Events for 10/28/2016 from all calendars

Working Seminar on Quantum Groups

Time: 11:00AM - 12:00PM

Location: BLOC 628

Speaker: Sanggyun Youn, Seoul National University

Title: The Schur orthogonality relations

Abstract: We will prove the quantum analogue of the Schur orthogonality relations for matrix elements of irreducible unitary representations.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Jacob White, UTRGV

Title: An introduction to Coloring Problems

Abstract: Many combinatorial objects, such as graphs, posets, and matroids, can be studied through numerical polynomial invariants, such as the chromatic polynomial and the order polynomial. Moreover, these invariants often have similar properties, which can be properly understood via combinatorial Hopf algebras. In studying Hopf monoids in Joyal's category of species, I have discovered an interesting combinatorial Hopf monoid, involving a new combinatorial object, called a coloring problem. We introduce the notion of an abstract coloring problem, which generalizes various aspects of graphs, posets, and matroids. We will discuss chromatic polynomials, which count the number of solutions of a coloring problem. We show that chromatic polynomials satisfy many nice identities, including having positive h-vectors. We mention relationships between this work and poset topology. If there is time remaining, we may discuss how coloring problems form a terminal combinatorial Hopf monoid.

Student Working Seminar in Groups and Dynamics

Time: 3:00PM - 4:00PM

Location: BLOC 624

Speaker: Roman Kogan, TAMU

Title: Introduction to Thompson's groups II

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Jason Crann, Carleton University

Title: Module injectivity of group von Neumann algebras

Abstract: This talk will feature recent results on the injectivity of VN(G) as an operator module over the Fourier algebra A(G) for general locally compact (quantum) groups G. Contrary to the operator space category, we show that amenability of G is equivalent to injectivity of VN(G), and present a variety of applications. In the group setting, we show that inner amenability of G is equivalent to relative injectivity of VN(G). This result, among other things, allows us to answer 3 open questions in abstract harmonic analysis. In the bimodule setting, we characterize the (relative) injectivity of VN(G) and apply our results to elucidate the operator amenability of Acb(G) - the cb-multiplier norm closure of A(G).

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Maurice Rojas, TAMU

Title: How Quickly Can we Find the Shapes of Algebraic Sets? Part 2: Computing Topology over R

Abstract: In this series of lectures, we review some old and new results on computing the topology of algebraic sets. We work mainly over the fields C, R, and F_p. These lectures are meant to be accessible to first year graduate students. We consider the complexity of computing the number of connected components of the real zero set of a single sparse polynomial. Whereas the first part of Hilbert's 16th Problem asks for the disposition of the ovals of a plane curve of degree d, we instead consider the analogous problem for n-variate polynomials (of arbitrary degree) having n+k monomial terms. We'll see an efficient classification valid for k<=2. We then see why we get NP-hardness for k on the order of n^epsilon.