GMM Reading Group

$\infty$-Categories and $\infty$-Operads

Last update: Jan 08, 2026 The aim of this reading group is to develop a basic understanding of $\infty$-operads and their algebras. We begin with a crash course on $\infty$-category theory (based on quasicategories) and then move on to reading some introductory literature for $\infty$-operads.
Our group will meet every Friday, 09:00 - 11:00 (CET) at TU Dresden. Our (admittedly ambitious) first goal is to reach $\mathbb{E}_1$ - and $\mathbb{E}_\infty$-monoids by Christmas, so that we will have covered the necessary background to introduce symmetric monoidal $\infty$-categories and can move on with a reference on $\infty$-operads in early 2026.

A provisional schedule for the upcoming talks is outlined below and may be revised as we move through the material.

Next talk: Jan 16, 2026 6: From operads with multiplication to Gerstenhaber algebras

Time Description
Jan 16
09:00

6: From operads with multiplication to Gerstenhaber algebras

Speaker: Ulrich Krähmer

Notes (Draft): PDF

I recall first parts of Florian's talk since a month has passed. Then I explain how Gerstanhaber showed that operads with multiplication are $\mathbb{E}_2$-algebras (in the incarnation as brace algebras), which is maybe the first nontrivial instance of the additivity theorem.