Past Seminars- Colloquium

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  • Yulij Ilyashenko
    Tue Oct 11, 2016
    3:00 pm
    The talk provides a new perspective of the global bifurcation theory on the plane. Theory of planar bifurcations consists of three parts: local, nonlocal and global ones. It is now clear that the latter one is yet to be created. Local bifurcation theory (in what follows we will talk about the plane only) is related to  ...
  • Jerry Goldstein
    Thu Apr 28, 2016
    4:00 pm
    We will discuss three one space dimensional time dependent linear parabolic equations: the heat equation, the Black-Scholes equation (describing stock options) and the Cox-Ingersoll-Ross equation (describing bond markets).  New results will involve representation of the solution semigroups, chaotic properties of the semigroups, and a new kind...
  • S. Shlosman
    Thu Mar 10, 2016
    4:00 pm
    I will talk about the Ising model -- the drosophila of the rigorous statistical physics. It turns out that some of the new phenomena which appear in modern mathematical physics can still be observed in the Ising model as well.  One example which I will focus on is the size of typical fluctuations of the extended systems. If the size of the...
  • Gunther Uhlmann
    Thu Jan 28, 2016
    4:00 pm
         We will consider the inverse problem of determining the sound speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes...
  • Vadim Kaloshin
    Thu Jan 21, 2016
    4:00 pm
    The classical Birkhoff conjecture states that the only integrable convex planar domains are circles and ellipses. In a joint work with A. Avila and J. De Simoi we show that this conjecture is true for perturbations of ellipses of small eccentricity. It turns out that the method of proof gives an insight into deformational spectral rigidity of...
  • Max Gunzburger
    Thu Dec 3, 2015
    4:00 pm
    We use the canonical examples of fractional Laplacian and peridynamics equations to discuss their use as models for nonlocal diffusion and mechanics, respectively, via integral equations with singular kernels. We then proceed to discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus...
  • Yuki Takahashi
    Thu Nov 12, 2015
    3:00 pm
    In this co-sponsored UCI Illuminations and Juggle Buddies event, we will talk about the math theories associated with the art of juggling, a form of prop manipulation. This theory involves the use of Siteswap notation. Siteswap is a juggling notation used to describe possible juggling patterns. For example, the most basic three-ball trick called a...