
Vadim Kaloshin
Thu Jan 21, 2016
4:00 pm
The classical Birkhoff conjecture states that the only integrable convex planar domains are circles and ellipses. In a joint work with A. Avila and J. De Simoi we show that this conjecture is true for perturbations of ellipses of small eccentricity. It turns out that the method of proof gives an insight into deformational spectral rigidity of...

Max Gunzburger
Thu Dec 3, 2015
4:00 pm
We use the canonical examples of fractional Laplacian and peridynamics equations to discuss their use as models for nonlocal diffusion and mechanics, respectively, via integral equations with singular kernels. We then proceed to discuss theories for the analysis and numerical analysis of the models considered, relying on a nonlocal vector calculus...

Yuki Takahashi
Thu Nov 12, 2015
3:00 pm
In this cosponsored UCI Illuminations and Juggle Buddies event, we will talk about the math theories associated with the art of juggling, a form of prop manipulation. This theory involves the use of Siteswap notation.
Siteswap is a juggling notation used to describe possible juggling patterns. For example, the most basic threeball trick called a...

Nicolaos Kapouleas
Thu Oct 22, 2015
4:00 pm
Abstract:
I will discuss various geometric gluing constructions. First I will discuss constructions for Constant Mean Curvature hypersurfaces in Euclidean spaces including my earlier work for twosurfaces in threespace which settled the Hopf conjecture for surfaces of genus two and higher, and recent generalizations in collaboration with...

Rodrigo Banuelos
Thu Oct 15, 2015
4:00 pm
Abstract

Yanyan Li
Thu Apr 16, 2015
4:00 pm
The mathematical problem of gradient estimates for solutions of divergence form elliptic systems with piecewise smooth coefficients arises in studying composite materials in applied science.
We will start with ideas in joint works with Vogelius (2000) and Nirenberg (2003) about a decade ago, in particular an open problem in the paper with...

Michael Bjorklund
Thu Apr 9, 2015
4:00 pm
After briefly reviewing some basic aspects of quantum
probability theory, especially questions surrounding a
celebrated theorem of Gleason, we turn to analogues of
quantum probabilities studied in symplectic geometry
known as quasistates, which are functions on Lie algebras
which are linear on abelian subalgebras.
A prototypical (and well...