GMM Reading Group

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

Last update: Jan 30, 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: Feb 06, 2026 9: Open Discussion

Time Description
Feb 06
09:00

9: Open Discussion

There will be no regular talk. Instead, we discuss and explore the concepts we have seen so far, by getting our hands dirty with explicit computations. We will be on BBB as usual, so online participants can join in on the discussion.
Jan 30
09:00

8: Additivity for beginners - Part 2

Speaker: Ulrich Krähmer

Notes: PDF
Jan 23
09:00

7: Additivity for beginners - Part 1

Speaker: Ulrich Krähmer

Notes: PDF
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.