Speaker
Ismael Sierra
Description
In this talk I will explain ongoing work with Kupers and Rudenko on a new approach to understanding the Rognes rank spectral sequence and the Goncharov program using the $E_\infty$-homology of the $E_\infty$-algebra associated to symmetric monoidal category of vector spaces over a field. One of the new ideas is to compute the Koszul dual Lie cobracket on the indecompodables of this algebra and use it to understand the $d^1$ differential of the Rognes rank spectral sequence. I will also mention some applications of these tools to weight 3 polylogarithms and algebraic K theory, and some open conjectures.
