Past Seminars

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  • Ilya Soloveychik
    Tue Apr 24, 2018
    12:00 pm
    Random matrices have become a very active area of research in the recent years and have found enormous applications in modern mathematics, physics, engineering, biological modeling, and other fields. In this work, we focus on symmetric sign (+/-1) matrices (SSMs) that were originally utilized by Wigner to model the nuclei of heavy atoms in mid-50s...
  • Abel Klein
    Fri Apr 20, 2018
    4:00 pm
  • Christoph Marx
    Fri Apr 20, 2018
    1:00 pm
    We prove the Hölder-continuity of the density of states measure (DOSm) and the integrated density of states (IDS) for discrete random Schrödinger operators with finite-range potentials with respect to the probability measure. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli...
  • Peter Hislop
    Thu Apr 19, 2018
    2:00 pm
    We discuss localization and local eigenvalue statistics for Schr\"odinger operators with random point interactions on $R^d$, for $d=1,2,3$. The results rely on probabilistic estimates, such as the Wegner and Minami estimate, for the eigenvalues of the Schr\"odinger operator restricted to cubes. The special structure of the point...
  • Vladimir Baranovsky
    Wed Apr 18, 2018
    2:00 pm
    We continue with Chapter 4 of Fulton-Harris
  • Todd Kemp
    Tue Apr 17, 2018
    11:00 pm
    Random matrix theory began with the study, by Wigner in the 1950s, of high-dimensional matrices with i.i.d. entries (up to symmetry).  The empirical law of eigenvalues demonstrates two key phenomena: bulk universality (the limit empirical law of eigenvalues doesn't depend on the laws of the entries) and concentration (the convergence is...
  • Weiyan Chen
    Tue Apr 17, 2018
    3:00 pm
    It is a classical topic dating back to Maclaurin (1698–1746) to study certain special points on smooth cubic plane curves, such as the 9 inflection points (Maclaurin and Hesse), the 27 sextatic points (Cayley), and the 72 points "of type 9" (Gattazzo). Motivated by these algebro-geometric constructions, we ask the following...