Past Events

Over the past decade we have dramatically changed our views of the generation of immune responses. In the earlier (conventional) view, the specific immune response to a pathogen was modeled by equations similar to a simple predator-prey systems in...

Sheaves of Categories and the Main Theorem After talking about how a sheaf of categories gives rise to a topological category, I will finish the proof of the main theorem of Galatius, Madsen, Weiss and Tillmann which states that the classifying space...

Log canonical thresholds are invariants of singularities that play an important role in birational geometry. After an introduction to these invariants, I will describe recent progress on a conjecture of Shokurov predicting the Ascending Chain...

At the International Congress of Mathematicians held in Hyderabad, India this past August, Louis Nirenberg, from the Courant Institute for the Mathematical Sciences at New York University, was awarded the inaugural Chern Medal for his role in the...

Many scientific, engineering and financial applications require solving high-dimensional PDEs. However, traditional tensor product based algorithms suffer from the so called "curse of dimensionality". We shall construct a new sparse spectral method...

I shall present an energetic variational phase field model for multiphase incompressible flows which leads to a set of coupled nonlinear system consisting a phase equation and the Navier-Stokes equations. We shall pay particular attention to...

Toric schemes admit a combinatorial description which, in turn, allows one to describe sheaves of modules by certain diagram categories. I will explain these basic constructions in some detail, and then give a non-standard approach to constructing...

The quadratic reciprocity law (dating back to Gauss) cute result of algebra letting you decide almost instantly whether a given integer is a square modulo a prime. This theorem is famous for having about 100 different proofs, and counting. I'll...

We consider the problem of existence and uniqueness of multi-soliton solutions for the L²-supercritical generalized Korteweg-de Vries equation. We recall that a multi-soliton is a solution which behaves as a sum of N solitons in large time. After a...

Cooperation has been often studied in the framework of evolutionary game theory. Usually each player adopts a single strategy against everyone: cooperation or defection. But humans can discriminate and adopt different strategies against different...