Past Seminars- Number Theory

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  • 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...
  • Bryden Cais
    Thu Apr 12, 2018
    3:00 pm
    Let Y --> X be a branched G-covering of curves over a field k.  The genus of X and the genus of Y are related by the famous Hurwitz genus formula.  When k is perfect of characteristic p and G is a p-group, one also has the Deuring-Shafarevich formula which relates the p-rank of X to that of Y.  In this talk, we will discuss...
  • Lê Thái Hoàng
    Thu Mar 15, 2018
    3:00 pm
    The Möbius randomness principle states that the Möbius function μ does not correlate with simple or low complexity sequences F(n), that is, we have non-trivial bounds for sums ∑ μ(n) F(n). By analogy between the integers and the ring F_q[t] of polynomials over a finite field F_q, we study this principle in the latter...
  • Danny Nguyen
    Thu Mar 1, 2018
    3:00 pm
    Short generating functions were first introduced by Barvinok to enumerate integer points in polyhedra. Adding in Boolean operations and projection, they form a whole complexity hierarchy with interesting structure. We study them in the computational complexity point of view. Assuming standard complexity assumption, we show that these functions...
  • Sean Howe
    Thu Feb 15, 2018
    3:00 pm
    A fundamental observation in Katz-Sarnak's study of the zero spacing of L-functions is that Frobenius conjugacy classes in suitable families of varieties over finite fields approximate infinite random matrix statistics. For example, the normalized Frobenius conjugacy classes of smooth plane curves of degree d over F_q approach the Gaussian...
  • Oleksiy Klurman
    Thu Feb 8, 2018
    3:00 pm
    Understanding joint behaviour of $(f(n),g(n+1))$ where f and g are given multiplicative functions play key role in analytic number theory with potentially profound consequences such as Riemann hypothesis, twin prime conjecture, Chowla's conjecture and many others. In the the first part of this talk, I will discuss joint work with A. Mangerel,...
  • Bianca Thompson
    Thu Jan 25, 2018
    3:00 pm
    The study of discrete dynamical systems boomed in the age of computing. The Mandelbrot set, created by iterating 0 in the function z^2+c  and allowing c to vary, gives us a wealth of questions to explore. We can ask about the number of rational preperiodic points (points whose iterates end in a cycle) for z^2+c. Can this number be uniform as...