Click on seminar heading to go to seminar page.
Frank Farris, Santa Clara University
One possible model for the shape of the universe is the Poincaré dodecahedral space, which is a quotient of the 3-sphere by the action of the icosahedral group. To help cosmologists, Jeff Weeks adopted a method originally proposed by Klein to find all the spherical harmonics invariant under the icosahedral and other polyhedral groups. In trying to connect the method to polyhedrally-invariant functions on the 2-sphere, we discovered an interesting connection to self-mappings of the 2-sphere, opening the door to a new technique for mathematical art. (Joint work with Jeff Weeks.)
Frank Farris, Santa Clara University
Standing at the always-intriguing intersection of mathematics and art, Frank Farris introduces the mathematics of symmetry and how to create mind-blowing symmetrical images using his new waveform technique. He came up with this concept by rejecting the traditional wisdom that wallpaper patterns must be built up from blocks - a sort of potato-stamp method. Instead, he created patterns from continuous waves. Whether you like art or mathematics, or both, Farris will help you understand his process. He shows how wave functions draw on photographic images to create beautifully symmetric patterns. The focus is on art, but in the background you can glimpse such mathematical topics as group theory, functional analysis, and partial differential equations.
Lisa Hartung, NYU
We study the structure of extreme level sets of a standard one dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height and shape of those clusters which carry such level sets. We also find the right tail decay of the distribution of the distance between the two highest particles. These results confirm two conjectures of Brunet and Derrida. (Joint work with A. Cortines, O Louidor.)
Luis Fernando Ragognette, Federal University of São Carlos, Brazil
We are going to recall the definition of Gevrey local solvability for a differential complex associated to a locally integrable structure and then we are going to give a necessary condition in terms of an a priori estimate. This kind of estimate was introduced by Hörmander and became a standard technique to study solvability.
Luca Di Cerbo, Stony Brook
In this talk, I will present a Price type inequality for harmonic forms on manifolds without conjugate points and negative Ricci curvature. The techniques employed in the proof work particularly well for manifolds of non-positive sectional curvature, and in this case one can prove a strengthened result. Equipped with these Price type inequalities, I then study the asymptotic behavior of Betti numbers along infinite towers of regular coverings. If time permits, I will discuss the case of hyperbolic manifolds in some detail. This is joint work with M. Stern.
There are no conferences this week.