# Colloquia

## Professor Petronela Radu 9/18/2013

Math in the City – A model for a project

based Learning Experience

Professor Petronela Radu

Date: 9/18/2013

Time: 4:00pm -5:00pm

Place: 315 Armstrong Hall

Abstract: The Math in the City course designed at University of Nebraska-Lincoln provides students with an opportunity to see how mathematics is used outside academia, and also to become more engaged with activities of businesses and research centers around the city of Lincoln, NE. During the seven offerings of the course we have seen that such experiences are beneficial to undergraduates on professional as well as personal levels; they learn how to set up and analyze mathematical models based on real world data, they learn how to find ``missing" information and how to account for it. Students also improve their communication skills (both oral and written), they learn how to better work in groups, how to meet deadlines, and many other soft skills that will help them on the job market and in the workplace.

## Professor Anthony Evans 9/6/2013

A class of orthogonal

latin square graphs

Professor Anthony Evans

Date: 9/6/2013

Time: 3:45PM-4:45PM

Place: 315 Armstrong Hall

An \emph{orthogonal latin square graph} is a graph whose

vertices are latin squares of the same order, adjacency being synonymous

with orthogonality. We are interested in orthogonal latin square graphs in

which each square is orthogonal to the Cayley table $M$ of a group $G$ and

is obtained from $M$ by permuting columns. These permutations, regarded as

permutations of $G$, are \emph{orthomorphisms} of $G$ and the graphs so

obtained are \emph{orthomorphism graphs}.

We will discuss results and problems in the study of orthomorphism graphs

## Professor Anant Godbole 8/22/2013

A Survey of Old and New Results on Universal Cycles

Date: 8/22/13 Thursday Friday

Time: 4:30PM-5:30PM

Place: Armstrong 315

Professor Anant Godbole

Department of Mathematics and Statistics

East Tennessee State University

Abstract:

A fundamental result in graph theory is that a connected graph with even

vertex degrees is Eulerian. For digraphs, we can state the result as

follows: A digraph, with at most one weakly connected component, for with

the indegree $i(v)$ of any vertex $v$ equals its outdegree $o(v)$, is

Eulerian. This result led to deBruijn proving the result that bears his

name, about universal cycles of words of arbitrary length from an

arbitrary alphabet; for example, the cyclic string 11101000 contains each

binary three-letter word exactly once as a substring. Chung, Diaconis and

Graham's landmark paper extended the notion of universal cycles to

subsets, partitions, and permutations. This talk will focus on further

progress, much of which has been made by students at my REU program. I

will present results on universal and overlap cycles of restricted words,

graphs, hypergraphs, matroids, venn diagrams, posets, subsets, words of

fixed weight, complementary classes, and juggling patterns.

## Dr. Zach Etienne 5/3/2013

Solving the Einstein-Maxwell Equations to Model the Most Energetic Outbursts in the Universe

Dr. Zach Etienne

Date: 5/3/2013

Time: 4:00PM-5:00PM,

Place: 315 Armstrong Hall

*Refreshments served at 3:30p in Armstrong Hall, Room 310

Abstract: Black hole--neutron star (BH-NS) and black hole--black hole (BH-BH) binary systems are among the most promising candidates for gravitational waves (GWs) detectable by Advanced LIGO and NANOGrav. In addition, spectacular and observable electromagnetic (EM) radiation may accompany these GWs. However, the knowledge we gain from such "multi-messenger" systems will be limited by our theoretical understanding of them. To improve this understanding, we have developed state-of-the art numerical relativity codes designed to model these systems. The codes solve a strongly hyperbolic formulation of Einstein field equations and a conservative formulation of the GRMHD equations for the magnetized plasma that preserves the critically-important divergenceless condition for the magnetic field. Our simulations were the first to demonstrate that BH-NS binary mergers not only produce GWs detectable by Advanced LIGO, but also under the right conditions may provide the engine for launching a gamma-ray burst. Our BH-BH-disk simulations, in which the binary is surrounded by a tenuous, magnetized accretion disk, were the first to show that when the binary is widely separated, a jet of EM energy from the binary forms, with the luminosity peaking at merger. We intend to consider binaries at even larger separations in the future to determine what EM signatures might be observed when the emitted GWs fall in the NANOGrav band. I will discuss the new algorithms we developed to perform these simulations, their mathematical underpinnings, and our latest results.

## Professor Brian Alspach 5/14/2013

The Coxeter Group

Project: A Progress Report

Professor Brian Alspach

Date: 5/14/2013

Time: 10:30AM-11:30AM,

Place: 315 Armstrong Hall

Abstract: If one forms a Cayley graph on the symmetric group using only

transpositions for the connection set, then the graph is bipartite. In

2006, Araki proved that if such a Cayley graph is connected, then for any

two vertices u and v in different parts, there is a Hamilton path whose

terminal vertices are u and v. Of course, the symmetric group is a

Coxeter group. The speaker has embarked on a project of extending Araki's

Theorem to Cayley graphs on other families of Coxeter groups. This talks

is a summary of what has been achieved so far.

