# Events for 03/22/2019 from all calendars

## Working Seminar on Quantum Groups

Time: 10:30AM - 12:30PM

Location: BLOC 624

Speaker: Kari Eifler, TAMU

Title: Infinite dimensional representations, II

## Probability Seminar

Time: 11:00AM - 12:00PM

Location: BLOC 628

Speaker: Eunghyun Lee, Nazarbayev University

Title: Exact formulas in the multi-species ASEP

Abstract: In this talk, we introduce the exact formulas of transition probabilities and the block probabilities" of ASEP with multi-species. In particular, we extend Chatterjee and Schutz's result (2010, JSP) on the TASEP with second class particles which gives some determinantal formulas to the ASEP with multi-species. Also, we discuss about similar results for other multi-species models.

## Combinatorial Algebraic Geometry

Time: 11:00AM - 11:00AM

Location: Bloc 605AX

Speaker: Emanuele Ventura, Texas A&M University

Title: On the monic rank

Abstract: We introduce the monic rank of a vector relative to an affine-hyperplane section of an irreducible Zariski-closed affine cone X. This notion is well-defined and greater than or equal to the usual X-rank. We describe an algorithmic technique based on classical invariant theory to determine, in concrete situations, the maximal monic rank. Using this technique, we establish three new instances of a conjecture due to Shapiro which states that a binary form of degree d\times e is a sum of d many d-th powers of forms of degree e. This is joint work with A. Bik, J. Draisma, and A. Oneto.

## Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: P. Kuchment, Texas A&M

Title: Non-degeneracy of spectral edges for periodic operators (Joint work with Ngoc Do (U. Arizona) and F. Sottile (TAMU))

Abstract: An old problem in mathematical physics deals with the structure of the dispersion relation of the Schroedinger operator -\Delta+V(x) in R^n with periodic potential near the edges of the spectrum, i.e. near extrema of the dispersion relation. A well known and widely believed conjecture says that generically (with respect to perturbations of the periodic potential) the extrema are attained by a single branch of the dispersion relation, are isolated, and have non-degenerate Hessian. In particular, the notion of effective masses hinges upon this conjecture. The progress in proving this conjecture has been rather slow. It is natural to try to look at discrete problems, where the dispersion relation is (in appropriate coordinates) an algebraic, rather than analytic, variety. Moreover, such models are often used for computation in solid state physics (the so called tight binding model). However, counterexamples exist that show that the genericity can fail in discrete situation. The authors consider the case of a general periodic discrete operator depending polynomially on some parameters and prove that the non-degeneracy of extrema either fails for all values of parameters, or holds for all values except of a proper algebraic subset. Thus, finding a single point in the parameter space where the non-degeneracy holds implies that it holds generically.

## Working Seminar in Groups, Dynamics, and Operator Algebras

Time: 2:00PM - 2:00PM

Location: BLOC 605AX

Speaker: Xin Ma, Texas A&M University

Title: Topological full groups of one-sided shifts of finite type XII

## Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Title:

## Student Working Seminar in Groups and Dynamics

Time: 3:00PM - 4:00PM

Location: BLOC 506A

Speaker: Alex Weygandt

Title: A crash course in operator K-Theory

Abstract: Operator K-Theory is a pair of functors, associating to each C^*-algebra A a pair of abelian groups K_0(A) and K_1(A), containing information about the structure of A. In this talk, I will show how these groups are constructed, some basic computational tools, and (time permitting) the calculation of K-groups of C*-algebras associated to groups and dynamics.

## Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Igor Zelenko, TAMU

Title: Projective and affine equivalence of sub-Riemannian metrics: generic rigidity and separation of variables conjecture.

Abstract: Two sub-Riemannian metrics are called projectively equivalent if they have the same geodesics up to a reparameterization and affinely equivalent if they have the same geodesics up to affine reparameterization. In the Riemannian case both equivalence problems are classical: local classifications of projectively and affinely equivalent Riemannian metrics were established by Levi-Civita in 1898 and Eisenhart in 1923, respectively. In particular, a Riemannian metric admitting a nontrivial (i.e. non-constant proportional) affinely equivalent metric must be a product of two Riemannian metrics i.e. certain separation of variable occur, while for the analogous property in the projectively equivalent case a more involved (twisted") product structure is necessary. The latter is also related to the existence of sufficiently many commuting nontrivial integrals quadratic with respect to velocities for the corresponding geodesic flow. We will describe the recent progress toward the generalization of these classical results to sub-Riemannian metrics. In particular, we will discuss genericity of metrics that do not admit non-constantly proportional affinely/projectively equivalent metrics and the separation of variables on the level of linearization of geodesic flows (i.e. on the level of Jacobi curves) for metrics that admit non-constantly proportional affinely equivalent metrics. The talk is based on the collaboration with Frederic Jean (ENSTA, Paris) and Sofya Maslovskaya (INRIA, Sophya Antipolis).

.