Vector-valued modular forms and cohomology (11rit175)


(Eötvös Loránd University)

Terry Gannon (University of Alberta)

Christopher Marks (University of Alberta)

Geoffrey Mason (University of California, Santa Cruz)


The "Vector-valued modular forms and cohomology" workshop will be hosted at The Banff International Research Station.

Modular forms are one of the oldest and best appreciated areas of number theory, with connections all over mathematics and mathematical physics. Surfaces like spheres and tori can be thought of as curves over the complex numbers, usually in many different ways, and modular forms are functions (differential forms) living on those curves. Because of their profound importance, many generalisations have been studied over the years. Perhaps the most natural is to make them vector-valued. Only in the last couple decades (largely due to the work of Fields' medalist Borcherds) has the significance of this generalisation become clear. This Research-in-Teams would bring together the twornmain groups developing this theory.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides 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 is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí255a (CONACYT).