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Mathematics Department

Colloquium Series

Fall 2017

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.

  • Dec
    06
  • On the rank of third order hypermatrices
    Prof. Edinah Gnang
    Johns Hopkins University
    Time: 03:45 PM

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    Third order hypermatrices are three dimensional analog of matrices. How do they come up in pure and applied math ? What is a natural hypermatrix algebra on such hypermatrices ? In addition answering these questions, the talk will describe a framework for extending the matrix rank-nullity theorem to third order hypermatrices. The talk is based on joint work with Yuval Filmus.
  • Nov
    29
  • Uncertainty quantification for partial differential equations: going beyond Monte Carlo
    Prof. Max Gunzburger
    Florida State University
    Time: 03:45 PM

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    We consider the determination of statistical information about outputs of interest that depend on the solution of a partial differential equation having random inputs, e.g., coefficients, boundary data, source term, etc. Monte Carlo methods are the most used approach used for this purpose. We discuss other approaches that, in some settings, incur far less computational costs. These include quasi-Monte Carlo, polynomial chaos, stochastic collocation, and multi-fidelity methods for all of which we also compare their relative strengths and weaknesses.
  • Nov
    15
  • Pattern Forming Swarms and the Physics of Mixed Reality
    Dr. Ira Schwartz
    Naval Research Laboratory
    Time: 03:45 PM

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    With the availability of ever more cheap and powerful computing, interest in the use of augmented and mixed-reality experiments has grown considerably in the engineering and physical sciences. Broadly speaking, these experiments consist of a simulated, or virtual model coupled directly to a physical experiment. Within the physical experiment, it is typical to find a good deal of uncertainty and noise since it is connected to the real world, and thus subjected to random perturbations. In contrast, the virtual part of the coupled system represents a somewhat idealized version of reality in which noise can be eliminated entirely, or at least well characterized. Thus, mixed-reality systems have very skewed sources of uncertainty spread through the entire system. In this talk, we consider the pattern formation of delay – coupled swarms theoretically and experimentally to illustrate the idea of mixed-reality. Motivated by physical experiments, we then consider a generic model of a mixed-reality system, and show how noise in the physical part of the system can influence the virtual dynamics through a large fluctuation, even when there is no noise in the virtual components. The virtual large fluctuation happens while the real dynamics exhibits only small random oscillations. We quantify the effects of uncertainty by showing how characteristic timescales of noise induced switching scale as a function of the coupling between the real and virtual parts of the experiment. This work is done in collaboration with Klimka Szwaykowska, Thomas Carr, M. Ani Hsieh, and Jason Hindes.
  • Oct
    24
  • The cosmic distance ladder
    Location: Mahan Auditorium
    Time: 07:00 PM

    View Abstract

    How do we know the distances from the earth to the sun and moon, from the sun to the other planets, and from the sun to other stars and distant galaxies? Clearly we cannot measure these directly. Nevertheless there are many indirect methods of measurement, combined with basic high-school mathematics, which can allow one to get quite convincing and accurate results without the need for advanced technology (for instance, even the ancient Greeks could compute the distances from the earth to the sun and moon to moderate accuracy). These methods rely on climbing a "cosmic distance ladder", using measurements of nearby distances to then deduce estimates on distances slightly further away; we shall discuss several of the rungs in this ladder in this talk.
  • Oct
    04
  • A New Algorithm in Group Theory
    Dr. Rita Gitik
    University of Michigan
    Time: 03:45 PM

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    We describe a new algorithm which determines if the intersection of a quasiconvex subgroup of a negatively curved group with any of its conjugates is infinite. The algorithm is based on the concepts of a coset graph and a geodesic core of a subgroup. This algorithm is utilized in several other new algorithms computing breadth, height, and width of a quasiconvex subgroup of a negatively curved group.
  • Aug
    30
  • A few remarks on two papers of E. N. Lorenz​
    Time: 03:45 PM

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    Among many papers of Edward Lorenz, two stand out, one published in 1963, on what we call the butterfly effect, ​and the other in 1996, where he introduced a 40-dimensional system of ODEs to model some of the main physical effects in the atmosphere -- the latter system is now called the Lorenz 96 equations. These two seminal papers have had enormous impact on mathematics and oceanography -- literally thousands of papers have subsequently been inspired by them. I will describe the derivations of these two systems and their numerical simulations.
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