# Equivariant Derived Algebraic Geometry (16w5133)

## Organizers

(University of California, Los Angeles)

(University of Texas, Austin)

(Michigan State University)

(University of Minnesota)

## Description

The Banff International Research Station will host the "Equivariant Derived Algebraic Geometry" workshop from February 14th to February 19th, 2016.

Algebraic topology has had a long and fruitful collaboration with algebraic geometry, with each providing techniques and problems to the other. This workshop is aimed at a novel and modern incarnation of this story: Recent work on the foundations of equivariant stable homotopy theory (starting with the Hill-Hopkins-Ravenel work on the Kervaire invariant one problem) and Lurie's development of the foundations of derived algebraic geometry'' now allows systematic exploration and organization of equivariant derived algebraic geometry."

New foundations in this area have the potential to describe phenomena seen in the trace methods approach to computing algebraic $K$-theory as well as in topological modular forms. For instance, although the theory of equivariant commutative ring spectra was described decades ago, few of the subtleties in the theory were understood or explored. Preliminary investigation suggests that many of the constructions in ordinary derived algebraic geometry are seen to naturally have equivariant extensions. Similarly, the modern approaches to computing algebraic $K$-groups step through equivariant commutative ring spectra. This workshop, at the vanguard of work in this area, seeks to bring together experts in algebraic topology, (derived) algebraic geometry, and representation theory to explore the ways one can do (derived) algebraic geometry in the equivariant setting.

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 U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).