Speaker
Paul Van Koughnett
Abstract
This talk will be an introduction to some uses of algebraic geometry in chromatic homotopy theory, both as an organizing tool and to make computations. I hope to demystify the concept of a stack, primarily focusing on three examples: the moduli of formal groups, whose structure encodes many of the basic phenomena of chromatic homotopy theory; the moduli of elliptic curves, which is used to construct the topological modular forms spectrum TMF; and its kid sibling, the “moduli of multiplicative groups” (aka BC_2). Afterwards, I will venture into some recent developments, including the pursuit of higher chromatic information via moduli of higher-dimensional abelian varieties, and the development of spectral algebraic geometry.