For Tuesday, April 19, 2011 the events for the next 3 months

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 4:00 pm   Tuesday, April 19, 2011 Algebraic Geometry Seminar: Multiplication on P^1, vector bundles, Hilbert schemes of points, and the golden ratio by Jack Huizenga (Harvard) in HB 227Consider the following basic problem about multiplication of polynomials in one variable. Fix a general 3-dimensional subspace V of the polynomials of degree a, and fix a second degree b. Given a subspace W of the polynomials of degree b, think of W as occupying the fraction dim(W)/(b+1) of the space of polynomials of degree b. For every such subspace W, does the product VW occupy at least as large a fraction of the polynomials of degree a+b as W does of the polynomials of degree b? That is, does multiplication by V always increase the fraction of the space occupied by W? Surprisingly, the answer to this question is connected to the golden ratio and its continued fraction expansion. We will further discuss how this question is connected with semistability and splitting properties of certain particularly nice vector bundles on P^2, known as Steiner bundles. These bundles can be viewed as natural generalizations of the tangent bundle. Finally, we will discuss how these bundles give rise to extremal effective divisors on the Hilbert scheme of points in P^2.Host Department: Rice University-MathematicsSubmitted by evanmb@rice.edu

 12:00 pm   Wednesday, April 20, 2011 Spectral Theory Brown Bag Seminar: Jitomirskaya-Last for OPUC by Darren Ong (Rice University) in HB 423Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 4:00 pm   Wednesday, April 20, 2011 Stulken Geometry-Analysis Seminar: A Characterization of Sets of Spectral Synthesis for $H^1$ by Raymond Johnson (Rice University) in HB 227Spectral synthesis is a topic that was discussed intensively in the early seventies, but which was marked by numerous counterexamples. It had very few remaining problems after that time. I will discuss spectral synthesis for $H^1$, and prove a number of positive results including a characterization of compact sets of spectral synthesis for $H^1$. Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 4:00 pm   Thursday, April 21, 2011 Colloquium: Global Rigidity for certain actions of higher rank lattices on the torus by Federico Rodriguez Hertz (Penn State) in HB 227In this talk we will give an approach to the following theorem: Let $\Gamma$ be an irreducible lattice in a connected semi-simple Lie group with finite center, no non-trivial compact factor and of rank bigger than one. Let $a:\Gamma \to Diff(T^N)$ be a real analytic action on the torus preserving an ergodic large measure (large means essentially that its support is non trivial in homotopy). $a$ induces a representation $a_0:\Gamma \to SL(N,Z)$. Assume further that $a_0$ has no zero weight and no rank one factor. Then $a$ and $a_0$ are conjugated by a real analytic map outside a finite $a_0$ invariant set. The theorem essentially says that nonlinear action $a$ is built from linear $a_0$ by blowing up finitely many point. This is joint work with A. Gorodnik, B. Kalinin and A. Katok.Host Department: Rice University-MathematicsSubmitted by dani@rice.edu

 12:00 pm   Friday, April 22, 2011 Stulken Geometry-Analysis Seminar: Ergodic Jacobi Matrices and Conformal Maps by Christian Remling (University of Oklahoma) in HB 427Given an ergodic Jacobi matrix, there is a natural conformal map (DOS + i Lyapunov exponent) onto a slit domain. This tool was first used by Marchenko and Ostrowski in their study of periodic problems. In this talk, I'd like to give an overview of the situation for general ergodic (or just invariant) models. This is joint work (in progress) with Injo Hur. Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 4:00 pm   Monday, April 25, 2011 Topology Seminar: To Be Announced by Ben McReynolds (University of Chicago) in HB 427Host Department: Rice University-MathematicsSubmitted by andyp@rice.edu

