Fri, May 24 2024
Tue, May 28 2024
  • 11:00 am
    Dr. Jacob Campbell - The University of Virginia
    Even hypergeometric polynomials and finite free probability

    Math 243, Functional Analysis

    APM 7218 and Zoom (meeting ID:  94246284235)

    In 2015, Marcus, Spielman, and Srivastava realized that expected characteristic polynomials of sums and products of randomly rotated matrices behave like finite versions of Voiculescu's free convolution operations. In 2022, I obtained a similar result for commutators of such random matrices; one feature of this result is the special role of even polynomials, in parallel with the situation in free probability.

    It turns out that a certain family of special polynomials, called hypergeometric polynomials, arises naturally in relation to convolution of even polynomials and finite free commutators. I will explain how these polynomials can be used to approach questions of real-rootedness and asymptotics for finite free commutators. Based on arXiv:2209.00523 and ongoing joint work with Rafael Morales and Daniel Perales.

     

  • 11:00 am
    Sebastian Pardo Guerra - UCSD
    Extending undirected graph techniques to directed graphs via Category Theory

    Math 278A - Center for Computational Mathematics Seminar

    APM 2402 and Zoom ID 982 8500 1195

    It is well known that any directed graph induces an undirected graph by forgetting the direction of the edges and keeping the underling structure. In fact, this assignment can be extended to consider graph morphisms, thus obtaining a functor from the category of simple directed graphs and directed graph morphism, to the category of undirected graphs and undirected graph morphisms. This particular functor is known as a “forgetful” functor, since it forgets the notion of direction.

    In this talk, I will present a bijective functor that relates the category of simple directed graphs with a particular category of undirected graphs, whose objects we call “prime graphs”. Intuitively, prime graphs are undirected bipartite graphs endowed with a label that evokes a notion of direction. As an application, we use two undirected graph techniques to study directed graphs: spectral clustering and network alignment.

  • 2:00 pm
    Harold Polo - UC Irvine
    Goldbach Conjecture for Polynomials

    Combinatorics Seminar (Math 269)

    APM 7321

    In this talk we explore analogues of the Goldbach conjecture for classes of polynomials. In particular, we show that every polynomial with positive integer coefficients can be written as the sum of two irreducibles. This talk is based on joint works with Nathan Kaplan and Sophia Liao.

Thu, May 30 2024
  • 10:00 am
    Carlos Ospina - University of Utah
    Some Real Rel trajectories in $\mathcal{H}(1,1)$ that are not recurrent

    Math 211B - Group Actions Seminar

    APM 7321

    In this talk we will define the Rel foliation for a stratum of translation surfaces with at least two singularities. We will focus on the real Rel flow in the stratum $\mathcal{H}(1,1)$. We will provide some examples of orbits, and their closures. Finally, we will describe the real Rel orbits of tremors of surfaces and provide explicit examples of trajectories that are not recurrent, but do not diverge.

  • 2:00 pm
    Ellen Eischen - University of Oregon
    Algebraic and p-adic aspects of L-functions, with a view toward Spin L-functions for GSp_6

    Math 209: Number Theory Seminar

    APM 6402 and online (see https://www.math.ucsd.edu/~nts/)

    I will discuss recent developments and ongoing work for algebraic and p-adic aspects of L-functions. Interest in p-adic properties of values of L-functions originated with Kummer’s study of congruences between values of the Riemann zeta function at negative odd integers, as part of his attempt to understand class numbers of cyclotomic extensions. After presenting an approach to studying analogous congruences for more general classes of L-functions, I will conclude by introducing ongoing joint work of G. Rosso, S. Shah, and myself (concerning Spin L-functions for GSp_6). I will explain how this work fits into the context of earlier developments, while also indicating where new technical challenges arise. All who are curious about this topic are welcome at this talk, even without prior experience with p-adic L-functions or Spin L-functions.
     

  • 4:00 pm
    Ellen Eischen - University of Oregon
    It’s what you do next that matters.

    Joint Colloquium (Math 295) and AWM Colloquium

    APM 6402

    In my experience, successes often arise from circumstances that appear to be less than ideal, or even hopeless.  In the AWM Colloquium, I will discuss some key developments along my career path.

    The target audience is graduate students and postdocs.  Audience engagement is encouraged.  In particular, I will allow ample time for questions.
     

Fri, May 31 2024
  • 9:30 am
    Jacob Keller - UC San Diego
    The Birational Geometry of K-Moduli Spaces

    PhD Thesis Defense

    AP&M 7321

    Zoom link: https://ucsd.zoom.us/j/99833378355

    For $C$ a smooth curve and $\xi$ a line bundle on $C$, the moduli space $U_C(2,\xi)$ of semistable vector bundles of rank two and determinant $\xi$ is a Fano variety. We show that $U_C(2,\xi)$ is K-stable for a general curve $C \in \overline{M}_g$. As a consequence, there are irreducible components of the moduli space of K-stable Fano varieties that are birational to $\overline{M}_g$. In particular these components are of general type for $g\geq 22$.

  • 4:00 pm
    Dr. Michael McQuillan - University of Rome Tor Vergata
    Flattening and algebrisation.

    Math 208: Seminar in Algebraic Geometry

    APM 7321

    Often natural moduli problems, e.g. foliated surfaces, come without an ample line bundle, so the algebraisability of formal deformations, and the very existence of a moduli space requires a study of the mermorphic functions on the aforesaid deformations, and the flattening (by blowing up) of the resulting meromorphic maps. In such a context the flattening theorem of Raynaud & Gruson, and derivatives thereof, is close to irrelevant since it systematically uses schemeness to globally extend local centres of blowing up. This was already well understood by Hironaka in his proof of holomorphic flattening, and his ideas are the right ones. Nevertheless, the said ideas can be better organised with a more systematic use of Grothendieck's universal flatifier, and, doing so, leads to a fully functorial, and radically simpler, proof provided the sheaf of nilpotent functions is coherent-which is true for excellent formal schemes, but, unlike schemes or complex spaces, is false in general.