GADEPs focused conference III: Noether-Lefschetz and Hodge loci

21-25 August 2023, IMPA, Rio de Janeiro.

The seminar “Geometry, Arithmetic and Differential Equations of Periods” (GADEPs), started in the pandemic year 2020 and its aim is to gather people in different areas of mathematics around the notion of periods which are certain multiple integrals. This is the the third GADEPs conference focused on Noether-Lefschetz and Hodge loci. A Noether-Lefschetz locus lives in parameter spaces of algebraic surfaces, and there are many challenging problems regarding the distribution of codimension of its components. Periods and Hodge theory give transcendental tools in order to study them as local analytic varieties. A generalization of this is known as Hodge loci, which are a priori, analytic varieties. A deep theorem of Cattani, Deligne and Kaplan implies that these are branches of algebraic varieties, however, it does not give any hint about their field of definition. The main goal of the meeting is to gather experts (online or face to face) in order to discuss the last developments in this topic.






Scientific Program

The scientific program contains three mini courses given by Roberto Villaflor (2 lectures), Gregorio Baldi (2 lectures), Patrick Brosnan (2 lectures) and François Greer (2 lectures). Other participants will give a talk in their field of research (8 lectures). Besides these, we will leave some time for the free discussion and communication for the participants.



Gregorio Baldi (IHES, France)
On the distribution of the Hodge locus

Patrick Brosnan (University of Maryland, USA)
Why Markman’s theorem saves the Hodge conjecture (for Weil type abelian fourfolds) from Kontsevich’s tropical counterexamples

Jin Cao (Tsinghua University, China)
Quasi Jacobi forms and moduli space of enhanced elliptic curve

Adrian Clingher (University of Missouri-St. Louis, USA)*
On K3 Surfaces with Lattice Polarization

Jorge Duque (Universidad de Chile, Chile)
Components of Hodge loci of minimal codimension

Tiago J. da Fonseca (UNICAMP, Brazil)
Motivic interpretation of higher Green’s functions

François Greer (Michigan State Univesity, USA)
Quasi-Modularity of Hodge Cycles

Khelifa Nazim (Université Paris-Saclay, France)
A criterion for density of Hodge loci (Joint with David Urbanik)

Gregory Pearlstein (Texas A&M University, USA)*
Infinitesimal Torelli and rigidity results for a remarkable class of elliptic surfaces

Christian Schnell (Stony Brook, USA)*
Finiteness for self-dual classes in variations of Hodge structure

Emre Sertöz (Leibniz University Hannover, Germany)
Computing linear relations between 1-periods

Salim Tayou (Harvard University, USA)
On the non-abelian Hodge locus

Roberto Villaflor (PUC, Chile)
Periods of algebraic cycles and Hodge loci

Claire Voisin (IMJ, France)*
Strong representability of 1-cycles on rationally connected threefolds

Hossein Movasati (IMPA, Brazil)
GADEPs problems


Hossein Movasati (IMPA, Brazil)
Younes Nikdelan (UERJ, Brazil)
Suely Lima (IMPA)