Polylogarithms and Algebraic K-theory seminar

Columbia University, Fall 2026, 4-5pm in room 507.

The goal of this seminar, organized by Andrew Blumberg and Soren Galatius, is to understand the preprint The Goncharov Lie coalgebra of a field, by Kupers, Rudenko, and Sierra. The main definition of that paper gives a new perspective on multiple polylogarithms (certain holomorphic functions of several variables, generalizing the classical logarithm -log(1-z)=Σ_n>0 n^-1zⁿ), and their relationship to motives and algebraic K-theory.

Time permitting, we also hope to discuss the sequel, which gives interesting applications to number fields.

Mailing list. Send an e-mail to sg4379@columbia.edu if you'd like to be on the mailing list for the seminar.

Tentative schedule with more detailed talk descriptions and some references, available here.

Lecture overview, tentative

Sep 10

Introduction by Soren Galatius.

Sep 17

Derived indecomposables 1 by Serena An. Quillen's preprint

Sep 24

Derived indecomposables 2 by Sangmin Ko.

Oct 1

The Quillen spectral sequence and the Rognes spectral sequence by Tan Su.

Oct 8

The Goncharov Lie coalgebra by Azélie Picot.

Oct 15

Polylogarithms and multiple polylogarithms 1 by Zhonghui Sun.

Oct 22

Polylogarithms and multiple polylogarithms 2 by Peter Moody.

Oct 29

Polylogarithms and multiple polylogarithms 3 by Semon Rezchikov.

Nov 5

Steinberg modules 1 by Carlos Andrés Alvarado Álvarez.

≥ Nov 12

see tentative schedule