Events for 11/03/2021 from all calendars

Probability Seminar

Time: 10:00AM - 11:00AM

Location: Zoom/BLOC 302

Speaker: Evgeni Dimitrov, Columbia University

Title: Gibbsian line ensembles and beta-corners processes

Abstract: Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability. Gibbsian line ensembles can be thought of as collections of finite or countably infinite independent random walkers whose distribution is reweighed by the sum of local interactions between the walkers. I will discuss some recent progress in the asymptotic study of Gibbsian line ensembles, summarizing some joint works with Barraquand, Corwin, Matetski, Wu and others. Beta-corners processes are Gibbs measures on triangular arrays of interacting particles and can be thought of as analogues/extensions of multi-level spectral measures of random matrices. I will discuss some recent progress on establishing the global asymptotic behavior of beta-corners processes, summarizing some joint works with Das and Knizel.

Number Theory Seminar

Time: 11:00AM - 12:00PM

Location: BLOC 302

Speaker: Matt Papanikolas, Texas A&M University

Title: Product formulas for periods of Drinfeld modules

Abstract: We investigate new formulas for periods and quasi-periods of Drinfeld modules, similar to the product formula for the fundamental period of the Carlitz module. To these ends we develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson generating functions. One particular advantage is that these infinite products can be obtained from only a finite amount of initial calculation. Joint with C. Khaochim.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: online

Speaker: Yuqing Frank Lin, Texas A&M

Title: On Invariant Random Orders

Abstract: We introduce a probabilistic analog of left-invariant total orders on countable groups called (left) invariant random orders (IROs). IROs have been applied in recent years to obtain results in entropy theory by providing a notion of a "past". We discuss several questions on IROs in analogy to (deterministic) left-invariant orders. For example IROs can be seen to be more flexible than (deterministic) left-invariant orders- IROs always exist for any countable group and partial orders can be extended to IROs for any amenable group. Nevertheless, we show an example of a partial order that cannot be extended to an IRO. Joint work with Yair Glasner and Tom Meyerovitch.

Topology Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Cheuk Yu Mak, University of Edinburgh

Title: Lagrangian Floer theory and a simplicity problem

Abstract: It is a classical and fundamental problem to study algebraic properties (e.g. simplicity, perfectness) of the automorphism group of an object. Building on the foundational works of Kirby, Thurston, Fathi and many others, there are a lot of studies for the automorphism group of compact (smooth) manifolds, possibly equipped with additional structures. When it comes to the simplicity of volume preserving homeomorphism groups, surprisingly, the higher dimensional cases are well-understood and the 2 dimensional case is more mysterious. In this talk, I will explain how to combine ideas from Lagrangian Floer theory and Hofer geometry to completely resolve this 40-year-old question. The technical heart of the proof is an extension of Calabi homomorphism, which answers a question of Ghys at his 2006 ICM talk on knots and dynamics. This is based on a joint work with Daniel Cristofaro-Gardiner, Vincent Humili`ere, Sobhan Seyfaddini and Ivan Smith.