Penn Arts & Sciences Logo

Geometry-Topology Seminar

Thursday, April 14, 2022 - 5:15pm

Allen Yuan



University of Pennsylvania


A central perspective in modern homotopy theory is that the category of cohomology theories, or spectra, is analogous to the derived category of abelian groups.  One can then view (commutatively) multiplicative cohomology theories as analogues of commutative rings and explore the commutative algebra of these so-called “brave new rings.”  In this talk, I will start by explaining some basics of chromatic homotopy theory and how it arises naturally by considering the analogue of prime fields in this setting.  Then I will explain joint work with Robert Burklund and Tomer Schlank which identifies Lubin-Tate theories as the analogue of algebraically closed fields, and I will finish with some applications of these results to chromatic redshift in algebraic K-theory.