in Multiplayer Stopping Games

  Abstract: Stopping games generalize optimal stopping to settings with multiple decision makers. We work in discrete time on a filtered probability space. There are $N$ decision makers. For each nonempty subset $S \subseteq \{1,...,N\}$ there is an $\mathbb{R}^N$-valued stochastic process ($X^S_t$). At each stage, each decision maker, given their current information, chooses whether to stop or to continue. The game terminates (for everyone) at the first stage in which at least one decision maker stops; if the set of stoppers at that stage is $S$, then decision maker $i$ receives the $i$-th coordinate of $X^S_t$. Each player aims to maximize the expectation of their payoff.
  
  An $\epsilon$ equilibrium is a profile of (possibly randomized) stopping times such that no decision maker can gain more than $\epsilon$ by deviating while the others keep their stopping times fixed. When $N \leq 3$, an $\epsilon$-equilibrium is known to exist (assuming the payoff processes ($X^S_t$) are integrable). $When N \geq 4$, the existence of $\epsilon$-equilibria is an open problem.
  
  I will describe the model, survey known results, and present intriguing examples.

• Oct 6

  Oriol Sole Pi (MIT)

• Oct 13

  Indigenous People's day

• Oct 20

  Oren Yakir (MIT)

• Oct 27

  Melanie Matchett Wood (Harvard)

• Nov 3

  Daniel Lacker (Columbia University)

• Nov 10

  Holiday

• Nov 17

• Nov 24

  Juan Carlos Pardo Millan (CIMAT)

• Dec 1

• Dec 8