Week of October 10, 2021

Mon Oct 11, 2021
12:00pm - Zoom - Probability and Analysis Webinar
Charles Bordenave - (Institute of Mathematics of Marseille)
Strong asymptotic freeness for independent uniform variables on compact groups

Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random permutations acting on the orthogonal of the Perron-Frobenius eigenvector. In this talk, we consider a new matrix unitary model appearing naturally from representation theory of compact groups. We fix a non-trivial signature, i.e. two finite sequences of non-increasing natural numbers, and for n large enough, consider the irreducible representation of Un associated to this signature. We show that strong asymptotic freeness holds in this generalized context when drawing independent copies of the Haar measure. We also obtain the orthogonal variant of this result. This is a joint work with Benoît Collins.


To see zoom ID and psscode click on the name of the speaker on the webstie of the seminar:

4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics
Durkbin Cho - (Dongguk University, Seoul, Korea)
BPX preconditioners for isogeometric analysis using analysis-suitable T-splines

In this talk, we propose optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern & Peterseim (2015, Analysis-suitable adaptive T-mesh refinement with linear complexity. Comput. Aided Geom. Design, 34, 50–66) we can guarantee that the obtained T-meshes have a multilevel structure and that the associated T-splines are analysis suitable, for which we can define a dual basis and a stable projector. Taking advantage of the multilevel structure, we prove that BPX preconditioners have optimal complexity and present several numerical experiments to confirm our theoretical results.


Tue Oct 12, 2021
4:00pm - NS2 1201 - Differential Geometry
Yiyue Zhang - (UC Irvine)
The hyperbolic positive mass theorem and harmonic level sets

I will introduce the harmonic level set method developed by Stern in 2019.
This technique has been used to prove the positive mass theorems in various
settings, for example, the Riemannian case, the spacetime case, the
hyperbolic case, and the positive mass theorem with charge. I will focus on
the positive mass theorem for asymptotically hyperbolic manifolds. We give a
lower bound for the mass in the asymptotically hyperbolic setting. In this
setting, we solve the spacetime harmonic equation and give an explicit
expansion for the solution. We also prove some rigidity results as
corollaries. This is joint work with Bray, Hirsch, Kazaras, and Khuri.

Wed Oct 13, 2021
2:00pm to 3:00pm - 510R - Combinatorics and Probability
March Boedihardjo - (UCI)
Sharp matrix concentration

Classical matrix concentration inequalities are sharp up to a logarithmic factor. This logarithmic factor is necessary in the commutative case but unnecessary in many classical noncommutative cases. We will present some matrix concentration results that are sharp in many cases, where we overcome this logarithmic factor by using an easily computable quantity that captures noncommutativity. Joint work with Afonso Bandeira and Ramon van Handel. Paper: https://arxiv.org/abs/2108.06312

Thu Oct 14, 2021
9:00am to 10:00am - Zoom - Inverse Problems
Elena Beretta - (NYU Abu Dhabi)
Title: Identification of cavities in a nonlinear model arising from cardiac electrophysiology via Gamma-convergence


10:00am to 11:00am - Zoom: https://uci.zoom.us/j/91257486031 - Number Theory
Sarah Arpin - (University of Colorado)
Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs

Supersingular elliptic curves have seen a resurgence in the past decade with new post-quantum cryptographic applications. In this talk, we will discover why and how these curves are used in new cryptographic protocol. Supersingular elliptic curve isogeny graphs can be endowed with additional level structure. We will look at the level structure graphs and the corresponding picture in a quaternion algebra.