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.

  • Apr
    27
  • Maximal Curves: An Excursion
    Prof. Beth Malmskog
    Villanova University

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    A curve with as many points as possible over a finite field F_q is known as a maximal curve. Well-studed examples include the Hermitian, Suzuki and Ree curves. Curves with many points also often have many symmetries. Maximal curves bring together combinatorics, algebra, algebraic geometry, and number theory. These objects have also found application in coding theory, through algebraic geometry codes, and cryptography, through variations of the McEliece cryptosystem. This talk will give an introduction to the area and a tour of some research directions and open problems. We will discuss error correcting codes, automorphism groups, and recent attacks on and variations of the McEliece cryptosystem.
  • Apr
    20
  • Minimum Rank Problems on Graphs
    Prof. Franklin Kenter
    Rice University

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    For an undirected graph $G$, we define the minimum rank of $G$ to be the minimum rank over all symmetric matrices with a sparsity pattern (i.e., zero/nonzero pattern) associated with the graph. A newer combinatorial approach known as zero forcing has aided the study of this otherwise linear-algebraic problem. As it turns out, these simple parameters have many different applications. Zero forcing, in particular, has been (unknowingly) reinvented several times within different contexts. These applications include topological embeddings of graphs, quantum systems, electrical networks, network search, and more. In this talk, we will discuss recent work integrating these efforts among these different fields with a focus two lines of research. The first is to develop computational approaches to these problems using numerical algorithms. The second is to establish linear-algebraic relationships to the combinatorial applications where none have existed before.
  • Apr
    13
  • Lattice Path Matroids, the Tutte Polynomial, and the G-Invariant
    Prof. Joseph Bonin
    George Washington University

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    Matroids are combinatorial abstractions of linear independence. They arise in linear algebra, coding theory, projective and affine geometry, graph theory, knot theory, hyperplane arrangements, optimization, algebraic geometry, physics, and other fields. While focusing on a very accessible class of matroids that come from lattice paths, we will discuss a number of topics in matroid theory, including the Tutte polynomial. Many of the applications of matroid theory revolve around the Tutte polynomial. We will also discuss a newer and more powerful matroid invariant, Derksen's G-invariant. This talk should be accessible to a wide audience.
  • Apr
    08
  • Collective Dynamics: Consensus, Emergence of Leaders, and Social Hydrodynamics
    Prof. Eitan Tadmor
    University of Maryland
    Time: 12:00 PM
  • Mar
    28
  • A model reduction approach to inversion
    Prof. Liliana Borcea
    University of Michigan

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    Model reduction is a dynamic field in computational mathematics that seeks accurate and computationally inexpensive approximations to dynamical system responses. We discuss very recent results which introduce a novel use of model reduction, for inverse problems. We consider two generic inverse problems for time dependent PDE's: the first seeks to determine the diffusion coefficient in a parabolic equation and the second is an inverse scattering problem for the wave equation. We will show how to construct reduced models that are useful for inversion, will describe the benefits of such an approach, and will illustrate the performance of the methods with numerical simulations. We will also describe open (future research) problems.
  • Mar
    03
  • Putting Big Data To Work
    Bill Franks
    Teradata
    Location: Rickover 110

    View Abstract

    Big data is everywhere. You can’t avoid being exposed to discussions around big data, and the analysis of it, on a regular basis. The downside of this attention is that there is a lot of hype and misinformation in the marketplace. Many organizations are confused about how to get started, what actions to take, and what pitfalls to avoid. Based on content from his two popular books Taming The Big Data Tidal Wave and The Analytics Revolution, Bill Franks, Chief Analytics Officer for Teradata Corporation, will provide an overview of important themes to understand regarding big data. The talk will address technological, methodological, and implementation points that must be considered. The US Navy, and the Midshipmen being trained at the U.S. Naval Academy, must adapt and implement big data analytics if they are to optimize performance, and minimize the cost, of protecting and managing the fleet.
  • Feb
    24
  • Stabilized Coexistence Among Mutual Cheaters in Cyclic Public Goods Games with Optimized Taxation
    Prof. Chris Griffin
    USNA

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    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

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    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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