Hodge theory, enumerative geometry and log Clemens conjectures

Dates: September 21–25, 2026

Location: CIMAT – Guanajuato, Mexico

About the Meeting

Rational curves on Calabi-Yau threefolds have received enormous attention since the eighties. A driving force has been the Clemens conjectures, which concern the finiteness of curves with fixed degree on the generic quintic threefold, their $(-1, -1)$-normal bundle, and their smoothness. These conjectures have inspired many developments in enumerative geometry, deformation theory, Hodge theory, and differential geometry.

This one-week conference and school aim to bring together researchers and students working in Hodge theory, singularities, enumerative geometry and differential geometry. We will discuss the recent introduction, solution, and consequences of the log Clemens conjectures as in (arXiv:2601.11813). The event will serve as a starting point for future progress in the relative Clemens program, exploring the wider settings where these conjectures are valid and expanding the applications of their solutions.

List of Speakers:

Cristhian Garay (CIMAT, Mexico)
Radu Laza * (Stony Brook, USA)
Erick David Luna Nuñez (Universidad de Aguascalientes, Mexico)
Hossein Movasati (IMPA, Brasil)
Adrian Zahariuc (University of Windsor, Canada)

*tbc

Target Audience & Impact

The event is specifically aimed at graduate students and early-career researchers from Mexico and Latin America, providing them with vital exposure to advanced Hodge-theoretic techniques. We also aim to reserve spots for established international researchers to present their work and mentor regional students, fostering long-term collaborative networks.

Proposed Program Structure

To create a level playing field for students and facilitate deep discussions among specialists, the format is designed as a hybrid school and conference:

Introductory Minicourses: 3 to 4 planned series covering foundational topics such as (tentatively) higher algebraic cycles, regulators, log-geometry, and the log Clemens conjectures.
Research Talks: A series of specialized afternoon lectures presenting cutting-edge progress and applications in the log settings.
Interactive Sessions: Optional poster sessions and problem-solving groups to foster collaboration.

Organizers

Rodolfo Aguilar (CIMAT)
Gabriela Guzmán (CIMAT)
Pedro Luis del Angel (CIMAT)
Patrick Brosnan (University of Maryland)

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