Abstracts

Annalisa Grossi, Automorphisms of irreducible holomorphic symplectic manifolds of OG6 type.
Abstract ± Abstract

Camilla Felisetti, Higgs bundles on genus 2 curves
Abstract ±

Gijs Heuts, Spectral Lie algebras and their applications
Abstract ± I will discuss the notion of spectral Lie algebra, which is an adaptation of the theory of Lie algebras to homotopy theory. These generalize differential graded Lie algebras over the rational numbers and admit similar applications. For example, these Lie algebras play a central role in deformation theory. Another application is the role of spectral Lie algebras as 'algebraic models' for homotopy theory, generalizing Quillen's rational homotopy theory.

Mirko Mauri, P=W conjectures for character varieties with symplectic resolution
Abstract ± Character varieties parametrise representations of the fundamental group of a curve. They are in general singular moduli spaces, and for this reason it is customary to shift attention to smooth analogues, called twisted character varieties. The P=W conjecture formulated by de Cataldo, Hausel and Migliorini posits a relation between the Hodge theory of twisted character varieties and the geometry of some holomorphic Lagrangian fibrations. In a joint work with Camilla Felisetti, we explore P=W phenomena in the untwisted case. We show that the P=W conjecture holds for character varieties which admit a symplectic resolution, namely in genus 1 and arbitrary rank and in genus 2 and rank 2. This involves a careful study of alterations of these character varieties. Notes for the talk

Raju Krishnamoorthy, Rank 2 local systems and abelian varieties
Abstract ± Let \(X/\mathbb{F}_q\) be a smooth, geometrically connected variety. Let \(L\) be an irreducible rank 2 lisse \(\overline{\mathbb Q}_l\) sheaf on \(X\) with cyclotomic determinant and infinite geometric monodromy. We conjecture that \(L\) comes from a family of abelian varieties. We explain partial progress on this problem. This is joint work with A. Pal.

Calum Spicer, Minimal models of foliations and transversely projective structures
Abstract ± I will explain a conjecture on the dynamics of codimension one holomorphic foliations on projective threefolds. I will then show how this conjecture can be related to the study of the birational geometry of foliations, and in particular, to the theory of minimal models of foliations. I will then discuss some developments on the foliated minimal model program.

Maciej Zdanowicz, Geometry of weakly ordinary varieties with trivial canonical class
Abstract ± In the talk I will report on the two papers concerning geometry of varieties with trivial canonical class in characteristic p>0 written jointly with Zsolt Patakfalvi. First, I will introduce characteristic p>0 condition of weak ordinarity, and then briefly indicate how it leads to a version of the Beauville--Bogomolov decomposition. Then, I will provide a counterexample to the decomposition statement without the ordinarity assumption, which is unsurprisingly related to the peculiar possibility of uniruledness of Calabi--Yau varieties in characteristic p>0. Finally, I will describe how weak ordinarity actually prevents varieties with trivial canonical class from being uniruled.

Videos

• July 11, timelapse: Annalisa, Camilla (1:20), Mirko (3:01), Calum (4:40)
• July 12, timelapse: Gijs, Maciej (1:29), Raju (3:02)