Program

The conference will be centered around three mini-courses of 3 hours each, completed by a series of research talks.

Mini-courses

"Derived categories with a view towards motives"

Nicolas Addington (University of Oregon)

Abstract: Fourier-Mukai transforms and their induced maps on cohomology, (topological) K-theory, and Hochschild homology.  Semi-orthogonal decompositions, which play the role of idempotent completion, and their interaction with those induced maps.  Detailed example: intersection of two quadrics.  Work of Bondal, Larsen, and Lunts on the Grothendieck ring of varieties.  Some work of Tabuada and Bernardara.  Work of Honigs on zeta functions and derived equivalences. 

"Arithmetic harmonic analysis on character varieties"

Emmanuel Letellier (University of Paris Paris-Diderot)

Abstract: The aim of this lecture is to indtroduce a new technic which we call "harmonic arithmetic analysis" to study the geometry of the moduli spaces of representations of fundamental groups of punctured Riemann surfaces in GL(n,C) with prescribed local monodromy. In the first part I will explain how to obtain a conjectural formula for the mixed Hodge polynomial of these character varieties. In the second part I will explain how to compute the ordinary Poincaré polynomial through the counting of geometrically indecomposable parabolic bundles over smooth projective curves over finite fields.

"On the Chow ring of hyperKähler varieties"

Charles Vial (University of Cambridge)

Abstract: More than 10 years ago, Beauville and Voisin discovered that  the Chow ring of K3 surfaces had a special structure : the intersection  of any two divisors is always a multiple of the class of a point lying  on a rational curve. This led Beauville to ask whether the Chow ring of hyperKaehler varieties has a structure similar to that of abelian varieties. The aim of this mini-cours will be to review the results of Beauville and Voisin, explain the conjectures surrounding the Chow ring of hyperKaehler varieties, and finally to study the Chow motive of two examples of hyperKaehler varieties, namely the Hilbert scheme of length-n subschemes on a K3 surface and the variety of lines on a smooth cubic fourfold.

Research Talks

Confirmed speakers:

Roland Abuaf

Asher Auel

Marcello Bernardara

Andrei Caldararu

Ana Maria Castravet

Alessandro Chiodo

Ben Davison

Eduardo Esteves

Manfred Lehn

Emanuele Macri

Gonçalo Tabuada

Hokuto Uehara

Michael Van den Bergh

Matthias Wendt