Past Seminars- Number Theory

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  • Nathan Pflueger
    Tue Jun 6, 2017
    2:00 pm
    To any point p on a smooth algebraic curve C, the Weierstass semigroup is the set of all possible pole orders at p of regular functions on C \ {p}. The question of which sets of integers arise as Weierstass semigroups is a very old question, still widely open. We will describe progress on the question, defining a quantity called the effective...
  • Carmelo Interlando
    Tue May 9, 2017
    2:00 pm
    In this talk a lattice will mean a discrete subgroup Λ of n-dimensional Euclidean space; the sphere packing associated to Λ is the arrangement of congruent spheres of radius equal to one half the minimum distance of Λ and centered at the lattice points.  The main parameter under consideration will be the packing...
  • Shahed Sharif
    Tue May 2, 2017
    2:00 pm
    The period and index of a curve C are two quantities which describe the failure of C to have rational points. The mismatch between the two is of interest for its impact on the Shafarevich-Tate group of the Jacobian of C. The period-index problem is to determine what values of period and index are possible for a given...
  • Cristian Popescu
    Tue Apr 25, 2017
    2:00 pm
    A special case of the GRS Conjecture predicts a surprising link between values of derivatives of p-adic and global L-functions. Recently, Dasgupta-Kakde-Ventullo have used Hida families of modular forms to make progress towards the proof of a rational form of this special case. In  this lecture I will report on an...
  • Liang Xiao
    Tue Apr 18, 2017
    2:00 pm
    The topic of this talk will be understanding the p-adic slopes of modular forms. Recently, Bergdall and Pollack, based on computer calculations, raised a very interesting conjecture on the slopes of overconvergent modular forms, which predicts that the Newton polygons of the characteristic power series of U_p are the same as the ...
  • Derek Garton
    Tue Feb 28, 2017
    2:00 pm
    Given two polynomials with integer coefficients, for how many primes p do the polynomials induce nonisomorphic dynamical systems mod p? This question will lead us to the study of the statistics of wreath products, the Galois theory of dynatomic polynomials, and other topics. This work is joint with Andrew Bridy.
  • Michiel Kosters
    Tue Feb 21, 2017
    2:00 pm
    Let P: ... -> C_2 -> C_1 -> P^1 be a Z_p-cover of the projective line over a finite field of characteristic p which ramifies at exactly one rational point. In this talk, we study the p-adic Newton slopes of L-functions associated to characters of the Galois group of P. It turns out that for covers P such that the genus of C_n is a...