Colloquium, Winter 2007

$Welcome to the Mathematics Department at UCSB$

Colloquium, Winter 2007

Thursdays at 3:30 p.m. in South Hall, Room 6635
Colloquium Chair: J. M^cKernan

February 8, 2007	Christopher Hacon, University of Utah Title Finite generation of canonical rings Abstract: abstract Contact person: James M^cKernan
February 15, 2007	Burkhard Wilking, University of Muenster Title Structure of fundamental groups of manifolds with Ricci curvature bounded below Abstract: We establish several structure theorems for fundamental groups of compact manifolds with lower Ricci curvature bounds. Among them is a bound on the number of generators in terms of the lower Ricci curvature bound and an upper diameter bound. We also established a generalized Margulis Lemma for manifold with lower Ricci curvature bound -1, i.e., we show that in such a manifold the loops of lenghth $\le \varepsilon(n)$ generate an almost nilpotent subgroup of the fundamental group, where $\varepsilon(n)$ is a universal constant which does not depend on the dimension. Contact person: Guofang Wei
March 1, 2007	Igor Rivin, Temple University Title Irreducibility of polynomials, matrices, and group of surface automorphisms Abstract: I start with the following question: is a "random" polynomial with integer coefficients irreducible over the integers? From there, we move on to the question of whether a random matrix has irreducible characteristic polynomial, and from there to the question of whether a random surface automorphism is pseudo-Anosov, and whether a random free group automorphism is irreducible with irreducible powers. The talk will be self-contained. Contact person: Daryl Cooper
March 15, 2007	Calin Chindris, University of Minnesota Title Non-log-concave Littlewood-Richardson coefficients Abstract: Motivated by physical considerations, Okounkov conjectured that the Littlewood-Richardson coefficients are log-concave as a function of their highest weights. The conjecture, if true, would immediately imply Knutson-Tao saturation theorem, a conjecture of Fulton proved by Belkale, and the log-concavity theorem for skew-Schur functions proved by Lam-Postnikov-Pylyavskyy. As it turns out, Okounkov’s conjecture can be reformulated in terms of the more general language of quiver theory. In fact, using the rich combinatorics and geometry of quiver representations, I will explain why Okounkov’s conjecture is bound to fail and present explicit counterexamples. This talk is based on joint work with Harm Derksen and Jerzy Weyman. Contact person: Birge Huisgen-Zimmermann

$Department of Mathematics, South Hall. Room 6607 University of California Santa Barbara, CA 93016, phone (805) 893-2171, fax (805) 893-2385, email www.ucsb.edu, office hours m-f 8-12, 1-4$