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Homotopy Theory Seminar -- Jun Hou Fung

Homotopy Theory Seminar
November 21, 2019
11:30 am - 12:30 pm
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.

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Seminar - Homotopy Theory