
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...

Hongzi Cong
Thu Jan 25, 2018
3:00 pm
In this talk, we will show that the full dimensional invariant tori obtained by Bourgain [J. Funct. Anal., 229 (2005), no. 1, 62–94] is stable in a very long time for 1D nonlinear Schrödinger equation with periodic boundary conditions.

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

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...

Albert Fathi
Tue Dec 5, 2017
3:00 pm
This is a joint work with Piermarco Cannarsa and Wei Cheng.
We study the properties of the set S of nondifferentiable points of viscosity solutions of the HamiltonJacobi equation, for a Tonelli Hamiltonian.
The main surprise is the fact that this set is locally arc connected—it is even locally contractible. This last property...

Dejan Slepcev
Tue Oct 17, 2017
3:00 pm
The general average distance problem, introduced by Buttazzo, Oudet, and Stepanov, asks to find a good way to approximate a highdimensional object, represented as a measure, by a onedimensional object. We will discuss two variants of the problem: one where the onedimensional object is a measure with connected onedimensional support and...

Zaher Hani
Tue Oct 10, 2017
3:00 pm
We consider the nonlinear Schroedinger equation posed on a large box of characteristic size $L$, and ask about its effective dynamics for very long time scales. After pointing out some “more or less” trivial time scales along which the effective dynamics can be easily described, we start inspecting some much longer time scales where we...