Mathematics Department

Colloquium Series

Spring 2016

All talks are from 3:45-4:45 p.m. in the Colloquium room, unless otherwise specified.

Tea and cookies will be served in the Lecture room starting at 3:30 p.m.

  • Feb
    24
  • Stabilized Coexistence Among Mutual Cheaters in Cyclic Public Goods Games with Optimized Taxation
    Prof. Chris Griffin
    USNA

    View Abstract

    We study the problem of stabilized coexistence in a three-species public goods game, in which each species simultaneously contributes to their own public good while freeloading off another species' public good. We assume population growth is governed by absolute success as a function of the return from ones own public good minus the cost and the return from free-loading off another public good. We show that proportional population growth is governed by a replicator dynamic with at most one interior unstable fixed point; i.e. that the population becomes dominated by a single species. We then show that applying an externally imposed ``tax" on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and un-taxed cases. We formulate an optimal taxation problem, and show that it admits a quasi-linearization that results in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second order ordinary differential equation.
  • Feb
    11
  • What are the Odds?
    Prof. Amie Wilkinson
    University of Chicago
    Location: Rickover 102
    Time: 07:30 PM

    View Abstract

    How do we think about the chances of rare events occurring, and are unlikely events really all that unlikely? This talk will explore two complementary themes: 1) the emergence of apparent structure and order from completely random processes; and 2) how unrandom, deterministic processes can produce seemingly random output.
  • Jan
    13
  • Symbolic dynamical (and other) approaches to the analysis of biological data
    Prof. David Koslicki
    Oregon State University

    View Abstract

    Symbolic dynamics (and more generally, discrete dynamical systems) offers a wide variety of tools for analyzing strings of symbols. In this talk, I will present a number of approaches for utilizing these tools in the analysis of biological data. In particular, I will discuss topological entropy and how it can be used to distinguish between different kinds of DNA sequences and also the usage of topological pressure in analyzing neuroscience data. Time permitting, I will also discuss how a certain class of Markov chains can characterize genomic data obtained from communities of microorganisms. This talk will be accessible to a broad audience, with little to no background required.
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