Week of May 22, 2022

Mon May 23, 2022
4:00pm to 5:00pm - RH 306 - Applied and Computational Mathematics
Solmaz Kia - (Mechanical and Aerospace Eng. Dept., University of California Irvine)
Tue May 24, 2022
4:00pm - ISEB 1200 - Differential Geometry
Pak-Yeung Chan - (UC San Diego)
Hamilton-Ivey estimates for gradient Ricci solitons

One special feature for the Ricci flow in dimension 3 is the
Hamilton-Ivey estimate. The curvature pinching estimate provides a lot of
information about the ancient solution and plays a crucial role in the
singularity formation of the flow in dimension 3. We study the pinching
estimate on 3 dimensional expanding and 4 dimensional steady gradient Ricci
solitons. A sufficient condition for a 3-dimensional expanding soliton to
have positive curvature is established. This condition is satisfied by a
large class of conical expanders. As an application, we show that any
3-dimensional gradient Ricci expander C^2 asymptotic to certain cones is
rotationally symmetric. We also prove that the norm of the curvature tensor
is bounded by the scalar curvature on 4 dimensional non Ricci flat steady
soliton singularity model and derive a quantitative lower bound of the
curvature operator for 4-dimensional steady solitons with linear scalar
curvature decay and proper potential function. This talk is based on a joint
work with Zilu Ma and Yongjia Zhang.

Wed May 25, 2022
2:00pm to 3:00pm - 510R Rowland Hall - Combinatorics and Probability
Roman Vershynin - (UCI)
Mathematics of synthetic data. II. Random walks.

In this talk we will construct a superregular random walk, which locally looks like a simple random walk, but which globally deviates from the origin much slower than the Brownian motion. This random walk will become a crucial tool in the construction of a private measure. Joint work with March Boedihardjo and Thomas Strohmer, https://arxiv.org/abs/2204.09167

Thu May 26, 2022
10:00am to 11:00am - Zoom - Number Theory
Amita Malik - (Max Planck Institute)
11:00am - RH 306 - Harmonic Analysis
Yizhe Zhu - (UCI)
The characteristic polynomial of sums of random permutations

Let $A_n$ be the sum of $d$ permutations matrices of size $n×n$, each drawn uniformly at random and independently. We prove that $\det( I_n−zA_n/\sqrt{d})$ converges when $n\to\infty$ towards a random analytic function on the unit disk. As an application, we obtain an elementary proof of the spectral gap of random regular digraphs with a sharp constant. Our results are valid both in the regime where $d$ is fixed and for $d$ slowly growing with $n$. Joint work with Simon Coste and Gaultier Lambert.

1:00pm - Rowland 510R - Algebra
Cris Negron - (University of Southern California)
Vanishing tests for (quantum) group representations

In this talk I will survey some results on the vanishing of (quantum) group representations, at the level of the stable category.  Equivalently, I will discuss effective ways to test projectivity of a given finite-dimensional G-representation, where G your favorite finite (quantum) group.  In the case of an elementary abelian p-group E, over k=\bar{F}_p,  for example, Carlson tells us that an object V in rep(E) is projective if and only if V has projective restriction along each flat algebra map \alpha: k[t]/(t^p) -> k[E] into the group ring.  One thus reduces a wild representation type calculation to a finite representation type calculation, via this P^{rank(E)}(k)-family of embeddings.  I will provide an analogous vanishing result for the small quantum group u_q(L), which involves the introduction of a G/B-family of small quantum Borels and an analysis of certain ``noncommutative complete intersections”.  This is joint work with Julia Pevtsova [arxiv:2012.15453, arxiv:2203.10764].

Fri May 27, 2022
4:00pm to 5:00pm - MSTB 124 - Graduate Seminar
Connor Mooney - (UC Irvine)