Events for 10/31/2014 from all calendars

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 624

Speaker: Frank Sottile , Texas A&M University

Title: Some more geometry in the secondary fan

Abstract: A polyhedral subdivision of finitely many points A in R^d is a decomposition of its convex hull into non-overlapping polytopes with vertices in A. It is regular if the polytopes are projections of facets of a polyhedron in R^{d+1}. Gelfand, Kapranov, and Zelevinsky introduced the secondary fan of A, which encodes all regular subdivisions of A. When A is integral, Kapranov, Sturmfels, and Zelevinsky showed how this fan encodes all possible limiting positions of a projective toric variety associated to A, under translation by the ambient torus. I will talk on work with Postinghel and Villamizar that generalizes this to the situation where the points of A are not necessarily integral. Here, the toric variety is replaced by a curvilinear copy of the convex hull in the simplex. In this case, one does not have the tools from algebraic geometry (Hilbert schemes), and we instead develop tools based on the geometry of sequences of points in the secondary fan. This work was motivated by questions in geometric modeling and algebraic statistics which I plan to mention.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Issan Patri, Institute of Mathematical Sciences, Chennai

Title: Automorphisms of Compact Quantum Groups

Abstract: This talk will be about automorphisms of Compact Quantum Groups. We will define a class of automorphisms which can be thought of as "inner" in the group theoretic sense. We will also look at group actions on Compact Quantum Groups and characterize various properties like ergodicity, compactness, etc. We will end with a intriguing question, which arises in the special case of integer actions, on number of orbits of automorphisms of Tarski Monsters.