
Sean Howe
Thu Feb 15, 2018
3:00 pm
A fundamental observation in KatzSarnak's study of the zero spacing of Lfunctions is that Frobenius conjugacy classes in suitable families of varieties over finite fields approximate infinite random matrix statistics. For example, the normalized Frobenius conjugacy classes of smooth plane curves of degree d over F_q approach the Gaussian...

Christoph Marx
Thu Feb 15, 2018
2:00 pm
We prove the Höldercontinuity of the density of states measure (DOSm) and the integrated density of states (IDS) for discrete random Schrödinger operators with finiterange potentials with respect to the probability measure. In particular, our result implies that the DOSm and the IDS for smooth approximations of the Bernoulli...

Dan Knopf
Tue Feb 13, 2018
4:00 pm
We describe Riemannian (nonKahler) Ricci flow solutions that develop finitetime TypeI singularities whose parabolic dilations converge to a shrinking Kahler–Ricci soliton singularity model. More specifically, the singularity model for these solutions is the “blowdown soliton” discovered in 2003 by Feldman, Ilmanen, and the...

Jeremy LeCrone
Tue Feb 13, 2018
3:00 pm
In this talk, I will discuss recent results produced with coauthors Ivan Blank (KSU) and Brian Benson (UCR) regarding a formulation of the Mean Value Theorem for the LaplaceBeltrami operator on smooth Riemannian manifolds. We define the sets upon which mean values of (sub)harmonic functions are computed via a particular obstacle problem in...

Xuehai Huang
Mon Feb 12, 2018
4:00 pm
A framework to systematically decouple high order elliptic equations into combination of Poissontype and Stokestype equations is developed using the tools of differential complexes and Helmholtz decompositions. The key step is to systematically construct the underling commutative diagrams involving the complexes and Helmholtz decompositions...

Qiongling Li
Mon Feb 12, 2018
4:00 pm
On a complex manifold, a Higgs bundle is a pair containing a holomorphic vector bundle E and a holomorphic End(E)valued 1form. In this talk, we focus on nilpotent Higgs bundles, for example, the ones arising from variations of Hodge structures for a deformation family of Kaehler manifolds. We first give an optimal upper bound of the curvature of...

Zach Norwood
Mon Feb 12, 2018
4:00 pm
A major project in set theory aims to explore the connection between large cardinals and socalled generic absoluteness principles, which assert that forcing notions from a certain class cannot change the truth value of (projective, for instance) statements about the real numbers. For example, in the 80s Kunen showed that absoluteness to ccc...