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Texas A&M University
Mathematics

Events for 09/18/2014 from all calendars

iCal  iCal

Time: 09:00AM - 10:00AM

Location: BLOC 220

Speaker: Prakash Belkale, U N Carolina

Title: Gauss-Manin representations of conformal block local systems, III

Abstract:

Conformal blocks give projective local systems on moduli spaces of curves with marked points. One can ask if they are “realizable in geometry”, i.e., as local subsystems of suitable Gauss-Manin local systems of cohomology of families of smooth projective varieties.

I will focus on the genus 0 situation where there is extensive contact with the theory of hyperplane arrangements. In genus zero, conformal blocks are surjected on to by constant vector bundles of classical coinvariants; which carry connections lifting the one on conformal blocks. One would like to have a consistent "integral" Hodge theoretic realization of this entire package. Formulating what one expects for the package is a challenge, and I want to get to that in the lectures. The following will be covered (in an "inverted" order),

1) I will discuss (in genus 0) the proof of Gawedzki et al’s conjecture that Schechtman-Varchenko forms are square integrable (this was proved first for sl(2) by Ramadas). Together with the flatness results of Schechtman-Varchenko, and the work of Ramadas, one obtains the desired realization and a unitary metric on conformal blocks.

2) Characterization of the image of conformal blocks in cohomology (joint with S. Mukhopadhyay)

3) Whether classical coinvariants can be characterized cohomologically (together with an integral structure).


iCal  iCal

Time: 11:00AM - 12:00PM

Location: BLOC 220

Speaker: Sean Keel, U Texas

Title: Theta functions, Canonical Bases, and Moduli of Calabi-Yaus, III

Abstract: In my second and third talks, where I will assume some (but not much) familiarity with algebraic geometry, I will explain the mirror symmetric ideas behind the construction, focusing on the simpler case of open Calabi-Yau, and in particular, cluster, varieties. Our main theorem (joint with Kontsevich) is (roughly) that if an affine Calabi-Yau variety U has a Zariski open cover by algebraic tori, then the algebra O(U) of regular functions has a canonical vector space basis. The theorem, and proof, has many interesting applications. E.g. it produces a vector space basis for each irreducible representation of a semi-simple Lie group G canonically determined by a choice of H \subset B \subset G (a maximal torus in a Borel in G), by a construction that involves no representation theory (just the fact that U = the associated open double Bruhat cell is a CY of the right sort).


iCal  iCal

Time: 2:00PM - 3:00PM

Location: BLOC 220

Speaker: Radu Laza, Stony Brook

Title: Moduli and Periods, II


Promotion Colloquium for Dr. Matthew Young

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Professor Matthew Young, Texas A&M University

Description:

Title: Moments of L-functions

Abstract:

Mean values of L-functions have been well-studied over many years in large part because they can serve as a way to sidestep the Riemann Hypothesis (and its generalizations) in solving arithmetical problems. I will discuss some of my recent work in this area, with emphasis on some problems in spectral geometry that can be solved using L-functions.

Graduate Student Organization Seminar

iCal  iCal

Time: 4:00PM - 5:00PM

Location: BLOC 506A

Speaker: Profs. Catherine Yan and Anne Shiu, Texas A&M University

Title: Mini-Talks

Abstract: C. Yan: "Enumerative Combinatorics with Fillings of Polyominoes" Abstract: An important and active area of Enumerative Combinatorics is the study of combinatorial statistics, which are simply functions from the combinatorial objects to the set of non-negative integers. Many interesting statistics have been investigated over families of combinatorial structures, such as permutations, words, matchings, set partitions, integer sequences, graphs, and multi-graphs. In this talk I will introduce a new combinatorial model, fillings of polyominoes, which provides a unified approach to the classical combinatorial analysis on all the above mentioned structures. I will discuss some recent results and open problems related to this model. ----A. Shiu: "What is the Global Attractor Conjecture? " Abstract: First posed forty years ago, the Global Attractor Conjecture posits that the dynamical systems arising from a certain class of chemical reaction networks are globally stable. In this mini-talk, I will give a history of this conjecture and describe how ideas from algebra and polyhedral geometry have contributed in recent years toward its partial resolution.