Fall 2016: The seminar takes place on Thursday 10:15-12:00 (at most).

Previous terms:

*Spring 2017*

**19 January: Marco Rampazzo, Room KE-D225**

Wall-crossing I

**26 January: Marco Rampazzo, Room KE-D225**

**2 February: Riccardo Moschetti, Room
KE-D225**

**9 February: Sammy A. Soulimani, Room
KE-D225**

16 February: Andrea Ricolfi, Room KE-D225

Introduction to motives

Fano variety and rationality problems for cubic fourfolds

Hilbert scheme degenerations

Explicit computations with artinian modules

Moduli Spaces (Mirror Symmetry Seminar)

(Twisted) Derived Categories of Enriques surfaces in positive characteristic

and explain some work in progress whose aim is to get a positve characterisitc derived Torelli theorem.

6 April:

April 20-25 events

**Thursday**** ****1st
June, 10:15-12:00, Room : D-225**

__Speaker__:
Alessandra Sarti.

__Title__: Pell's
equation and automorphisms of Hilbert schemes.

__Abstract__: I will
report on recent results in collaboration with Samuel BoissiÃ¨re, Andrea
Cattaneo and Marc Nieper-Wisskirchen on the

automorphism group of the Hilbert scheme of two points on a
generic K3 surface
of any polarization.

In this case the Picard number of the Hilbert scheme is
two, which is the
minimal possible.

In particular by using ampleness results of Bayer-Macri and a
detailed study of the isometries of the Picard lattice, I show
the existence of

non-natural non-symplectic involutions on some Hilbert scheme,
depending on the degree of the polarization. In all the results
the

solutions of certain Pell's equation play a fundamental role.
Time permitting I will give some overview on the situation for
higher

dimension which is the PhD topic of Alberto Cattaneo.

**Friday 2nd June,
10:15-12:00, Room : D-225**

__Speaker__: Samuel BoissiÃ¨re

__Title__: Cubic hypersurfaces and hyperkaehler manifolds
uniformized by the 10-dimensional complex ball.

__Abstract__: In a famous paper, Allcock, Carlson and Toledo
described the moduli space of cubic threefolds as an arithmetic

quotient of the complementary of a hyperplane arrangement
in a 10-dimensional complex ball. In this talk, I will

give an interpretation of this moduli space as the space
parametrizing the deformations of non-symplectic

automorphisms of order three acting on some classical family of
polarized hyperkaehler

manifolds. This is a work in collaboration with Chiara Camere
and Alessandra Sarti.