# News Archive

## Graduate Open House

## Math Major Info Session

## Math Opening Social

## Heather M. Russell (University of Richmond)

Abstract: A graph is a collection of dots (called vertices) connected by lines (called edges). Graphs model many different types of information, and a rich theory of graphs has been developed to study their properties. In this talk, we will introduce the concept of graph coloring and then explore a graph coloring reconfiguration problem. No prior knowledge of graphs is necessary. We will begin with the definition of a graph and give lots of examples along the way!

Bio: Dr. Heather M. Russell is an Assistant Professor of Mathematics at the University of Richmond. She received her Ph.D. in mathematics from The University of Iowa in 2009 and held positions at Louisiana State University, University of Southern California, and Washington College prior to coming to Richmond. Trained as a topologist, her research applies combinatorial methods to problems in knot theory, representation theory, and graph theory. She is passionate about involving students in her research and building a more inclusive math community. Outside of mathematics, Dr. Russell enjoys exercise, cooking, and spending time with her dog.

## Robert Schneider(University of Georgia)

**Abstract**

Since the dawn of time, if not earlier, mathematicians have been fascinated by prime numbers. Euclid, Eratosthenes and other ancient thinkers rigorously studied the primes, yet these enigmatic integers defy our understanding even in the twenty-first century. Another ancient number theory pioneer, Pythagoras, also pioneered modern music theory. He found pleasing-sounding chords and melodies to be related to whole number ratios of waveforms on vibrating strings. These musical experiments of Pythagoras resonate throughout the mathematical sciences, from applications of Fourier series to the mysteries of quantum physics and string theory. One of the most famous open problems in all of mathematics, the Riemann Hypothesis, suggests beautiful waveform-like behavior in the distribution of prime numbers among the integers, which some authors poetically liken to “music of the primes.”

But this is a talk about actual music. We will discuss and hear new directions in composition that explore prime numbers through the superposition of sound waves and rhythms, such as the experimental “Dream House” installation by composer La Monte Young, and somewhat less far-out pieces by the speaker.

**Bio**

Robert Schneider is a number theorist and lecturer at the University of Georgia (Athens), having received his Ph.D. in 2018 from Emory University under the supervision of Ken Ono. His primary research interests lie in partition theory, analytic number theory, combinatorics and physics; he is also a professional composer, musician and indie record producer, and is interested as in using ideas from mathematics to seek new modes of expression in music.

## Peter Howard (Texas A&M)

**Phase-asymptotic stability of transition front solutions**

**in Cahn-Hilliard equations and systems**

**Abstract**

I will discuss the asymptotic behavior of perturbations of transition

front solutions arising in Cahn–Hilliard equations and systems on

$\mathbb{R}$ and $\mathbb{R}^n$. Such equations arise naturally in

the study of phase separation processes, where a two-phase process

can often be modeled by a Cahn-Hilliard equation, while a process

with more than two phases can be modeled by a Cahn-Hilliard system.

When a Cahn–Hilliard equation or system is linearized about

a transition front solution, the linearized operator has an

eigenvalue at 0 (due to shift invariance), which is not separated

from essential spectrum. In many cases, it’s possible to

verify that the remaining spectrum lies on the negative

real axis, so that stability is entirely determined by the

nature of this leading eigenvalue. Working primarily in

the case of a single equation on $\mathbb{R}$, I will discuss

the nature of this leading eigenvalue and also the verification

that spectral stability—defined in terms of an

appropriate Evans function—implies phase-asymptotic stability.

Results for scalar and multidimensional systems will be

summarized.

## Oscar P. Burno (Caltech)

**Abstract**

**Oscar P. Bruno, Biographical Sketch**

## Devotional By Dr. Michael Dorff

Dr. Dorff, the Mathematics Department Chair, addressed BYU faculty, students, and staff in BYU’s weekly devotional Tuesday, April 3rd. You can view his devotional, titled “Seeing Things Differently” at https://speeches.byu.edu/talks/michael-j-dorff_seeing-things-differently/

## The Andre Weil Lecture: Shou-Wu Zhang (Princeton University)

**Title:** Heights and *L*-functions

**Abstract:** Height and *L*-series are two of most important tools in number theory and arithmetic geometry. They were originally invented by Andre Weil in his Ph.D. thesis on Mordell—Weil theorem and his work on Weil conjecture. In this lecture, I will first review original work of Weil, and then survey recent developments.

**Date:** Tuesday, April 3

**Time:** 4:00 pm

**Room:** 135 TMCB

## Focus on Math: Alissa S. Crans

Date: April 12th, 2018 4:00 PM 1170 TMCB

Title: Frosting Fairness, Finally!

Abstract: Many of us are familiar with how to slice a cake ensuring equal sized slices for all. But what about those of us who want an equal amount of frosting as well?! This question is a classic with the problem solvers amongst us. In 1975, Martin Gardner considered a square cake cut into 7 pieces in his Scientific American column. More than a decade earlier, H.S.M. Coxeter posed the problem for a square cake sliced into 9 pieces as an exercise in his book, Introduction to Geometry. Together, we will solve this problem for a square cake cut into 5 pieces, and investigate the other cake shapes for which the same procedure will produce slices with equal cake and frosting.

Bio: Alissa S. Crans has been recognized nationally for her enthusiastic ability to share and communicate mathematics, having been honored by the MAA with the Hasse Prize and Alder Award. Her research lies in the field of higher-dimensional algebra and is currently supported by a Simons Foundation Collaboration Grant. Alissa is known for her active mentoring of women and underrepresented students, as well as of junior faculty as a member of the MAA Project NExT leadership team. When not enticing students with the beauty of mathematics at Loyola Marymount University or sharing her enthusiasm for math in settings ranging from “Nerd Night Los Angeles” to public school classrooms, you can find her rehearsing with the Santa Monica College Wind Ensemble or on her quest to find the spiciest salsa in LA.