Events for 11/04/2009 from all calendars
Inverse Problems Seminar
Time: 1:00PM - 2:00PM
Location: BLOC 628
Speaker: Bill Rundell, Texas A&M University
Title: Recovery of obstacles using equivalent sources
Number Theory Seminar
Time: 1:45PM - 2:45PM
Location: MILN 317
Speaker: Dermot McCarthy, University College Dublin
Title: p-adic hypergeometric series and supercongruences
Abstract: We discuss recent work in which we generalise Greene's hypergeometric series over finite fields in the p-adic setting. We provide congruences between these p-adic hypergeometric series and truncated ordinary hypergeometric series. We also relate a special value of the p-adic hypergeometric series to the p-th Fourier coefficient of a modular form, thus resolving an outstanding supercongruence conjecture of Rodriguez-Villegas.
Groups and Dynamics Seminar
Time: 3:00PM - 3:50PM
Location: MILN 216
Speaker: Volodymyr Nekrashevych, Texas A&am;M University
Title: Simplicial approximations of Julia sets
Abstract: We will show that the Julia set of any expanding map is an inverse limit of a sequence of simplicial complexes, which are constructed by a recurrent combinatorial "cut-and-paste" rule. The construction is a generalization of such low-dimensional objects as Hubbard trees or subdivision rules. Our construction can be applied to the study of Julia set of maps in several variables. Some examples will be presented.
Numerical Analysis Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 627
Speaker: Massimo Fornasier, Radon Institute, Linz
Title: Efficient numerical methods for L1-minimization
Abstract: Iteratively least squares and gradient iterations intertwined with
thresholding operations have been recently investigated for addressing
inverse problems whose solutions are characterized by a few significant
degrees of freedom.
We retrace some of the history of these algorithms and known results, and also address a variety of improved methods.
While the convergence of these algorithms is quite clarified, convergence rates and complexity are known only in special situations. In this talk we would like to focus on the complexity of compressive algorithms when addressing certain infinite dimensional problems. It is known that they may perform "arbitrarily bad" when applied for the regularized inversion of compact operators. Indeed for such operators the (infinite) matrix representation with respect to a "good basis", in the sense that it quasi-diagonalizes the operator, turns out to be diagonal dominant with fast decaying diagonal entries. The rate of convergence of the algorithms is related to the "local conditioning" of such a matrix, i.e., how well-conditioned is any relatively small group of columns. This is the case, for instance, when we deal with potential operators, such as in magnetic tomography, and matrix representations with respect to multiscale bases or wavelets. We discuss how to precondition these problems in order to obtain a uniform condition number of the resulting matrices over any small group of columns. In particular, we will show how block-diagonal preconditioning will produce infinite matrices with a "Restricted Isometry Property (RIP)", as the one introduced for finite dimensional situations in compressed sensing problems. We will use this property in order to show how adaptive numerical iterations can be performed guaranteeing a controlled linear convergence of these algorithms.
Analysis/PDE Reading Seminar
Time: 4:00PM - 5:00PM
Location: MILN317
Speaker: Andrew Comech, Texas A&M University
Title: Scattering Theory and Nonlinear Waves
Abstract: We continue studying the connection between Schroedinger equation and KdV.