Thursday, November 21, 2019 - 11:30am to 12:30pm
MW 154
Speaker: Jun Hou Fung (Harvard)
Title: Strict units of commutative ring spectra
Abstract: Just as an ordinary commutative ring has a multiplicative group of units, a $E_\infty$-ring spectrum $R$ also has a spectrum of units $gl_1 R$, which plays an important role for example in twisted cohomology theories. However, these spectra are typically very large, and to understand twists by Eilenberg-Mac Lane spaces or to isolate those units that come from geometry, it sometimes suffices to study the space of \emph{strict units} of $R$. Previously, Hopkins and Lurie have computed the strict units of Morava $E$-theories, but much remains unknown about them in general.
In this talk, I will introduce these strict units and illustrate various methods for computing them for other commutative ring spectra $R$, and describe how these calculations relate to other interesting questions in homotopy theory.