This talk will discuss the so-called ``generic cohomology’’ of function fields over algebraically closed fields, from the point of view of motives and/or Zariski geometry. In particular, I will describe some interesting connections between cup products, algebraic dependence, and (geometric) valuation theory. As an application, I will mention a new result which reconstructs higher-dimensional function fields from their generic cohomology, endowed with some additional motivic data. 

   Everyone welcome!
 

The chromatic number of a graph is trivially bounded from above by the maximum degree plus one, and from below by the size of a largest clique. Reed proved in 1998 that compared to the trivial upper bound, we can always save a number of colors proportional to the gap between the maximum degree and the size of a largest clique. A key step in the proof deals with how to spare colors in a graph whose every vertex "sees few edges" in its neighborhood. We improve the existing approach, and discuss its applications to Reed's theorem and strong edge coloring.  This is joint work with Thomas Perrett (Technical University of Denmark) and Luke Postle (University of Waterloo).

The goal of this talk will be to give an overview of recent work, joint with Kim Moore, on a short time existence problem in Lagrangian mean curvature flow. More specifically, we consider a compact initial Lagrangian submanifold with a finite number of singularities, each asymptotic to a pair of transversely intersecting planes. We show it is possible to construct a smooth Lagrangian mean curvature flow, existing for positive times, that attains the singular Lagrangian as its initial condition in a suitable weak sense.  The construction uses a family of smooth solutions whose initial conditions approximate the singular Lagrangian. In order to appeal to compactness theorems and produce the desired solution, it is necessary to first establish uniform curvature estimates on the approximating family. As time allows I hope to focus in particular on the proof of these estimates, and their role in the proof of the main theorem.