MenuEvents for 01/30/2015 from all calendars
Algebra and Combinatorics Seminar
Time: 3:00PM - 3:50PM
Location: BLOC 628
Speaker: Kevin Tucker , University of Illinois Chicago
Title: On the Limit of the F-signature Function in Characteristic Zero
Abstract: The F-signature of a local ring in positive characteristic gives a measure of singularities by analyzing the asymptotic behavior of the number of splittings (F-splittings) of large iterates of the Frobenius endomorphism. One can also incorporate ideal pairs by restricting the set of "allowable" splittings, and varying the coefficient of the ideal gives rise to the F-signature function of the pair. While for each fixed characteristic p > 0 these functions tend to be extremely complicated, in the few examples that have been computed they tend to limit to a piecewise polynomial function as p tends to infinity. In this talk I will discuss what is known about these functions and their limits, and present a number of new computations for diagonal hypersurfaces. The new computations (joint with Shideler) build on the techniques of Han and Monsky used to compute the Hilbert-Kunz multiplicities of diagonal hypersurfaces.
Seminar on Banach and Metric Space Geometry
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Quentin Menet, Université de Mons
Title: Hypercyclic subspaces
Abstract: An operator T on a Banach space X is said to be hypercyclic if there is a vector x in X (also called hypercyclic) whose the orbit under T is dense. An important question about hypercyclic operators is to know if there exists an infinite-dimensional closed subspace in which every non-zero vector is hypercyclic for T. Such a subspace is called a hypercyclic subspace. After a state of the art about hypercyclic operators and the structure of the set of hypercyclic vectors, we will see how we can obtain a characterization of weighted shifts with hypercyclic subspaces.
Numerical Analysis Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Simon Foucart, University of Georgia
Title: Excursion into the Mathematics of Compressive Sensing
Abstract: About a decade ago, it was realized that many signals could be faithfully recovered from far fewer measurements than expected. This realization gave rise to a vigorous scientific field called Compressive Sensing (or simply Sparse Recovery). There is a rich and elegant mathematical theory behind the scene, drawing from --- and contributing to --- optimization, probability, high-dimensional geometry, numerical analysis, etc. Fundamental aspects of the theory will be summarized as an overview biased towards my own contributions. In addition, I will sprinkle the talk with recent results on sparsity relative to a dictionary, on sparsity combined with disjointedness, and on an extreme quantization scenario. A concrete application in metagenomics will also be highlighted.
Colloquium - Simon Foucart
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Simon Foucart, University of Georgia
Description:
Title: Excursion into the Mathematics of Compressive Sensing
Abstract:
About a decade ago, it was realized that many signals could be faithfully recovered from far fewer measurements than expected. This realization gave rise to a vigorous scientific field called Compressive Sensing (or simply Sparse Recovery). There is a rich and elegant mathematical theory behind the scene, drawing from --- and contributing to --- optimization, probability, high-dimensional geometry, numerical analysis, etc. Fundamental aspects of the theory will be summarized as an overview biased towards my own contributions. In addition, I will sprinkle the talk with recent results on sparsity relative to a dictionary, on sparsity combined with disjointedness, and on an extreme quantization scenario. A concrete application in metagenomics will also be highlighted.