## Dr. Gesham Magombedze 4/29/2013

Mathematical modeling of host-pathogen immunological interactions and

molecular biological systems

Dr. Gesham Magombedze

Date: 4/29/2013

Time: 3:30PM-4:30PM,

Place: 315 Armstrong Hall

*Refreshments served at 3:00p in Armstrong Hall, Room 310

Abstract: Mycobacterial infections, such as Mycobacterium avium subspecies paratuberculosis which causes Johne's disease in cattle and other ruminants and Mycobacterium tuberculosis, which is the etiological agent of tuberculosis in humans, are characterized by a persistent and slow infection progression, that can be rapid under certain conditions. Mycobacterial pathogens have the ability to adapt to the changing intracellular environment in response to a dynamic immune response. The underlying mechanisms of how the bacteria can persist despite of the host mounting a robust immune response are not clearly understood. In this talk I will illustrate how mathematical models can be used to: (i) address questions arising from biological systems and (ii) provide insights in understanding some of the bacterial mechanisms associated with its persistence using a mathematical framework that integrates gene expression data and biochemical systems theory. I will present a mathematical immunological model that describes the cattle immune response mechanisms associated with mycobacterial infection progression.

## Dr. Arvind Baskaran 4/26/2013

Kinetic Density Functional Theory : A mesoscale approach to understanding the effect of flow on freezing transition

Dr. Arvind Baskaran

Date: 4/26/2013

Time: 3:30PM-4:30PM,

Place: 315 Armstrong Hall

*Refreshments served at 3:00p in Armstrong Hall, Room 310

Abstract: A clear understanding of freezing and melting is of great importance in many applications starting from growth of nano-crystals in solutions for solar cells to making the perfect ice cream. This work aims to understand how the flow of the liquid phase affects the freezing process (solid-liquid phase transition).This talk will outline the problem with the perspective of an interdisciplinary mathematician.The mathematical challenges involved in developing a solvable predictive model and developing efficient methods of solving the so developed model will be discussed.Some results demonstrating the predictive ability of the so developed approach will be discussed.

This work was done in collaboration with John Lowengrub and Aparna Baskaran

## Dr. Carlos Palenzuela 4/23/2013

Revealing the dark side of the

Universe with gravitational waves

Dr. Carlos Palenzuela

Date: 4/23/2013

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

*Refreshments served at 3p in Armstrong Hall, Room 310

Abstract:In the next few years a new generation of gravitational wave detectors will allow us to "listen" some of the most energetic events in the universe; the coalescence of binary compact objects such as black holes and/or neutron stars. If the magnetic field around these objects is sufficiently strong, the binary may produce an electromagnetic burst which we may be able to "see", especially if it is in the form of a collimated jet. A new era of multi-messenger astronomy, involving detections of EM, GW and possible neutrino signals, will provide more insight into the physical processes involved in the collisions. After giving an overview on gravitational waves and the underlying equations, I will describe the dynamics of compact binary mergers, focusing on the gravitational waveforms and the possible EM counterparts from these systems.

## Dr. Casian Pantea 4/22/2013

Geometry of interaction networks: dynamics from structure

Dr. Casian Pantea

Date: 4/22/2013

Time: 3:30PM-4:30PM,

Place: 315 Armstrong Hall

*Refreshments served at 3:00p in Armstrong Hall, Room 310

Abstract: The behavior of biological interaction networks (such as networks of biochemical reactions, infectious diseases within a population, or species in an ecosystem) is commonly modeled using intricate systems of differential equations. These models usually contain a large number of parameters whose values are rarely known in practice. However, even when no information regarding parameter values is available, wide classes of interaction networks can be shown to have surprisingly stable behavior, induced by the topology of the network alone. In this talk I will consider some of the problems and results of chemical reaction network theory, a body of work which attacks the question: "What behaviours of an interaction network are a function of its structure, and are robust to different choices of parameters?" In particular, I will discuss recent results relating the topology of a network with the possibility for Hopf bifurcations in the corresponding ODE system.

## Professor Yue Zhao 4/19/2013

On Edge Chromatic

Critical Graphs

Date: 4/19/2013

Time: 3:30PM-4:30PM,

Place: 315 Armstrong Hall

Professor Yue Zhao

Abstract: Around 1965, Vizing proposed four conjectures about edge

chromatic critical graphs. Since then, many people have been working on

these conjectures. But these four conjectures remain open. In this talk, we will present some results on these four conjectures.

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