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# Events for 02/14/2020 from all calendars

## Several Complex Variables Seminar

## Working Seminar on Quantum Computation and Quantum Information

## Algebra and Combinatorics Seminar

## Geometry Seminar

## Linear Analysis Seminar

**Time:** 10:20AM - 11:10AM

**Location:** BLOC 605AX

**Speaker:** Ciaran Buckley, Texas A&M University

**Title:** *Approximation by random complex functions*

**Abstract:** A presentation of some results from a recent paper by Paul M. Gauthier, Thomas Ransford, Simon St-Amant, and Je ́re ́mie Turcotte. In particular, generalizations of Runge's Theorem and the Oka-Weil Theorem.

**Time:** 2:00PM - 3:00PM

**Location:** Bloc 624

**Speaker:** Andrew Nemec, TAMU CS

**Title:** *Quantum Error Correction*

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

**Location:** BLOC 628

**Speaker:** Chun-Hung Liu, Texas A&M University

**Title:** *Well-quasi-ordering graphs by the topological minor relation*

**Abstract:** A well-quasi-ordering is a reflexive and transitive binary relation such that every infinite sequence has a non-trivial increasing subsequence. The study of well-quasi-ordering can be dated back to two conjectures of Vazsonyi proposed in 1940s stating that trees and subcubic graphs are well-quasi-ordered by the topological minor relation. Both conjectures have been solved, where the second conjecture is particularly difficult in the sense that the only known proof is via Robertson and Seymour's celebrated Graph Minor Theorem stating that the minor relation is a well-quasi-ordering. On the other hand, the topological minor relation is not a well-quasi-ordering in general. Robertson in 1980s conjectured that the known obstruction is the only obstruction. Joint with Robin Thomas, we solved Robertson's conjecture and proved a characterization of well-quasi-ordered topological-minor ideals. We will sketch some ideas in the proof.

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

**Location:** BLOC 628

**Speaker:** Vladimir Dragovic, UT Dallas

**Title:** *Periodic ellipsoidal billiards and Chebyshev polynomials on several intervals*

**Abstract:** A comprehensive study of periodic trajectories of the billiards within ellipsoids in the d-dimensional Euclidean space is presented. The novelty of the approach is based on a relationship established between the periodic billiard trajectories and the extremal polynomials of the Chebyshev type on the systems of d intervals on the real line. As a byproduct, for d = 2 a new proof of the monotonicity of the rotation number is obtained and the result is generalized for any d. The case study of trajectories of small periods T, d < T < 2d is given. In particular, it is proven that all d-periodic trajectories are contained in a coordinate-hyperplane and that for a given ellipsoid, there is a unique set of caustics which generates d + 1-periodic trajectories. A complete catalog of billiard trajectories with small periods is provided for d = 3. This talk is based on: V. Dragovic, M. Radnovic, Periodic ellipsoidal billiard trajectories and extremal poly- nomials, arXiv 1804.02515, Comm. Math. Physics. https://doi.org/10.1007/s00220- 019-03552-y, 2019, Vol. 372, p. 183-211. V. Dragovic, M. Radnovic, Caustics of Poncelet polygons and classical extremal polynomials, arXiv 1812.02907, Regular and Chaotic Dynamics, (2019), Vol. 24, No. 1, p. 1-35. A. Adabrah, V. Dragovic, M. Radnovic, Periodic billiards within conics in the Min- kowski plane and Akhiezer polynomials, arXiv; 1906.0491, Regular and Chaotic Dy- namics, No. 5, Vol. 24, 2019, p. 464-501.

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

**Location:** BLOC 220

**Speaker:** Michael Brannan, TAMU

**Title:** *Non-local Games and the Connes Embedding Conjecture*

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