Rognes' connectivity conjecture and the Koszul dual of Steinberg

Peter Patzt (University of Oklahoma)

Monday 25th October 16:00-17:00 Online

Abstract

In this talk, I will explain how a homotopy equivalence
between certain E_k-buildings both proves Rognes' connectivity
conjecture for fields and computes the Koszul dual of Steinberg. Rognes'
connectivity conjecture states that the common basis complex is highly
connected. This is relevant as the equivariant homology of this complex
appears in a rank filtration spectral sequence computing the homology of
the K-theory spectrum. The Steinberg modules appear in various contexts,
importantly as the dualizing modules of special linear groups of number
rings. They can be put together to form a ring. When considered
equivariantly over the general linear groups of fields, one can show
that this ring is Koszul and we compute its Koszul dual. Results in this
talk include joint work with Jeremy Miller, Rohit Nagpal, and Jennifer
Wilson.


The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/98078798957 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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