Categorical and Geometric Structures in the Langlands Program (25w5416)


Ana Caraiani (Imperial College London)

Matthew Emerton (University of Chicago)

Brandon Levin (Rice University)

David Savitt (Johns Hopkins University)

Mingjia Zhang (Princeton University)


The Casa Matemática Oaxaca (CMO) will host the "Categorical and Geometric Structures in the Langlands Program" workshop in Oaxaca, from September 14 to September 19, 2025.

The year 2024 will mark the 30th anniversary of the resolution of Fermat’s Last Theorem, one of the most celebrated applications of the Langlands program. In the three decades since, many seemingly disparate areas of research within the Langlands program have blossomed, some inspired by the ideas introduced in the proof of Fermat, some with a more geometric flavor, made possible in part by the theory of perfectoid spaces, and some with a more representation-theoretic flavor.

The categorical Langlands program is an emerging conceptual framework that encompasses these disparate areas of research: the $p$-adic Langlands program, the geometrization of the local Langlands correspondence, and the cohomology of Shimura varieties in its many incarnations, just to name a few. This workshop brings together architects of the categorical Langlands program in the number field setting as well as emerging experts. The goals are to take stock of the state of the art in the field, to chart a course for future developments, and to provide mentorship and support to a diverse group of early-career participants.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta's Advanced Education and Technology.