Algebraic Geometry and Number Theory External Ical Atom

Let $G$ be a $p$-adic group. I shall introduce the Bernstein center, review its construction and properties and explain how to use it in order to study distributions on spherical spaces.

More specifically, we shall discuss the wave front of distributions and how to control it in case the distribution is “finite” with respect to the Bernstein center. Then we discuss whether this condition of “finiteness” is reasonable assumption.

The tools used will involve very little analysis, but rather facts from commutative algebra and connections of the representation theory of $p$-adic groups to commutative algebra.

We define a Chern-Simons functional on spaces of suitable Galois representations and speculate on relations to the theory of L-functions.

Joyce and others have used shifted symplectic geometry to define Donaldson–Thomas Invariants. This kind of geometry naturally appears on derived moduli stacks of perfect complexes on Calabi-Yau varieties. One wonderful feature of shifted symplectic geometry (developed by Pantev, Toën, Vaquié and Vezzosi) is that fibre products (i.e. intersections) of Lagrangians automatically carry Lagrangian structures. Using a strange property of triple intersections from arXiv:1309.0596, this extra structure can be organized into a $2$-category. We discuss a partial linearization using Joyce’s perverse sheaves. I will also talk about the relationship of this $2$-category with TQFTs, algebraic versions of the Fukaya categories and categories of Lagrangians. This is joint work with Lino Amorim and available at http://arxiv.org/abs/1601.01536