The algebraic tmf resolution

The algebraic tmf resolution

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Mark Behrens, University of Notre Dame

Online Talk 

Zoom link: https://princeton.zoom.us/j/96282936122

Passcode: 998749

Let tmf denote the spectrum of topological modular forms. The tmf-resolution is the tmf-based Adams based spectral sequence for the sphere.  I will discuss the algebraic behavior of this spectral sequence (e.g. after applying Ext). The algebraic E_1-term is described as Ext_A(2) of the bo-Brown-Gitler modules. I will then discuss joint work with JD Quigley and Mark Mahowald, where we identify how various parts of the algebraic tmf resolution pick out various parts of Ext of the mod 2 Steenrod algebra.  This is the key technical input to our determination of the 2-primary Hurewicz image of tmf. Then I will discuss recent work with Prasit Bhattacharya and Dominic Culver, where we completely compute the v2-localized E_1-term of the algebraic tmf resolution.