
10:30 am
Zhichao Wang  UC San Diego, Department of Mathematics
Spectral Properties of Neural Network Modelsectra
PhD Defense
APM 6402

12:30 pm

1:00 pm
Nandagopal Ramachandran  University of California San Diego
Some Fitting ideal computations in Iwasawa theory over Q and the theory of Drinfeld module
Final Defense
APM 6218 & Zoom
(email naramach@ucsd.edu for Zoom link)

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)
AbstractIn 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 realrootedness 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
AbstractIt 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
AbstractIn 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.

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
AbstractIn 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 padic aspects of Lfunctions, with a view toward Spin Lfunctions for GSp_6
Math 209: Number Theory Seminar
APM 6402 and online (see https://www.math.ucsd.edu/~nts
/ )AbstractI will discuss recent developments and ongoing work for algebraic and padic aspects of Lfunctions. Interest in padic properties of values of Lfunctions 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 Lfunctions, I will conclude by introducing ongoing joint work of G. Rosso, S. Shah, and myself (concerning Spin Lfunctions 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 padic Lfunctions or Spin Lfunctions.

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
AbstractIn 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.

5:00 pm
Gongping Niu  UCSD
Singular Isoperimetric Regions and Twisted Jacobi fields on Locally Stable CMC Hypersurfaces with Isolated Singularities
PhD Defense
APM 7321
AbstractIn this talk, we will demonstrate that the wellknown singularity Hausdorff dimension estimates for isoperimetric regions are sharp by constructing singular examples in dimensions 8 and higher. Then, to explore the isoperimetric regions under generic Riemannian metrics, we will discuss the twisted Jacobi field of singular constant mean curvature hypersurfaces under certain regularity assumptions.

9:30 am
Jacob Keller  UC San Diego
The Birational Geometry of KModuli Spaces
PhD Thesis Defense
AP&M 7321
Zoom link: https://ucsd.zoom.us/j/
99833378355 AbstractFor $C$ 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 Kstable for a general curve $C \in \overline{M}_g$. As a consequence, there are irreducible components of the moduli space of Kstable Fano varieties that are birational to $\overline{M}_g$. In particular these components are of general type for $g\geq 22$.

10:30 am
Ryan Schneider  UC San Diego
Pseudospectral DivideandConquer for the Generalized Eigenvalue Problem
Final Defense
APM 6402
(optional Zoom link: https://ucsd.zoom.us/j/
7559761801 )AbstractCome find out how to (randomly) diagonalize any $n \times n$ matrix pencil in fewer than $O(n^3)$ operations!

4:00 pm
Dr. Michael McQuillan  University of Rome Tor Vergata
Flattening and algebrisation.
Math 208: Seminar in Algebraic Geometry
APM 7321
AbstractOften 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 coherentwhich is true for excellent formal schemes, but, unlike schemes or complex spaces, is false in general.