Events for 09/04/2015 from all calendars

Several Complex Variables Seminar

Time: 11:00AM - 12:00PM

Location: BLOC 220

Speaker: Masanori Adachi , Tokyo University of science

Title: The Diederich-Fornaess index and vanishing theorems

Abstract: The Diederich-Fornaess index is a numerical index that measures hyper convexity of weakly pseudoconvex domains in complex manifolds; in other words, it describes to what extent a domain carries exhaustions by strictly pseudoconvex domains. In this talk, we shall focus on the case of Levi-flat bounded domains and discuss L^2 vanishing theorems which are closely related with the index. We will explain some (non-)vanishing theorems on L^2 holomorphic sections over Levi-flat bounded domains and L^2 CR sections over Levi-flat CR manifolds with emphasis on the role of the index, or a special one-form describing the holonomy of the Levi foliation. The talk is partly based on joint work with Judith Brinkschulte.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Christopher ONeill and Catherine Yan, Texas A&M University

Title: Organizational Meeting

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Alexandru Chirvasitu, University of Washington

Title: Negative curvature and quantum rigidity

Abstract: Hopf algebra coactions are studied in non - commutative geometry as analogues of algebraic or compact group actions on various structures (algebras, graphs, metric or measure spaces, etc.). Some structures exhibit a rigidity property whereby they admit no``truly non-commutative`` symmetries: Whenever a nice enough Hopf algebra coacts inner faithfully on such a structure, the Hopf algebra in question is commutative and consists of functions on an ordinary compact / algebraic group. I will talk about this phenomenon in the context of metric spaces. Having defined the notion of isometric coaction of a Hopf algebra on a compact metric space, the main result is that the underlying geodesic metric spaces of negatively curved Riemannian manifolds are rigid in the sense above. Conjecturally, the curvature condition should be unnecessary.

Geometry Seminar

Time: 4:00PM - 4:50PM

Location: BLOC 628

Speaker: Frank Sottile, Texas A&M University

Title: Galois Groups via Numerical Algebraic Geometry

Abstract: Galois groups, which are a mainstay of number theory and arithmetic geometry, may be studied using methods from numerical algebraic geometry, when the base field is a transcendental extension of the complex numbers. This is because the well-known observation (which goes back to Hermite) that in this case Galois=monodromy, and computing monodromy is a basic operation in numerical algebraic geometry.

While simply computing monodromy enables the exploration of a Galois group, it can only determine the group when it is the full symmetric group, for there is no stopping criterion. In work with Hauenstein and Rodriguez we offer two methods to determine a Galois group. For the first, we compute the branch locus, which leads to permutations that generate the Galois group. The second uses numerical irreducible decomposition of fiber products to determine the action of the Galois group, from which it may be determined.