Regulators, Log-Geometry and Log Clemens Conjectures

Dates: September 21–25, 2026

Location: CIMAT – Guanajuato, Mexico

About the Meeting

Log Calabi-Yau varieties have recently emerged as a central theme across several frontiers of algebraic geometry. While the enumerative geometry of these varieties has seen rapid progress, the corresponding Hodge-theoretic landscape—specifically concerning Abel-Jacobi maps and their higher analogues in the log and relative settings—remains significantly less explored.

This proposed one-week conference and school aims to bring together researchers and advanced students working at the intersection of Hodge theory, regulators, higher algebraic cycles, log-geometry, and the relative Clemens conjectures. The event will serve as a catalyst for future progress in the relative Clemens program, exploring (tentatively) how algebraic $K$-theory and regulator maps provide the infrastructure necessary to generalize classical results.

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)

Page updated

Google Sites

Report abuse