Homotopy, geometry, and arithmetic

Over the past two decades, higher category theory and homotopy-coherent methods have become indispensable not only within homotopy theory itself, but across a rapidly growing range of neighboring fields. These include derived and spectral algebraic geometry, p-adic and arithmetic geometry, motivic homotopy theory, geometric and symplectic topology,  deformation theory, topological and quantum field theories, and aspects of the Langlands program. A key insight underlying many of these developments is that by working homotopy-coherently, it becomes possible to do algebra — in the sense of studying rings, modules, and representations — in settings such as derived categories, or in stable homotopy theory, where classical algebraic structures are unavailable or insufficient. This shift has led to both structural insights and powerful new computational tools.

The goal of this conference is to bring together researchers from diverse communities who employ homotopy-theoretic and higher-categorical techniques as tools in their work in geometry and arithmetic, broadly construed. We hope to foster dialogue between specialists with different backgrounds and perspectives, and to stimulate new interactions at the interface of homotopy theory, geometry, and arithmetic.