Abstracts

Speaker: Jeffrey Kuan

Title: Shift invariance for the multi-species q-TAZRP on the infinite line.

Abstract:

We prove a shift--invariance for the multi-species q--TAZRP (totally asymmetric zero range process) on the infinite line. Similar-looking results had appeared in works by [Borodin-Gorin-Wheeler] and [Galashin], using integrability, but are on the quadrant. The proof in this talk relies instead on a combinatorial approach, in which the state space is generalized to a poset, and the totally asymmetric process is generalized to a monotone process on a poset. The continuous-time process is decomposed into its discrete embedded Markov chain and its exponential holding times, and the shift-invariance is proved using explicit contour integral formulas. Open problems about multi-species ASEP will be discussed as well.

Speaker: Greta Panova

Title: Asymptotic Algebraic Combinatorics

Abstract:

Algebraic Combinatorics has been studying discrete structures coming from Representation Theory and Algebraic Geometry, which have since seen applicability to Statistical Mechanics in a natural way, like Gelfand-Tseltin patterns (Semi-Standard Young Tableaux) turning into lozenge tilings and Schur generating function being used to understand limit shapes.

The era of nice compact formulas, however, has passed and major open problems within the understanding of representation theoretic multiplicities (like Littlewood-Richardson and Kronecker coefficients) remain unsolved.

More recently, a connection with Computational Complexity Theory, has put a new demand towards understanding such quantities.

In this talk I will briefly explain some of these connections, and then show recent advances in understanding the asymptotics of quantities from Algebraic Combinatorics like the Littlewood-Richardson and Kronecker coefficients.

No special background will be assumed.

Speaker: Li-Cheng Tsai

Title: Some recent development in the weak noise theory for the KPZ equation

Abstract:

The variational principle, or the least action principle, offers a framework for the study of the Large Deviation Principle (LDP) for a stochastic system. The KPZ equation is a stochastic PDE that is central to a class of random growth phenomena. In this talk, we will study the Freidlin--Wentzell LDP for the KPZ equation through the lens of the variational principle. Such an approach goes under the name of the weak noise theory in physics. We will explain how to extract various limits of the most probable shape of the KPZ equation in the setting of the Freidlin--Wentzell LDP. We will also review the recently discovered connection of the weak noise theory to integrable PDEs.

This talk is based in part on joint works with Pierre Yves Gaudreau Lamarre and Yier Lin.

Speaker: Karl Liechty

Title: Introduction to the six-vertex model

Abstract:

This talk will be about the six-vertex model, a well-known integrable model in 2-dimensional statistical physics which was first suggested in the work of the Nobel Laureate chemist (and Oregon State alumnus) Linus Pauling back in 1935. I’ll talk a bit about the history of the model, but the talk will focus developments in the 21st century. Namely, I will discuss the six-vertex model with fixed boundary conditions which induce the phenomenon of spatial phase separation, giving rise to many unanswered questions and connections to various other problems in mathematics and physics.