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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
    16
  • Mark Levi
    Penn State
    Time: 03:45 PM
  • Sep
    18
  • Rita Gitik
    U. Michigan
    Time: 03:45 PM
  • May
    01
  • John Gemmer
    Wake Forest
    Time: 03:45 PM
  • Apr
    17
  • Hadi El-Amine
    George Mason
    Time: 03:45 PM
  • Apr
    10
  • 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
    03
  • Darren Creutz
    USNA
    Time: 03:45 PM
  • Mar
    27
  • Leonardo Mihalcea
    Virginia Tech
    Time: 03:45 PM
  • Mar
    20
  • The Waring-Goldbach Problem
    Angel Kumchev
    Towson U.
    Time: 03:45 PM

    View Abstract

    The Waring-Goldbach problem is the central question in the additive theory of prime numbers. In simplest terms, this is the question which positive integers can be represented as sums of $s$ $k$-th powers of primes: Given fixed positive integers $s > k \ge 1$, under what conditions on $n$ does the Diophantine equation $$ p_1^k + p_2^k + \dots + p_s^k = n $$ have solutions in primes $p_1, p_2, \dots, p_s$? When $k=1$, this question turns into Goldbach’s problem; and when the variables are not restricted to the primes, it becomes Waring’s problem. I will review the history of the Waring-Goldbach problem, including some recent developments, and will provide a brief glimpse into the kind of mathematics that lies behind the proofs of the theorems.
  • Jan
    25
  • Growth and groups
    Moon Duchin
    Tufts
    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
    14
  • 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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