Past Events

In many large-scale inverse problems and optimization problems, the objective function (to be minimized) is composed of many terms, each term or group of terms requiring an expensive simulation/computation. In the cases discussed here, we need to...

I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces...

The first order language on graphs consists of sentences, or graph properties, that are expressible using the relations of vertex equality (x = y) and vertex adjacency (x \sim y). In their 1988 paper, Shelah and Spencer showed that when 0 \alpha ...

I will describe how to use the recent theory of prismatic cohomology of Bhatt--Morrow--Scholze to say something about the de Rham cohomology of classifying spaces of algebraic groups such as PGL_p in characteristic p. This leads to interesting new...

Single particle tracking is a powerful tool to study the mobility of molecules in the cell membrane. The most common approaches in analyzing these kinds of data are mean squared displacement and analyses with one or more hidden Markov states. However...

In this talk, we first introduce the inverse mean curvature flow and its well known application in the the proof of Riemannian Penrose inequality by Huisken and Ilmanen. Then we discuss our main result which addresses the existence and behavior of...

I will discuss recent results on the analysis of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations converge to solutions of the Euler equations, for incompressible fluids when walls are present. At small...

The ternary Goldbach problem stated that every odd integer greater than 5 can be written as sums of three primes. This was proved by Vinogradov for all sufficiently large odd integers and completely proved by Helfgott. On the other hand, by using...

We are faced with a flood of molecular and clinical data. We are measuring interactions between various bio-molecules in a cell that form large, complex systems. Patient omics datasets are also increasingly becoming available. These systems-level...