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Today

Charis Tsikkou, West Virginia University, Radial solutions to the Cauchy problem for the wave equation and compressible Euler system

SAS 4201

In the first part of this work, we consider the strategy of realizing the solution of the three-dimensional linear wave equation with radial Cauchy data as a limit of radial exterior solutions satisfying vanishing Neumann and Dirichlet conditions, on the exterior of vanishing balls centered at the origin. We insist on robust arguments based on energy methods and strong convergence. Our findings show that while one…

Sarah Yeakel, University of Maryland, Isovariant Homotopy Theory

Fixed point theory studies the extent to which fixed points of a self map of a space are intrinsic. In many mathematical settings, the existence of a solution can be rephrased in terms of the existence of a fixed point for an appropriate map, leading to applications across mathematics. Variations of fixed point problems have…

Irina Kogan, NC State, A story of two postulates

“I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallel alone”, wrote a Hungarian mathematician Farkas Bolyai to his son János, horrified at the thought that his son is attracted by the problem of parallels. János was not deterred, however, and discovered,…

Zev Woodstock, NC State, Proximal methods for optimization

SAS 1220

Convex optimization problems appear naturally across the sciences in fields such as compressed sensing, statistics, machine learning, image processing, and inverse problems. This talk will discuss the theory, applications, and methods of proximal minimization: a wide-reaching subset of convex optimization. Advantages: you do not need your optimization problem to be differentiable (e.g. minimization problems with l-1…

Troy Butler, University of Colorado Denver, Data Consistent Inversion: An Interactive Talk Using Jupyter Notebooks

(Brief Note: In this talk, we utilize Jupyter notebooks to re-create some of our published results in real-time and also build a "computational intuition" for the ideas presented. In this way, we are (mostly) transparent about all the computations involved in our work. I will email these materials to anyone interested after the presentation.) Models are useful for…

H.T. Banks, North Carolina State University, Population Models-The Prohorov Metric Framework and Aggregate Data Inverse Problems

SAS 4201

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other)…

Randall LeVeque, University of Washington, Adjoint Error Estimation for Adaptive Refinement of Hyperbolic PDEs

SAS 1102

Time-dependent hyperbolic partial differential equations can be efficiently solved using adaptive mesh refinement, with a hierarchy of finer grid patches in regions where the solution is discontinuous or rapidly varying. These patches can be adjusted every few time steps to follow propagating waves. For many problems the primary interest is in tracking waves that reach…

Phillip Andreae, Meredith College, Infinite sums, infinite products, and million dollar prizes

SAS 2102

In calculus, we study series and learn how to add infinitely many numbers--but how about multiplying infinitely many numbers? In this talk, we'll start with familiar series from calculus, and then move on to study more exotic infinite sums and infinite products and the interactions between them. We'll see some number theory, complex analysis, and…

Adam Marcus, Princeton University, Ramanujan colorings

An important construction for (the information theoretic version of) semantic security is a "Biregular Irreducible Function" (BRI). These can be constructed from a complete biregular graph on $2^k d \times 2^k d$ by by coloring it with $2^k$ colors in such a way that each vertex has degree $d$ in each color. Good BRI's are…