Sp 2020

Jan 22

Speaker: Dr. Tricia Brown

Title: Independent chessboard arrangements

Abstract: Over the last 150 years, mathematical questions on a chessboard have generated an abundance of results from recreational puzzlers as well as professional mathematicians, statisticians, and computer scientists. In this talk, we look at two combinatorial questions dealing with independent arrangements, that is, a chessboard arrangement in which none of the pieces on the board may attack any other. We'll restrict ourselves to a uniform army of each of the six standard chess pieces - rooks, bishops, knights, kings, queens, and pawns - to try to determine first the size of a maximum independent arrangement and second the number of such arrangements.

Feb 5

Speaker: Dr. Dawit Denu

Title: A stochastic model to assess the roles of delay time to treatment, information intervention and random supply of domestic and foreign aids on HIV/AIDS epidemics

Abstract: In this talk we will examine a nonlinear system of Ito-differential equation to model HIV/AIDS epidemics with the goals to assess the roles of delayed treatment, information intervention and random supply of aids on HIV/AIDS epidemics. After validating the model, we will discuss how poverty/living standards, delayed treatment, information intervention and random and sporadic supply of aids on HIV/AIDS epidemics will affect the transmission of the infection. Finally, numerical simulations and examples will be presented to support some of the theoretical results.

Feb 19

Speaker: Timothy Eller

Title: Reciprocal hyperelliptic curves

Mar 11

Speaker: Jack Wagner

Title: A Quick Overview of Perverse Sheaves

Abstract: Two ubiquitous philosophies in modern mathematics are (1) in order to study a type of mathematical object, we should study the morphisms, or functions, between them, and (2) try to reduce any problem to a linear algebra problem. These notions can be realized through the tools of category theory. In particular, when our desired objects are geometric in nature, we can apply these notions directly using sheaves. Smooth objects, such as spheres, have a lot of useful sheaves. This can be a lot more challenging when your object is not smooth, which led to the development of perverse sheaves in the 1970s by Goresky and MacPherson. Since then, perverse sheaves have had far reaching applications in algebraic geometry, partial differential equations, and representation theory. I will start this talk by introducing and motivating the language of category theory and sheaves, then I will describe the structure of perverse sheaves and mention some properties and uses in modern representation theory. I will end my talk describing my experience as a graduate student at the University of Georgia for people interested in graduate school.

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