Previous Special Year Seminar

I will discuss some of the topology of the fibers of proper toric maps and a combinatorial invariant that comes out of this picture. Joint with Luca Migliorini and Mircea Mustata.

I will outline a construction of "tropical current", a positive closed current associated to a tropical variety. I will state basic properties of tropical currents, and discuss how tropical currents are related to a version of Hodge conjecture for...

The relevant preprints are: arXiv:1405.5154 "The Fano variety of lines and rationality problem for a cubic hypersurface", Sergey Galkin, Evgeny Shinder arXiv:1405.4902 "On two rationality conjectures for cubic fourfolds", Nicolas Addington

Esnault asked whether a smooth complex projective variety with infinite fundamental group has a nonzero symmetric differential, meaning a section of some symmetric power of the cotangent bundle. We prove a partial result in this direction, using...

In this talk I will focus on two examples of K3 categories: bounded derived categories of (twisted) coherent sheaves and K3 categories associated with smooth cubic fourfolds. The group of autoequivalences of the former has been intensively studied...

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge...

Many of the major results of modern ergodic theory can be understood in terms of a sequence of finite metric measure spaces constructed from the marginal distributions of a shift-invariant process. Most simply, the growth rate of their covering...

We present the key ideas of a new proof of Landau damping for the Vlasov-Poisson equation obtained in a joint work with Bedrossian and Masmoudi. This nonlinear transport equation is a fundamental model for describing self-interacting plasmas or...

We consider a typical situation in which probability model itself has non-negligible cumulated uncertainty. A new concept of nonlinear expectation and the corresponding non-linear distributions has been systematically investigated: cumulated...