## Past Seminars

• Konstantin Tikhomirov
Thu Jan 18, 2018
4:00 pm
Convex-geometric methods, involving random projection operators and coverings, have been successfully used in the study of the largest and smallest singular values, delocalization of eigenvectors, and, among further applications, in establishing the limiting spectral distribution for certain random matrix models. Conversely, random linear...
• Niccolo' Ronchetti
Thu Jan 18, 2018
3:00 pm
I will introduce the mod p derived spherical Hecke algebra of a p-adic group, and discuss its structure via a derived version of the Satake homomorphism. Then, I will survey some speculations about its action on the cohomology of arithmetic manifolds.
• Daniel Litt
Wed Jan 17, 2018
4:00 pm
Let X be an algebraic variety -- that is, the solution set to a system of polynomial equations.  Then the fundamental group of X has several incarnations, reflecting the geometry, topology, and arithmetic of X.  This talk will discuss some of these incarnations and the subtle relationships between them, and will describe an...
• Jonathan Zhu
Tue Jan 16, 2018
4:00 pm
We describe the construction of closed constant mean curvature (CMC) hypersurfaces using min-max methods. In particular, our theory allows us to show the existence of closed CMC hypersurfaces of any prescribed mean curvature in any closed Riemannian manifold. This work is joint with Xin Zhou.
• Yi Zhang
Tue Jan 16, 2018
3:00 pm
Given a planar infinity harmonic function u, for each $\alpha>0$ we show a quantitative $W^{1,\,2}_{\loc}$-estimate of $|Du|^{\alpha}$, which is sharp when $\alpha\to 0$.  As a consequence we obtain an $L^p$-Liouville property for infinity harmonic functions in the whole plane
• Shiwen Zhang
Fri Jan 12, 2018
2:00 pm
The Favard length of a set E has a probabilistic interpretation: up to a constant factor, it is the probability that the Buffon's needle, a long line segment dropped at random, hits E. In this talk, we study the Favard length of some random Cantor sets of dimension 1. Replace the unit disc by 4 disjoint sub-discs of radius 1/4 inside. By...
• Gautam Iyer
Thu Jan 11, 2018
4:00 pm
Consider a diffusive passive scalar advected by a two dimensional incompressible flow. If the flow is cellular (i.e.\ has a periodic Hamiltonian with no unbounded trajectories), then classical homogenization results show that the long time behaviour is an effective Brownian motion. We show that on intermediate time scales, the effective behaviour...