The 2022-2023 WVU Math Colloquium is organized by Chris Ciesielski, Robert Mnatsakanov and Casian Pantea. Talks are usually held on Mondays at 4pm in Armstrong Hall 315.

In some cases we will schedule the seminar at different days/times, to accommodate speakers. If you'd like to suggest speakers for the fall semester please contact Chris, Robert, or Casian.

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euclid2022
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## Upcoming Colloquia

## Fall 2022 Colloquium Abstracts

### Dehua Wang, September 15

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Elastic effects on vortex sheets and vanishing viscosity
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Elasticity is important in continuum mechanics with a wide range of applications and is challenging in analysis. In this talk we shall first review some basic mathematical results and then discuss some special elastic effects in fluid flows. The first elastic effect is the stabilizing effect of elasticity on the vortex sheets in compressible elastic flows. Some recent results on linear and nonlinear stability of compressible vortex sheets will be presented. The second effect is on the vanishing viscosity process of compressible viscoelastic flows in the half plane under the no-slip boundary condition. Our results show that the deformation tensor can prevent the formation of strong boundary layers. The talk is based on the recent joint works with several collaborators.

### Farhad Jafari, October 17

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Variational Problems, Moment Sequences and Positive Definiteness
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Our ability to reformulate many problems in science and engineering in terms of variational (and control) problems continue to keep this area of mathematics current and of great interest. In this presentation we reformulate these problems as problems in measure theory and use moment methods to study them. Relating variational problems to moment methods has brought new interest in moment methods, moment completion problems and algebras of rational functions. This talk will connect these areas and (briefly) will show applications of moment methods to reconstruction problems in tomography.

### Tóth János, October 24

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The concept of reaction extent
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The concept of reaction extent or the progress of a reaction, advancement of the reaction, conversion, etc. was introduced around 100 years ago. Most of the literature provides a definition for the exceptional case of a single reaction step or gives an implicit definition that cannot be made explicit. Starting from the standard definition we extend the classic definition of the reaction extent in explicit form for an arbitrary number of species and of reaction steps and arbitrary kinetics. Then, we study the mathematical properties (evolution equation, continuity, monotony, differentiability, etc.) of the defined quantity, and connect them to the formalism of modern reaction kinetics. Our approach tries to adhere to the customs of chemists and be mathematically correct simultaneously.

We also show how to apply this concept to exotic reactions: reactions with more than one stationary state, oscillatory reactions, and reactions showing chaotic behavior. With the new definition, one can calculate not only the time evolution of the concentration of each reacting species but also the number of occurrences of the individual reaction events.

This is joint work with Vilmos Gáspár.

### Zi-Xia Song, October 31

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Coloring Graphs with Forbidden Minors
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Hadwiger’s conjecture from 1943 states that every graph with no $K_{t}$ minor is $(t-1)$-colorable: it remains wide open for all $t≥7$. For positive integers $t$ and $s$, let $K^{-s}_{t}$ denote the family of graphs obtained from $K_{t}$ by removing $s$ edges. We say that a graph $G$ has no $K^{-s}_{t}$ minor if it has no $H$ minor for every $H ∈ K^{-s}_{t}$. Jakobsen in 1971 proved that every graph with no $K^{-2}_{7}$ minor is 6-colorable. In this talk, we consider the next two steps and present our recent work that every graph with no $K^{-4}_{8}$ minor is 7-colorable, and every graph with no $K^{-6}_{9}$ minor is 8-colorable. Our result implies that $H$-Hadwiger's Conjecture, suggested by Paul Seymour in 2017, is true for all graphs $H$ on eight vertices such that $H$ is a subgraph of every member in $K^{-4}_{8}$, and all graphs $H$ on nine vertices such that $H$ is a subgraph of every member in $K^{-6}_{9}$.

This is joint work with Michael Lafferty.