**Junior Colloquium - 2016-2017**

**Tuesday, April 25, 2017**

*Speaker: Professor Chris Rodger, Auburn *

Title: Amalgamations and Hamilton Decompositions

Time: 3:40pm - 4:30pm (pizza at 3:20)

Room: Ayres Hall 401

In this talk, we will explore the use of amalgamations in the construction of graph decompositions, most often looking for hamilton cycle decompositions. This method uses graph homomorphisms to envision an "outline" of the structure of interest, then attempts to disentangle the merging of new vertices created by the homomorphism in such an outline structure. As will be shown, this method has proved to be very effective, for example, in the studying the embedding of edge-colorings of graphs into hamilton decompositions. Fair division of colors in factorizations of graphs is also a very useful property that crops up in this setting, surprisingly even leading to symmetric versions of Sudoku squares.

**Thursday, March 2, 2017**

Title: Piecewise isometric maps

*Speaker: Richard Schwartz, Professor at Brown University *

Time: 3:40pm – 4:30pm

Room: Ayres 405

I will explain maps which are based on the idea of cutting a polygon (or the plane) apart into smaller pieces and moving each piece around by isometries. These maps, when treated as dynamical systems, often produce beautiful and intricate pictures. I'll give some examples of these maps and show pictures of what they do.

**Thursday, February 23, 2017**

Title: Discovering Latent Relationships in Highly heterogeneous Data: Mathematical Methods, Scalable Algorithms and Life Science Applications

**Speaker: Mike Langston, Prof in Electrical Engineering and Computer Science, UTK**

Time: 3:40pm – 4:30pm

Room: Ayres 405

We will discuss the use of novel mathematical techniques such as fixed-parameter tractability in the analysis of highly inhomogeneous data. Important concerns center on noise, and the role model organisms can play in the study of human health. Critical resources include enormous repositories of emergent data, suites of novel statistical and graph theoretical methods, deep domain knowledge and high performance computing platforms. We will describe how the potential of these resources can be harnessed to help realize the promise of new strategies for the elucidation and interpretation of previously unknown relationships. Machine learning, load balancing and efficient combinatorial search can be key considerations. Examples will be drawn from a variety of biological and health science applications.

**Thursday, February 3, 2017**

Title: An Epidemiological Journey

**Speaker: Christian Edholm, UTK**

Time: 3:40pm-4:30pm

Room: Ayres 405

In November 2014 I started my work with epidemiology when I attended the South African Mathematical Sciences Association Masamu program in Victoria Falls, Zimbabwe. I will talk about two of the projects that we worked on during that year and the following years.

In light of the Ebola outbreak in 2014, we worked on an Ebola model during our South Mrica Mathematical Sciences Association Masmau program in 2014 and 2015. Our model partitions the population into those who take precautions against contracting the disease and those who do not. We consider new infections arising in both hospital settings as well as in the community, and include transmission from dead bodies and the environment. Our goal is to illustrate role of education in limiting a potential future Ebola outbreaks in Sudan using data and modeling. We considered implications of a new strain with respect to different death rates and recovery rates.

Buruli Ulcers is a debilitating disease induced by Mycobacterium ulcer- ans. The transmission mechanism is not known at this time, but the bacteria is known to live in natural water environments. To understand the role of human con- tact with water environments in the spread of this disease, we formulate a model to emphasize the interaction between humans and the pathogen in a water environ-ment. Therefore, we included two susceptible classes with one having more expo- sure to the water environment than the other in our system of differential equations. We analyze stability of our model and estimate model parameters from data from Ghana. A global sensitivity analysis of certain parameters using the total number of infecteds as the output was completed. This work gives insight into the importance of various components of the mechanisms for transmission dynamics.

**Thursday, January 26, 2017**

Title: Attention Rising Math Seniors: are you ready?

**Speaker: Ken Stephenson, UTK**

Time: 3:40pm-4:30pm

Room: Ayres 405

Are you prepared for your senior year? Our program will give you a chance to share questions and experiences with other math students and to get a timely look at what's coming your way. We will have student panels on the GRE and on the graduate school application process, information about summer programs and research with faculty, and open discussions. And pizza! Join us and share (whether you're a rising senior or not).

Pizza in A 408 at 3:30

**Thursday, January 19, 2017**

Title: Boolean Formulas, Hypergraphs, and Combinatorial Topology

**Speaker: Oliver Thistlewaite, UTK **

Time: 3:40pm – 4:30pm

Room: Ayres 405

For this talk, our goal will be to study the shape of spaces of Boolean formulas. These formulas consist of variables which can be assigned TRUE or FALSE together with the logical operations AND, OR, and NOT. To do this, we will introduce a simplicial complex, called the theta complex, associated to any hypergraph. Simplicial complexes are a generalization of topological spaces one may obtain by gluing together line segments and solid triangles and a hypergraph is a generalization of a graph where an edge can connect any number of vertices.

