# Math Talks

The Department of Mathematics weekly seminar series, Math Talks, is open to all KSU faculty, students, and invited visitors to present any math or math-related topic. Seminars typically require little or no advanced mathematical knowledge are open to anyone.

*Unless specified otherwise, seminars are held Thursdays 12:30-1:45pm in D-218 (Marietta campus).

### SPRING 2017

Thursday, February 2, 2017

• Dr. Chuck Dunn, Linfield College
• "Clique-Relaxed Graph Coloring"
• ABSTRACT: We consider a variation of the following game played on a finite graph G. Two players, Alice and Bob, alternate coloring the uncolored vertices of G from a set of r colors. At each step, the players must ensure that adjacent vertices receive different colors. Alice always goes first. She wins the game if the entire graph is eventually colored; otherwise, Bob wins if there comes a time such that there is an uncolored vertex that cannot be colored. The least r such that Alice has a winning game strategy for this game on G is called the game chromatic number G. We will examine a variation of this game in which the players ensure that the subgraphs induced by the color classes have bounded clique size. Our focus with these variations will be on the classes of outer planer graphs and planar graphs.

### FALL 2016

Thursday, September 8, 2016

• John McCuan, Georgia Institute of Technology
• "Euler's elastic curves and special liquid shapes"

Thursday, September 22, 2016

• Michael Lacey, Georgia Institute of Technology
• "One Bit Sensing"
• ABSTRACT: A signal is a high dimensional vector $x$, and a measurement is $a \cdot x$ for appropriately chosen $a$. Compressive sensing shows that under reasonable assumptions on $x$, you can recover it exactly, with very few measurements, in particular many fewer than the dimension of $x$. I will explain this, and then discuss one bit sensing where you only keep the sign of the dot product $a \cdot x$. Remarkably, one bit measurements can be just as effective as linear measurements.

Thursday, October 6, 2016

• Dhruba Adhikari, Kennesaw State University
• "Topological Degree Theory and Some Applications"

Thursday, October 13, 2016

• Ted Dobson, Mississippi State University and the University of Primorska
• "Vertex-Transitive Graphs"
• ABSTRACT: A graph Γ is vertex-transitive if its automorphism group Aut(Γ) acts transitively on the vertex set V (Γ) of the graph. That is, if for every x; yV (Γ), there exists ϒ ∈ Aut(Γ) such that ϒ(x) = y. Intuitively, a graph is vertex-transitive if it is not possible to distinguish between vertices. Many important graphs are vertex-transitive graphs (e.g. the Petersen graph, the Coxeter graph), and vertex-transitive graphs are important in chemistry and theoretical computer science, amongst other areas. Recently, vertex-transitive graphs have received a fair amount of interest.

The purpose of this talk is to introduce what I consider some of the main problems (or perhaps just some of my favorite problems) in the study of vertex-transitive graphs, as well as indicate the kinds of results that have been and are currently being obtained concerning these problems. These problems include determining the full automorphism group of a vertex-transitive graph, determining necessary and sucient conditions for two vertex-transitive graphs to be isomorphic, and Lovász's conjecture that every connected vertex-transitive graph contains a Hamilton path. By determining the automorphism group, we mean either an explicit list of groups, or a polynomial time algorithm to list a set of generators of the automorphism group. By "necessary and sucient conditions for two graphs to be isomorphic" it is usually meant an explicit list L of maps, and two vertex-transitive graphs with a common minimal transitive subgroup are isomorphic if and only if they are isomorphic by a map on L.

Thursday, October 20, 2016

• Michael Lott
• "Diffusion Reaction Equation using Random Walks"

Thursday, October 27, 2016

• Jun Ji, Kennesaw State University

Thursday, November 3, 2016

• Farzan Jafeh, Kennesaw State University

Thursday, November 10, 2016

• Eve Torrence, Randolph-Macon College
• "Fun with Hyparhedra"

Thursday, November 17, 2016

• Christina Lee
• "Neuronal Network Sensory Processes"
• ABSTRACT: The brain is an amazingly complex living system, in which a myriad of simultaneous processes takes place on vast ranges of spatial and temporal scales.

While much too rich to be modeled in its entirety, for mathematicians, it presents specific modeling opportunities on levels ranging from the molecular through single neurons to even some brain areas.

And while the answers to questions such as "what is the mind?" or "what is a percept?" or "what is the neural code?" remain for now far out of our reach, mathematical models, grounded in experimental data, can be used to successfully hypothesize plausible mechanisms underlying some of the basic neuronal processing in areas such as early sensory pathways. Some of these models are surprisingly simple, including the integrate-and-fire and the firing-rate models, which are amenable both to numerical simulations as well as dynamical-systems and bifurcation analysis.

The talk will focus on describing some of the neuronal responses to stimuli arriving along the early visual and olfactory pathways.

Thursday, December 1, 2016

• Joseph Fadyn, Kennesaw State University
• "Solving Quadratic Congruences Modulo a Prime"