Mathematics Department

Upcoming Talks

This is a list of all upcoming talks for the next two weeks. Talks are from 3:45-4:45 p.m. in the Colloquium or Seminar Room, unless otherwise specified.

  • Mar
    31
  • Modeling epidemic rare events: A dynamical systems perspective of disease extinction and control
    Dr. Ira Schwartz
    Naval Research Laboratory
    Time: 12:00 PM
    Applied Math Seminar
  • Apr
    01
  • Tools from Computational Topology, with applications in the life sciences
    Prof. Sarah Day
    College of William and Mary
    Time: 03:45 PM
    Colloquium Series

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    The field of topology, and in particular computational topology, has produced a powerful set of tools for studying both model systems and data measured directly from physical systems. I will focus on three classes of topological tools: computational homology, topological persistence, and, very briefly, Conley index theory. To illustrate their use, I will discuss recent projects studying coupled-patch population dynamics, flickering red blood cells, and pulse-coupled neurons.
  • Apr
    02
  • Symbolic Dynamics and Entropy via Conley Index Theory
    Prof. Sarah Day
    College of William and Mary
    Operator Algebras and Dynamics Seminar

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    Conley index theory, a generalization of Morse theory using algebraic topology, may be used in a computational framework to prove the existence of dynamics of various types. When searching for highly complicated dynamics, however, the Conley index may also become highly complicated and difficult to interpret. We present an automated approach to processing Conley index information for discrete-time dynamical systems. This approach produces a topologically semi-conjugate symbolic system whose entropy serves as a lower bound for the entropy of the system under study. Recent modifications of the original approach published in 2006 produce symbolic systems that capture more of the complexity encoded by the index, in some cases leading to substantial increases in computed lower bounds on system entropy. Sample results will be shown for the 2-dimensional Henon map and the infinite-dimensional Kot-Schaffer map. This is joint work with Rafael Frongillo.
  • Apr
    07
  • Fast Times in Linear Programming: Early Success, Two Revolutions, and Continuing Mysteries
    Prof. Margaret Wright
    New York University
    Time: 07:30 PM
    Colloquium Series

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    Linear programming (LP), which isn't really about programming, is a simple-to-state mathematical problem of enormous practical importance. The dramatic saga of LP solution methods began immediately after World War II with unexpected practical success that continued for more than 30 years despite theoretical reservations; next came two sweeping revolutions whose effects are often misunderstood. This talk will describe mathematical and computational issues from the history of LP, enlivened by controversy and international politics, as well as some remaining mysteries.
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