Past Seminars- Probability

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  • Roman Vershynin
    Tue May 1, 2018
    11:00 am
    The most fundamental kind of functions studied in computer science are Boolean functions. They take n bits as an input and return one bit as an output. Most Boolean functions oscillate a lot, which is analogous to the fact that "most" continuous functions on R are nowhere differentiable. If we want to generate a "smooth...
  • 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...
  • 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...
  • Stanislav Molchanov
    Tue Mar 6, 2018
    3:00 pm
    The talk will present the review of the mathematical models of the phase transitions and diffusion of the proteins. Content. Kindergarten biophysics Physical Brownian motion Folding – unfolding phase transition Diffusion coefficient as the function of the temperature Intermediate asymptotics Diffusion with aggregation
  • Ian Charlesworth
    Tue Feb 27, 2018
    11:00 am
    Free entropy theory is an analogue of information theory in a non-commutative setting, which has had great applications to the examination of structural properties of von Neumann algebras. I will discuss some ongoing joint work with Paul Skoufranis to extend this approach to the setting of bi-free probability which attempts to study simultaneously...
  • Gene Kim
    Tue Feb 20, 2018
    11:00 am
    The distribution of descents in certain conjugacy classes of S_n have been previously studied, and it is shown that its moments have interesting properties. This paper provides a bijective proof of the symmetry of the descents and major indices of matchings (also known as fixed point free involutions) and uses a generating function approach...
  • Yan Shuo Tan
    Thu Feb 8, 2018
    11:00 am
    Mathematical phase retrieval is the problem of solving systems of rank-1 quadratic equations. Over the last few years, there has been much interest in constructing algorithms with provable guarantees. Both theoretically and empirically, the most successful approaches have involved direct optimization of non-convex loss functions. In the first half...