Conference: Modular forms, L-functions, and Eigenvarieties

This award supports US-based scientists to attend the conference "Modular Forms, L-functions, and Eigenvarieties". The event will take place in Paris, France from June 18, 2024, until June 21, 2024. Whole numbers are the atoms of our mathematical universe. Number theorists study why patterns arise among whole numbers. In the 1970's, Robert Langlands proposed connections between number theory and mathematical symmetry. His ideas revolutionized the field. Some of the most fruitful approaches to his ideas have come via calculus on geometric spaces. The conference funded here will expose cutting edge research on such approaches. The ideas disseminated at the conference will have a broad impact on the field. The presentations of leading figures will propel junior researchers toward new theories. The US-based participants will make a written summary of the conference. The summaries will encourage the next generation to adopt the newest perspectives. Writing them will also engender a spirit of collaboration within the research community. The summaries along with details of the events will be available on the website https://www.eventcreate.com/e/bellaiche/. The detailed aim of the conference is exposing research on modular forms and L-functions in the context of eigenvarieties. An eigenvariety is a p-adic space that encodes congruence phenomena in number theory. Families of eigenforms, L-functions, and other arithmetic objects find their homes on eigenvarieties. The conference's primary goal is exposing the latest research on such families. The presentations will place new research and its applications all together in one place, under the umbrella of the p-adic Langlands program. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.