Seminars by Matteo Penegini and Massimo Bagnarol (remind)

[Fabio Perroni]

UNIVERSITA’ DEGLI STUDI DI TRIESTE
DIPARTIMENTO DI MATEMATICA E GEOSCIENZE


Monday, April 8th, 2019, at 14:30.

Prof. Matteo Penegini (University of Genova) will speak on "Tate and Mumford--Tate conjecture for surfaces of general type with p_g=q=2”.

Abstract. In this talk we discuss the cohomology of smooth projective complex surfaces S
of general type with invariants p_g = q = 2 and surjective Albanese morphism.
We show that on a Hodge-theoretic level, the cohomology is described
by the cohomology of the Albanese variety and a K3~surface X  that we call the K3 partner of S.
Furthermore, we show that in suitable cases we can geometrically construct
the K3 partner X  and an algebraic correspondence in S \times X that relates the cohomology of S  and X .
Finally, we prove the Tate and Mumford--Tate conjectures for those surfaces S 
that lie in connected components of the Gieseker moduli space that contain a product-quotient surface.


Tuesday, April 9th, 2019, at 16:00.

Massimo Bagnarol (SISSA) will speak on "Operad formalism for varieties and its applications”.

Abstract. Motivated by the study of the geometry of certain moduli spaces, I will discuss some operations between quasi-projective varieties with a symmetric group action, which were introduced by Getzler and Pandharipande. 
I will highlight the relation between those and some well-known structures arising in operad theory, and I will prove their properties using this correspondence. 
I will show that those operations induce a so-called composition algebra structure on the Grothendieck group of varieties with a symmetric group action, which can be used to investigate the cohomology of moduli spaces of stable maps from genus 0 curves to certain targets.


Venue: Seminar Room  (Sezione di Matematica e Informatica, H2 building, Via Valerio 12/1, 3rd floor, room 334).

Everybody interested is much welcome to attend.
Best regards,
Fabio Perroni