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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: |
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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.
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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. |
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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 |
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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 |
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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. |