Program - December 21, 2021 (Aula Dottorato, first floor)
You can download the poster and the program.
9:15-10:05
Arthur Renaudineau
Topology of real algebraic varieties near the tropical limit
Abstract:
Describing all the possible topologies of real projective hypersurfaces of
fixed degree and dimension is a very difficult problem, going back to
Hilbert's sixteenth problem. We will show some progress on this
problem when assuming that the variety is closed to some
degeneration, called tropical limit. We will recall some basics on real
algebraic geometry and tropical geometry and then relate the Betti
numbers of a real variety near the tropical limit to the dimension of some
tropical homology groups (by the way of a spectral sequence). It is
based on joint works with Kris Shaw and Johannes Rau and Kris Shaw.
10:15-11:05
Emma Lepri
L-infinity liftings of semiregularity maps
Abstract:
The Buchweitz-Flenner semiregularity map, introduced in 1999 and generalising Bloch's semiregularity map, has applications to both the variational Hodge conjecture and deformation theory. The subject of this talk is the construction of a lifting of each component of the Buchweitz-Flenner semiregularity map to an L-infinity morphism between differential graded Lie algebras, which allows to interpret components of the semiregularity map as obstruction maps of morphisms of deformation theories. As a consequence, we obtain that the semiregularity map annihilates all obstructions to deformations of a coherent sheaf on a complex projective manifold. Based on a joint work with R. Bandiera and M. Manetti.
11:45-12:35
Camilla Felisetti
Topology of Lagrangian fibrations and P=W phenomena on irreducible symplectic varieties.
Abstract:
Irreducible holomorphic symplectic (IHS) varieties can be thought as a
generalization of hyperkähler manifolds allowing singularities.
Among them we can find for example moduli spaces of sheaves on K3
and abelian surfaces, which have been recently shown to play a crucial
role in non abelian Hodge theory.
After recalling the main features of IHS varieties, I will present several
results concerning their intersection cohomology and the perverse
filtration associated with a Lagrangian fibration, establishing a compact
analogue of the celebrated P=W conjecture by de Cataldo, Hausel and
Migliorini for varieties which admit a symplectic resolution.
The talk is based on joint works with Mirko Mauri, Junliang Shen and
Qizheng Yin.
This event is supported by the reasearch project ERC-2017-CoG-771507, StabCondEn (
web page).