Thursday, November 17, 2016

Title: Where Can Graduate Study in Mathematics Take Me?

**Speaker: Peter Perry, University of Kentucky**

Time: 3:40pm-4:30pm

Room: Ayres 405

Graduate study in mathematics can open up many different career possibilities in teaching, industry, and government. In this talk we'll look at some career trajectories of graduate students, how graduate school connected these students with opportunities, and how you can apply to graduate programs, evaluate offers, and make a sound decision. After a thirty-minute presentation I'll open up the floor for questions and discussion.

Note: Perry was Director of Graduate Studies at the University of Kentucky from 2012 to 2016 and directs the Graduate Scholars in Mathematics program at the University of Kentucky.

Pizza in A 408 @ 3:20, bring your own drink.

**Thursday, November 10, 2016**

Title: Drugs, Beer, Sex and Rock'n-Roll: What's Math got to do with it?

*Speaker: Louis J. Gross, UTK*

Time: 3:40pm-4:30pm

Room: Ayres 405

Mathematics underlies much of everyday experience, even if most people don't realize it. I'll discuss the process of mathematical modeling, point out how each of us use models regularly, and we'll play a game to illustrate the non-intuitive nature of even very simply described systems. We'll then go on to consider some biological examples that illustrate the utility of taking a quantitative perspective in making beer, the evolution of sex, drug dosing, and concert sound engineering.

**Thursday, October 13, 2016**

Title: Reproducibility in natural sciences: are all mathematical modeling-based studies fully reproducible?

*Speaker: Dr. Vitaly Ganusov, Math and Microbiology*

Time: 3:40pm-4:30pm

Room: Ayres 405

In the past several years there have been many reports indicating inability of some authors to reproduce large percent of published studies, mainly in medicine and psychology. Some funding agencies such as the NIH have responded to such reports by changing guidelines for grant applications to include indications of reproducibility. Mathematical modeling is now becoming a commonly used tool to understand mechanisms of biological system. Yet, as far as I know there have been no studies investigating reproducibility of mathematical modeling studies. In my talk I will discuss the issue of reproducibility of scientific studies, how mathematical modeling may have contributed to this issue, and what steps we need to take to reduce the degree of unreproducibility in natural sciences including studies using mathematical modeling.

Pizza at 3:15 in A 408, bring your own drink.

**Thursday, September 22, 2016**

Title: “The Mathematics of Poker”

**Speaker: Tim Schulze, UTK **

Time: 3:40pm – 4:30pm

Room: Ayres 405

In the January 9th, 2015 issue of Science, Bowling, Burch, Johanson and Tammelin announced that they had "solved" the game of heads-up, limit Texas Hold 'em. This news was widely reported in the main stream media. Motivated by this, we will take a somewhat broader look at the mathematics behind the game of poker and what it means to solve a game. We quickly find that a complete analysis is not practical. Multiple players, multiple rounds of betting, multiple raises, and variable bet sizes combine to make the game intractable. We are able to make progress, however, if we restrict our attention to heads-up play with some simplified betting rules. We expand upon this basic situation to include some elements of the popular game of Texas Hold 'Em, and conclude with a discussion of how heads-up, limit Hold 'em was solved.

Pizza in A 408 at 3:15, bring your own drink.

**Thursday, September 8, 2016**

TITLE: Decentralization and Pseudonymity in Bitcoin

**SPEAKER: Max Schuchard, Electrical Engineering and Computer Science UTK**

TIME: 3:40pm-4:30pm

ROOM: Ayres 405

Bitcoin is a cryptocurrency launched started seven years ago with the goal of providing a decentralized and pseudonymous way for individuals to transfer currency digitally. In this talk I will discuss how well Bitcoin has managed to maintain those goals. I will share some of my research examining how adversaries can, through careful observation and statistical analysis, link transaction pseudonyms with real world identities. We will also briefly examine how Bitcoin's proof of work scheme functions, look at why it fails to democratize mining, and examine alternative proof of work schemes which might provide better decentralization. The talk will cover all necessary background information, and no prior knowledge of Bitcoin or cryptocurrencies is required.

Pizza will be served in A 408 at 3:15 but bring your own drink.

**Thursday, August 25, 2016**

TITLE: Exploring the Effects of Order of Events in population Models

**SPEAKER: Suzanne Lenhart, UTK**

TIME: 3:40pm - 4:35pm

ROOM: Ayres 405

Exploring the effects of order of events in population models with discrete time Careful consideration of the order of events will be discussed for formulating population models with discrete time. Two examples will show how the order of events can affect optimal control results; the control actions include harvesting and augmentation of a population . One of the models is an integrodifference system which is continuous in its spatial variable..

Pizza in A 401 at 3:15 (bring your own drink)

Previous Junior Colloquiums: