# Events for 10/04/2019 from all calendars

## Probability Seminar

**Time: ** 11:30AM - 12:30PM

**Location: ** BLOC 628

**Speaker: **Axel Sáenz, Tulane

**Title: ***Stationary dynamics in finite time for the totally asymmetric simple exclusion process*

**Abstract: **The totally asymmetric simple exclusion process (TASEP) is a
Markov process that is the prototypical model for transport phenomena in
non-equilibrium statistical mechanics. It was first introduced by
Spitzer in 1970, and in the last 20 years, it has gained a strong
resurgence in the emerging field of "Integrable Probability" due to
asymptotic results from Johansson in 2000 and Tracy and Widom in 2007
(among other related results). In particular, these formulas led to
great insights regarding fluctuations related to the Tracy-Widom
distribution and scalings to the Kardar-Parisi-Zhang (KPZ) stochastic
differential equation.
In this joint work with Leonid Petrov (University of Virginia), we
introduce a new and simple Markov process that maps the distribution of
the TASEP at time t>0 , given step initial time data, to the
distribution of the TASEP at some earlier time t−s>0. This process "back
in time" is closely related to the Hammersley process introduced by
Hammersley in 1972, which later found a resurgence in the longest
increasing subsequence problem in the work of Aldous and Diaconis in
1995. Hence, we call our process the backwards Hammersley-type process
(BHP). As a fun application of our results, we have a new proof of the
limit shape for the TASEP. The central objects in our constructions and
proofs are the Schur point processes and the Yang-Baxter equation for
the sl_2 quantum affine Lie algebra. In this talk, we will discuss the
background in more detail and will explain the main ideas behind the
constructions and proof.

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 1:50PM - 2:50PM

**Location: ** BLOC 628

**Speaker: **Wencai Liu, Texas A&M University

**Title: *** Anderson localization for multi-frequency quasi-periodic operators on higher dimensional latices*

**Abstract: **The first part of the talk, based on a joint work with S. Jitomirskaya and Y. Shi, is devoted to study
multi-frequency quasi-periodic operators on higher dimensional lattices. We establish
the Anderson localization for general analytic $k$-frequency quasi-periodic
operators on $\Z^d$ for arbitrary $k, d$.
This is a generalization of Bourgain-Goldstein-Schlag's result $b=d=2$ and Bourgain's result $b=d\geq 3$. Our proof works for Toeplitz operators as well. In the second part of the talk, I will discuss several closely related topics. For example,
1. Use the quantitative unique continuation to establish the Anderson localization of random Schr\"odinger operators with singular distributions.
2. Use rotation $C^{\star}$ algebra to tackle the dry ten Martini problem (gap labelling theorem).
3. Use the machinery of proof of Anderson localization to construct KAM (Kolmogorov-Arnold-Moser) tori for NLS and NLW equations.

## Algebra and Combinatorics Seminar

**Time: ** 3:00PM - 3:50PM

**Location: ** BLOC 628

**Speaker: **Daniel Eman, Wisconsin

**Title: ***Asymptotic syzygies*

**Abstract: **Asymptotic syzygies refers to the study of the syzygies of a
variety under increasingly ample embeddings; the canonical example is to
study the syzygies of projective space under the d-uple embedding as d
goes to infinity. I’ll discuss some open questions related to asymptotic
syzygies, and some recent work of myself and Jay Yang which uses a
combinatorial model to produce new heuristics about this topic.

## Geometry Seminar

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

**Location: ** BLOC 628

**Speaker: **Ursula Whitcher, University of Michigan

**Title: ***Zeta functions of alternate mirror Calabi-Yau families*

**Abstract: **Mirror symmetry predicts surprising geometric correspondences between
distinct families of algebraic varieties. In some cases, these
correspondences have arithmetic consequences. For example, one can use
mirror symmetry to explore the structure of the zeta function, which
encapsulates information about the number of points on a variety over a
finite field. We prove that if two Calabi-Yau invertible pencils in
projective space have the same dual weights, then they share a common
polynomial factor in their zeta functions related to a hypergeometric
Picard-Fuchs differential equation. The polynomial factor is defined
over the rational numbers and has degree greater than or equal to the
order of the Picard-Fuchs equation. This talk describes joint work with
Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, and John
Voight.

## Linear Analysis Seminar

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

**Location: ** BLOC 220

**Speaker: **Jurij Volcic, TAMU

**Title: ***Noncommutative polynomials describing convex sets*

**Abstract: **The free semialgebraic set D determined by a hermitian noncommutative
polynomial f is the set of tuples of hermitian matrices X such that f(X)
is positive semidefinite. When f is a hermitian monic linear pencil, D
is called a free spectrahedron. Since it is the feasible set of a linear
matrix inequality (LMI), it is evidently convex. Conversely, it is
well-known that every convex free semialgebraic set is a free
spectrahedron. This talk presents a solution to the basic problem of
determining those noncommutative polynomials f for which D is convex. A
consequence is an effective probabilistic algorithm that not only
determines if D is convex, but also produces its LMI representation.
Further results address 1x1 noncommutative polynomials describing convex
sets.