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)

• Sep 29

  Eilon Solan (Tel-Aviv University)

• 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