Past Events

I will present some new asymptotic formulas for the sums of complex-valued multiplicative functions whose values are near 1 on primes.

We show how the method of Green and Tao can be used to obtain the correct order of magnitude for the number of k-term arithmetic progressions in the integers representable as the sum of two squares, with a similar Roth-like theorem for subsets of...

A simple random walk (SRW) on a graph is a Markov chain whose state space is the vertex set and the next state distribution is uniform among the neighbors of the current state. A graph is called recurrent if a SRW on it returns to the starting vertex...

We consolidate an unorganized point cloud with noise, outliers, non-uniformities, and in particular interference between close-by surface sheets as a preprocess to surface generation, focusing on reliable normal estimation. Our algorithm includes two...

The theory of optimal transport is concerned with phenomena arising when one matches two mass distributions in a most economic way, minimizing transportation cost of moving mass from one location to another. We consider an optimal transportation...

I will report on joint work with E. Macri on the space of stability conditions for the derived category of the total space of the canonical bundle on the projective plane. It is a 3–dimensional manifold, with many chamber decompositions coming from...

Motivated by basic questions from robotics and molecular biology, we consider certain configuration spaces, and some associated maps to two dimensional Euclidian space. We are able to understand the singular sets for a natural subset of these maps...

Cluster expansions give convergent expressions for measures on infinite dimensional spaces, such as those that occur in statistical mechanics. One approach to these convergence questions is via fixed points for infinite dimensional increasing...

We derive a general Hardy inequality and show most Hardy inequalities can be seen as special cases of this inequality. In addition we characterize the improvements of this inequality and (time permitting) we show an application of this inequality to...

A one-face map is a graph embedded in a compact surface, in such a way that its complement is a topological disk. Dually, it can be viewed as a polygon of even size, in which edges have been pasted pairwise to create a surface. These objects have...