### MATH 7310 • Real Analysis and Linear Spaces I

[Spring 2019 semester]

### Gibbs measures, arctic curves, and random interfaces

This talk outlines connections between 2-dimensional Gibbs measures with a height function and particle systems in the Kardar-Parisi-Zhang universality class.

### The q-Hahn PushTASEP

[2018/11/15]

We introduce the $q$-Hahn PushTASEP — an integrable stochastic interacting particle system which is a 3-parameter generalization of the PushTASEP, a well-known close relative of the TASEP (Totally Asymmetric Simple Exclusion Process). The transition probabilities in the $q$-Hahn PushTASEP are expressed through the $_4\phi_3$ basic hypergeometric function. Under suitable limits, the $q$-Hahn PushTASEP degenerates to all known integrable (1+1)-dimensional stochastic systems with a pushing mechanism. One can thus view our new system as a pushing counterpart of the $q$-Hahn TASEP introduced by Povolotsky. We establish Markov duality relations and contour integral formulas for the $q$-Hahn PushTASEP. We also take a $q\to1$ limit of our process arriving at a new beta polymer-like model.

### Virginia Integrable Probability Summer School

Virginia Integrable Probability Summer School will be held at University of Virginia from May 27 to June 8, 2019

### Generalizations of TASEP in discrete and continuous inhomogeneous space

[2018/08/29]

We investigate a rich new class of exactly solvable particle systems generalizing the Totally Asymmetric Simple Exclusion Process (TASEP). Our particle systems evolve in discrete or continuous space and can be thought of as new exactly solvable examples of tandem queues, directed first- or last-passage percolation models, or Robinson-Schensted-Knuth type systems with random input. One of the features of the particle systems we consider is the presence of spatial inhomogeneity which can lead to the formation of traffic jams.

### Workshop on Representation Theory, Combinatorics, and Geometry

Workshop on Representation Theory, Combinatorics, and Geometry will be at University of Virginia on October 19-21, 2018. The workshop precedes the Virginia Mathematics Lectures by Andrei Okounkov (October 22-24)

### MATH 3100 • Introduction to Probability (2 sections)

[Fall 2018 semester]