# Mathematics Topology Seminar - J.D. Quigley

This event is in the past.

**Date:**November 12, 2019

**Time:**2:00 p.m. - 3:00 p.m.

**Category:**Seminar

Speaker: J.D. Quigley, Cornell University

Title: The motivic kq-resolution

Abstract: (joint work with Dominic Culver) Let kq denote the very effective cover of Hermitian K-theory. The kq-based motivic Adams spectral sequence, or kq-resolution, is a motivic analog of Mahowald’s bo-resolution. We applied the kq-resolution in the C-motivic setting to calculate the eta-periodic stable stems (recovering results of Andrews, Guillou, Isaksen, and Miller) and v_1-periodic stable stems. I will summarize these calculations and discuss work in progress towards analogous results over general base fields and in the C_2-equivariant setting.

In addition to large-scale calculations of periodic phenomena, the kq-resolution can be used to calculate low-dimensional 2-complete Milnor-Witt stems. I will present some calculations in the C- and R-motivic settings (recovering results of Dugger-Isaksen), then discuss work in progress towards analogous results over general base fields and the 2-complete version of calculations of Röndigs-Spitzweck-Østvær.