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# Events for January 26, 2018 from General and Seminar calendars

## Newton-Okounkov bodies seminar

**Description:** Title: Overview of "Mixed volumes and an extension of intersection theory of divisorsâ€ť by Kaveh-Khovanskii, and organizational matters.

## Algebra and Combinatorics Seminar

**Abstract:** In this talk, we will characterize the irreducible quasifinite highest weight modules of some subalgebras of the Lie algebra of matrix quantum pseudodifferential operators N x N. In order to do this, we will first give a complete description of the anti-involutions that preserve the principal gradation of the algebra of NxN matrix quantum pseudodifferential operators and we will describe the Lie subalgebras of its minus fixed points. We will obtain, up to conjugation, two families of anti-involutions that show quite different results when n=N and n

## Hiring Candidate - Dr. Jeffrey Kuan

**Description:**

**Time:** 1:00PM - 2:30PM

**Location:** BLOC 624

**Speaker:** Frank Sottile, Texas A&M University

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Karina Batistelli, U. N. Cordoba

**Title:** *Some Lie subalgebras of the matrix quantum pseudo-differential operators*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Dr. Jeffrey Kuan, Columbia University

Title: Algebraic constructions of Markov duality functions

Abstract: Markov duality in spin chains and exclusion processes has found a wide variety of applications throughout probability theory. We review the duality of the asymmetric simple exclusion process (ASEP) and its underlying algebraic symmetry. We then explain how the algebraic structure leads to a wide generalization of models with duality, such as higher spin exclusion processes, zero range processes, stochastic vertex models, and their multi-species analogues.