 12:00 pm   Wednesday, April 27, 2011 Spectral Theory Brown Bag Seminar: Jitomirskaya-Last for OPUC II by Darren Ong (Rice University) in HB 423Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 4:00 pm   Tuesday, May 3, 2011 Stulken Geometry-Analysis Seminar: Eigenvector Localization for Random Band Matrices with Power Law Band Width by Jeffrey Schenker (Michigan State University) in HB 453Random symmetric matrices with entries that vanish outside a band around the diagonal, but otherwise have independent identically distributed matrix elements, were introduced in the physics literature as an effective model of a ”localization/delocalization” transition seen in disordered materials. In this talk, it will be shown that such matrices satisfy a localization condition which guarantees that eigenvectors have strong overlap with only $W^\mu$ standard basis vectors where W is the band width and $\mu$ is a positive exponent. Thus if $W^\mu << N$, with $N$ the size of the matrix, then a typical eigenvector is essentially supported on a vanishing fraction of standard basis vectors. Some open problems and conjectures will also be discussed. Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 1:00 pm   Wednesday, May 4, 2011 Spectral Theory Brown Bag Seminar: Estimating the Hausdorff Dimension of the Spectrum of a Quasiperiodic Schrödinger Operator by Paul Munger (Rice University) in HB 423Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 4:10 pm   Thursday, May 26, 2011 Student Mathematical Philosophy: An Introduction to Mathemmatical Philosophy Seminar by Arunima Ray (Rijce University) in Herman Brown 423I will give a broad overview of why one might want to think about the philosophy of mathematics, and what various mathematicians through the ages have thought about the philosophy of mathematics. Hopefully, this talk will introduce some topics which will be expanded upon in upcoming talks in this seminar. So if you've committed to giving a talk, or haven't because you don't know what to speak on, this talk could be taken as a menu of topics to choose from. Host Department: Rice University-MathematicsSubmitted by mageemd@rice.edu

 4:10 pm   Thursday, June 2, 2011 Student Mathematical Philosophy Seminar: A reconstruction of the Frege-Hilbert controversy by Michael Barkasi in Herman Brown 423I discuss a famous dispute between two titans: Frege and Hilbert's dispute over what it means to show the consistency of a set of axioms, especially with regards to Hilbert's book Grundlagen der Geometrie. Along the way I give a fairly clear reconstruction of Frege's logicism and Hilbert's early structuralism as well as a crash course in what philosophers call semantic ascent.'' Some grasp of semantic ascent is helpful, it seems to me, not only in understanding just what Frege and Hilbert were arguing over but also for understanding just what contemporary philosophers of math'' are up to. Host Department: Rice University-MathematicsSubmitted by mageemd@rice.edu

 4:00 pm   Thursday, June 9, 2011 Student Mathematical Philosophy Seminar: Pythagoras, Descartes, and Leibniz: Magic, Models, and Fictions by Jacob Mills (Rice University) in George R. Brown W212A historical journey from the birth of the concept of an immortal soul to the rise of Greek geometrical mathematics, from Descartes's geometrical arithmetic to Leibniz's infinitesimal calculus and fictionalism in mathematics.Host Department: Rice University-MathematicsSubmitted by do3@rice.edu

 4:00 pm   Tuesday, June 14, 2011 Stulken Geometry-Analysis Seminar: Minimal And Very Non-uniquely Ergodic Interval Exchange Transformations by Jon Fickenscher (Rice University) in HB 427In 1977, Keane constructed an Interval Exchange Transformation (IET) that was minimal but supported two distinct ergodic probability measures. In 1978, Veech gave an upper bound on the number of distinct ergodic probability measures for any IET. We show that this bound is sharp by constructing minimal IETs that realize this bound in every Rauzy Class. Host Department: Rice University-MathematicsSubmitted by damanik@rice.edu

 4:00 pm   Wednesday, June 15, 2011 Summer Topology Seminar: Motivating filtrations of the knot concordance group by Tim Cochran (Rice) in HB 427 (tentative)Host Department: Rice University-MathematicsSubmitted by cochran@rice.edu

 3:00 pm   Thursday, June 16, 2011 Student Mathematical Philosophy Seminar: Quid Est Veritas? Mathematics and the (failed) search for certainty by Darren Ong   [mail] (Rice University) in HBH 423Bertrand Russell once wrote that "I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere." We examine the progress of this quest for certainty in mathematics, and explore how modern developments have posed new questions about the tenuous relationship between mathematics and "truth".Host Department: Rice University-MathematicsSubmitted by do3@rice.edu