Schedule
Thursday [30.05.2024]
10:00 - 11:00 D. Oprea
11:15 - 12:15 R. Laza
Lunch
14:00 - 15:00 F. Moretti
15:15 - 16:15 M. Lelli Chiesa
16:30 - 17:30 D. Ranganathan
Workshop Dinner
Friday [31.05.2024]
10:00 - 11:00 O. de Gaay Fortman
11:15 - 12:15 T. Krämer
Lunch
14:00 - 15:00 A. Iribar López
15:15 - 16:15 R. Pandharipande
Titles and Abstracts
Federico Moretti (HU Berlin)
Families of Jacobians with isotrivial factors
Let Y be a variety equipped with a top form. I will present a simple genus
bound for a family of subvarieties covering
Y in term of the dimension of
the family. As an application I will prove a genus bound for families of
Jacobians with a
given isotrivial factor. If the dimension of the family
is big enough, the bound is sharp and realized only by the family
of degree
2 covers of a given curve. This is based on joint work with Josh Lam and
Giovanni Passeri.
Radu Laza (Stony Brook)
The Core of Calabi-Yau degenerations
It is problem of high interest to construct meaningful compactifications for moduli spaces of algebraic varieties.
For varieties of general type and Fano type the situation is fairly well understood via KSBA theory
and K-stability
respectively. In the remaining K-trivial case, one understands the “classical cases” (abelian varieties, K3 surfaces,
and hyper-Kaehler manifolds) via period maps and Hodge theory. Thus, the only remaining primitive case
for constructing compact moduli spaces is that of strict Calabi-Yau’s of dimension at least 3.
In this talk, I conjecture the existence of a minimal compactification for the moduli of Calabi-Yau varieties, an
analogue of the Baily-Borel compactification in the classical case. I will then explain a construction that produces
such a compactification at least at the set-theoretic level. The key concept here is the Type and Core of a Calabi-Yau
degeneration. The Type is an integer invariant that measures the depth of the degeneration, while the Core is a
pure Hodge structure of Calabi-Yau type, which should be understood as the Hodge theoretic piece that survives
in any reasonable model of the degeneration.
Dhruv Ranganathan (Cambridge)
Gromov-Witten theory and the tautological ring
Gromov-Witten theory is a natural source of cohomology classes on the moduli space of curves. I will explain a
speculation, going back to Levine and Pandharipande, that the cohomology classes produced by Gromov-Witten
theory lie in
a surprisingly small part of cohomology: the tautological ring. I will explain how logarithmic
Gromov-Witten theory can be used to approach
this speculation, and try to share some of the subtleties involved
in this approach. Based on recent and ongoing work with Davesh Maulik.