Fall 2020 – Summer 2021 – Abstracts

Wednesday, April 21, 2021.  Mathematics Thesis Defense.

Matthew Ackley, Mathematics MA student. (Advisor: Peter Stechlinski)
“Lexicographic sensitivity functions for nonsmooth models in mathematical biology”
3:30 – 4:20 pm, via videoconference

Abstract:

Wednesday, April 14, 2021.  Mathematics Graduate Seminar.

Matthew D’Angelo, Mathematics MA student.
“An Introduction to Evolutionary Game Theory”
3:00 – 3:50 pm, via videoconference

Abstract: The first of a series of two talks will focus on introducing some basic game theory concepts.  The main object of study will be symmetric, normal-form games, which are games defined by a payoff matrix.  Pure and mixed strategies, represented as points on the simplex, will be explored, including special classes of strategies, such as Nash equilibria and evolutionarily stable strategies, and their relations.  We will illustrate these concepts using games such as Rock-Paper-Scissors or Hawk-and-Dove as examples.  Important results will be discussed, such as conditions guaranteeing the existence of a Nash equilibrium for a given game.  This talk sets the stage for the second talk in the series, which will use game theory concepts to build a framework for modeling population dynamics.

Wednesday, March 24, 2021.  Mathematics Graduate Seminar.

Matthew Ackley, Mathematics MA student.
“Quantifying parametric dependence in nonsmooth systems of ordinary differential equations”
4:00 – 4:50 pm, via videoconference (click to join)

Abstract: Systems of ordinary differential equations (ODEs) are a common framework for mathematical models in engineering and biology; however, different choices for parameter values can cause ODE solutions to exhibit drastically different behavior over time. Classical forward-parametric sensitivity functions are capable of providing a local measure of a model’s predicted reactivity to parametric perturbations about some particular reference values and are hence useful when comparing parametric influence. Even so, the existence of these functions requires the ODEs at hand to be at least once continuously differentiable, which is restrictive when trying to model phenomena exhibiting hybrid or switching behaviors. In this talk, we will discuss recently-developed lexicographic sensitivity functions, which are based on lexicographic calculus and analogous to the classical functions but applicable to a much larger class of functions which are not necessarily $C^1$. Relevant background theory in nonsmooth analysis will be given and illustrative examples discussed.