Rice University Math Department Calendar

     January 2013          February 2013            March 2013     
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                                               31

4:00 pm Monday, February 18, 2013
Stulken Topology Seminar: Transverse knots, infinite cyclic covers and Heegaard Floer homology
by Shea Vela-Vick (LSU) in HB 427

In recent years, Heegaard Floer theory has proven an invaluable tool for studying contact manifolds and the Legendrian and transverse knots they contain. I plan to discuss a method for defining a variant of Heegaard Floer theory for infinite cyclic covers of transverse knots in the standard contact 3-sphere. Thi s invariant takes the form of a Z[t,t^-1]-module and generalizes one defined in joint work with Baldwin and Vertesi for transverse knots braided about open book decompositions. In this talk, I will discuss how our invariant is constructed and present some basic properties and computations. This is joint work with Tye Lidman, Robert Lipshitz and Sucharit Sarkar.Host Department: Rice University-Mathematics
Submitted by shelly@rice.edu

4:00 pm Wednesday, February 20, 2013
Geometry-Analysis: H\"older continuity of an extended CMV matrix
by Darren Ong (Rice) in HB227

Abstract: The CMV matrix is an operator on $\ell^2(\mathbb Z_+)$ that serves as a unitary analogue of the self-adjoint Jacobi matrix. It is a central tool in the study of orthogonal polynomials on the unit circle. We may extend the CMV matrix to an operator on $\ell^2(\mathbb Z)$, and this extended matrix is useful for understanding quantum random walks. We prove that power law bounds on the formal eigenvectors of the one-sided CMV matrix implies that the two-sided extension has spectral measure that is H\"older continuous, using techniques developed in the self-adjoint case by Damanik, Killip and Lenz. Our result implies spreading in the corresponding quantum random walk Host Department: Rice University-Mathematics
Submitted by hardt@rice.edu