# Math Calendar

### Upcoming Events

## Algebraic Actions: A Max-min Principle for Local Weak* Convergence

Ben Hayes, University of Virginia

Location: Stevenson 1432

I will discuss the entropy theory of algebraic actions of sofic groups. An algebraic action of a group G is an action by continuous automorphism of a compact group X. We typically think of these actions as probability measure-preserving actions, giving X the Haar measure. It is an interesting problem to find conditions when you can guarantee that the topological entropy and the measure-theoretic entropy of these actions agree. I will discuss some methods to attack this problem, which involve ultraproduct analysis, particularly the use of the Loeb measure space.

## Localized Basis Functions on Graphs and Applications

John Paul Ward, North Carolina A&T State University

Location: Stevenson 1432

Graph domains are being used for many signal processing applications. They provide a more general framework than integer lattices, and they can be used to incorporate additional structural or geometric information. In this talk, we define intrinsic basis functions derived from the graph Laplacian, in analogy with polyharmonic splines on euclidean spaces. We consider the associated Lagrange basis functions and discuss their decay properties. The applications of such bases include kernel-based machine learning algorithms where data is well represented using a graph framework, and we shall present some preliminary experiments in this direction.

## Localized Basis Functions on Graphs and Applications

John Paul Ward, North Carolina A&T State University

Location: Stevenson 1432

Graph domains are being used for many signal processing applications. They provide a more general framework than integer lattices, and they can be used to incorporate additional structural or geometric information. In this talk, we define intrinsic basis functions derived from the graph Laplacian, in analogy with polyharmonic splines on euclidean spaces. We consider the associated Lagrange basis functions and discuss their decay properties. The applications of such bases include kernel-based machine learning algorithms where data is well represented using a graph framework, and we shall present some preliminary experiments in this direction.

## Compressed sensing for the real world: Closing the Gap Between Theory and Practice

Bernhard G. Bodmann, University of Houston

Location: Stevenson 5211

The theory of compressed sensing promises to revolutionize remote sensing, biomedical imaging and perhaps even digital photography. Mathematically, this theory is appealing because of the interplay of elements from random matrix theory, optimization theory and analysis. However, the randomized sensing model and the grid-based sparsity assumption central to many results are somewhat disconnected from typical signal spaces and sensor architectures used in engineering. This talk explores recent trends in narrowing the gap between theory and practice. Instead of sparsity in an orthonormal basis, we define a notion of sparsity in reproducing kernel spaces. The signal space is permitted to be infinite-dimensional while obtaining recovery from a finite number of measured quantities. The recovery procedure is based on optimization of a total variation norm. This work, in collaboration with Gitta Kutyniok and Axel Flinth, extends results by Candes and Fernandez-Granda as well Recht et al. This talk is intended for a general mathematics audience. Despite the claims made in the title, little knowledge of the real world will be assumed.Tea at 3:33 pm in Stevenson 1425. (Contact Person: Akram Aldroubi)

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Dan Farley, Miami University

Location: Stevenson 1308

## The Many Faces of Dispersive Equations

Gigliola Staffilani, Massachusetts Institute of Technology

Location: Stevenson 5211

In recent years great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a variety of techniques including Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of problems connected with dispersive and wave equations, such as the derivation of a certain nonlinear Schrodinger equation from a quantum many-particles system, periodic Strichartz estimates, the concept of energy transfer, the invariance of a Gibbs measure associated to an infinite dimension Hamiltonian system and, if time permits, non-squeezing theorems for such systems when they also enjoy a symplectic structure. Tea at 3:33 pm in Stevenson 1425. (Contact Person: Giusy Mazzone)

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Denis Osin, Vanderbilt University

Location: Stevenson 1308

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Lawrence Craig Evans, University of California, Berkeley

Location: Stevenson 5211

Tea at 3:30 pm in Stevenson 1425. (Contact Person: Vaughan Jones)

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Tarek Elgindi, UC San Diego

Location: Stevenson 1307

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Darren Creutz, U.S. Naval Academy

Location: Stevenson 1432

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Thomas Hagen, University of Memphis

Location: Stevenson 1307

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Ivan Levcovitz, CUNY, New York

Location: Stevenson 1308

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Mehdi Lejmi, CUNY Bronx Community College

Location: Stevenson 1310

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Sujan Pant, Alvernia University

Location: Stevenson 1432

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