Applied Mathematics Seminar, Fall 2020

## Mondays 4:00 PM - 5:00 PM MT, online (zoom information will be provided before the seminars)

• This seminar can be taken for credit: Students can get 1-3 credits by registering to the Applied Math Seminar class Math 7875 Section 010 for Fall 2020. Students should talk to the seminar organizer before taking it for a credit. Grading is based on attendance and giving a talk by presenting an applied-mathematics paper (not necessarily your own). Student talks will be appropriately labeled to distinguish them from visitor talks. The seminar organizer is available to review your slides, for dry-runs etc.
• Please direct questions or comments about the seminar (or its class) to Yekaterina Epshteyn (epshteyn (at) math.utah.edu) or to Akil Narayan (akil (at) sci.utah.edu)
• Talks are announced through the applied-math mailing list. Please ask the seminar organizers for information about how to subscribe to this list.

August 24.
Title: TBA
Abstract: TBA

September 14. Claremont & Utah Joint Applied Math Seminar.
Speaker: Leandro Recova, T-Mobile, INC
Title: Applications of Critical Point Theory to Semilinear Elliptic Boundary Value Problems
Abstract: Abstract of Leandro Recova's talk

September 21. Utah Joint Applied Math/Stochastics Seminar.
Speaker: Sean Lawley Department of Mathematics, University of Utah
Title: Extreme first passage times
Abstract: Why do 300 million sperm cells search for the oocyte in human fertilization when only a single sperm cell is necessary? Why do 1000 calcium ions enter a dendritic spine when only two ions are necessary to activate the relevant receptors? The seeming redundancy in these and many other systems can be understood in terms of extreme first passage time (FPT) theory.
While FPT theory is often used to estimate timescales in biology, the overwhelming majority of studies focus on the time it takes a given single searcher to find a target. However, in many scenarios the more relevant timescale is the FPT of the first searcher to find a target from a large group of searchers. This fastest FPT is called an extreme FPT and is often orders of magnitude faster than the FPT of a given single searcher. In this talk, we will explain recent results in extreme FPT theory and show how they modify traditional notions of diffusion timescales.

September 28. Claremont & Utah Joint Applied Math Seminar.
Title: Nonlocal operators: from interior to the boundary
Abstract: The emergence of nonlocal theories as promising models in different areas of science (continuum mechanics, biology, image processing) has led the mathematical community to conduct varied investigations of systems of integro-differential equations. In this talk I will present some recent results on systems of integral equations with weakly singular kernels, flux-type boundary conditions, as well as some recent results on nonlocal Helmholtz-Hodge type decompositions with applications at both, theoretical, and applied levels.

October 5. Claremont & Utah Joint Applied Math Seminar.
Speaker: Jennifer Ryan, Department of Applied Mathematics and Statistics, Colorado School of Mines
Title: Multiwavelet discontinuous Galerkin methods and automated parameters for troubled cell indication
Abstract: This talk focuses on using a multiwavelet representation of the discontinuous Galerkin (DG) approximation for trouble cell indication. The multiwavelet representation is related to the jumps in the (derivatives of) the DG approximation. We then compare this indicator with other, more established indicators as well as machine learning approaches and demonstrate that it is possible to choose the parameters for troubled cell indicators automatically and appropriately.

October 12. Claremont & Utah Joint Applied Math Seminar.
Speaker: Heather Zinn-Brooks, Department of Mathematics, Harvey Mudd College
Title: Bounded-confidence models for opinion dynamics on online social networks
Abstract: Online social media networks have become extremely influential sources of news and information. Given the large audience and the ease of sharing content online, the content that spreads on online social networks can have important consequences on public opinion, policy, and voting. To better understand the online content spread, mathematical modeling of opinion dynamics is becoming an increasingly popular field of study. In this talk, I will introduce you to a special class of models of opinion dynamics on networks called bounded-confidence models. I will then discuss some of the applications and theory that my collaborators and I have been developing with these models, including the impact of media, opinion dissemination, mean-field dynamics, and extensions to hypergraphs and multilayer networks. This talk will also include some unsolved questions for future work.

October 26 (Stundent's talk). Claremont & Utah Joint Applied Math Seminar.
Title: Thin liquid film resulting from a distributed source on a vertical wall
Abstract: In this talk, we will talk about the thin film model derived for liquid film resulting from a distributed source on a vertical wall and some distinct properties about the model. We will discuss the different behavior and properties of the model with and without considering surface tension. When the surface tension is neglected, a critical source strength is found below which the film flows entirely upward due to the airflow, and above which some of the flow is carried downward by gravity. In both cases, a steady state is established over the region where the finite source is located. The presence of surface tension, even when small, causes a dramatic change in the film profiles and the speed and structure of the shock waves. These are studied in more detail by examining the traveling wave solutions away from the source region.

November 2. Claremont & Utah Joint Applied Math Seminar.
Speaker: Franziska Weber, Department of Mathematical Sciences, Carnegie Mellon University
Title: Numerical approximation of statistical solutions of hyperbolic systems of conservation laws
Abstract: Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions for multi-dimensional hyperbolic systems of conservation laws. We present a numerical algorithm to approximate statistical solutions of conservation laws and show that under the assumption of 'weak statistical scaling', which is inspired by Kolmogorov's 1941 turbulence theory, the approximations converge in an appropriate topology to statistical solutions. We will show numerical experiments which indicate that the assumption might hold true.

November 9. Claremont & Utah Joint Applied Math Seminar.
Speaker: Qing Xia, Department of Mathematical Sciences, Rensselaer Polytechnic Institute
Title: Multiscale analysis and high-order schemes for nonlinear multilevel Maxwell-Bloch equations
Abstract: In this talk, we will present a recent study of the Maxwell-Bloch equations that model the nonlinear interactions of light and matter, where the light is modeled classically by the Maxwell's equations with dispersions and the medium is modeled quantum-mechanically by the multilevel rate equations. We will show the connection between rate equations and the density matrix, where the former formulation is widely used in the engineering community and the latter in the Physics literature. A multiscale analysis of the Maxwell-Bloch equations based on asymptotic expansions will also be discussed. The resulting reduced envelope equations (or slow equations) capture amplitude dynamics of the underlying solutions accurately and efficiently. In addition, we will talk about high-order accurate numerical schemes based on finite difference approximations in space and modified equation approach in time. The proposed schemes allow point-wise update of the solutions for both single domains and domains with material interfaces, thus enabling superb parallelism for arbitrary geometry. This is joint work with A. V. Kildishev and L. J. Prokopeva from Purdue's Birck Nanotechnology Center, and J. W. Banks, W. D. Henshaw, G. Kovacic and D. W. Schwendeman from RPI.

November 23. Claremont & Utah Joint Applied Math Seminar: Social Hour

Seminar organizers: Yekaterina Epshteyn (epshteyn (at) math.utah.edu) and Akil Narayan (akil (at)sci.utah.edu).

155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, T:+1 801 581 6851, F:+1 801 581 4148