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Mathematics Department

Colloquium Series

Spring 2019

All talks are 3:45-4:45 p.m. in the Colloquium room (Chauvenet 110), unless otherwise specified.

Cookies will be served in the lecture room starting shortly before the talk.

  • Oct
  • Mark Levi
    Penn State
    Time: 03:45 PM
  • Sep
  • Rita Gitik
    U. Michigan
    Time: 03:45 PM
  • May
  • John Gemmer
    Wake Forest
    Time: 03:45 PM
  • Apr
  • Hadi El-Amine
    George Mason
    Time: 03:45 PM
  • Apr
  • Theta polynomials in geometry, Lie theory, and combinatorics
    Harry Tamvakis
    U. Maryland
    Time: 03:45 PM

    View Abstract

    The classical Schur polynomials form a natural basis for the ring of symmetric polynomials, and have geometric significance since Giambelli showed that they represent the Schubert classes in the cohomology ring of Grassmannians. Moreover, these polynomials enjoy rich combinatorial properties. In the last decade, an exact analogue of this picture has emerged in the symplectic and orthogonal Lie types, with the Schur polynomials replaced by the theta and eta polynomials of Buch, Kresch, and the speaker. I will discuss this correspondence in the case of the symplectic group and theta polynomials.
  • Apr
  • Darren Creutz
    Time: 03:45 PM
  • Mar
  • Leonardo Mihalcea
    Virginia Tech
    Time: 03:45 PM
  • Mar
  • Angel Kumchev
    Towson U.
    Time: 03:45 PM
  • Jan
  • Growth and groups
    Moon Duchin
    Time: 12:00 PM

    View Abstract

    Mathematicians have long studied the question of volume growth in manifolds and combinatorial growth in groups. I want to explain some of how these are related and why they're interesting, and I'll use the Heisenberg group and its geometry as the main example.
  • Jan
  • Population persistence under prolonged and reoccurring disturbances
    Amy Veprauskas
    U. Louisiana-Lafayette
    Time: 03:45 PM

    View Abstract

    An important focus for management and conservation is determining whether a species or a system of interacting species can sustain itself. This question becomes increasingly important as populations are exposed to various disturbances, both natural and anthropogenic, such as hurricanes, habitat fragmentation, toxicants, and invasive species. Here we examine how disturbances may impact species persistence from two perspectives. First, for short-lived species, prolonged exposure to a disturbance has the potential to result in rapid evolution of toxicant resistance. We apply evolutionary game theory to a Leslie matrix model for daphniids to obtain Darwinian equations that couple population and evolutionary dynamics. Using bifurcation analysis, we examine how evolutionary changes in response to a disturbance may allow a population to persist at higher levels of the disturbance than is possible without evolution. Next, we develop a non-autonomous matrix model to consider the effect of reoccurring disturbances on population persistence. This model uses a two-state Markov chain to describe the frequency and average length of effect of the disturbances. We derive an approximation for a population’s stochastic growth rate and apply sensitivity analysis to examine how best to mitigate the impact of disturbances.
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