Research Seminar on Algebraic Topology, Summer Term 2025

Julian Holstein, Birgit Richter

In the summer term 2025 we will meet roughly every second Thursday in the gaps of the ZMP seminar. The exact dates are: 17/04, 15/05, 05/06, 12/06, 26/06 and 10/07.

If you are interested in participating, then please register for the mailing list of the seminar by sending "subscribe" to topologieseminar.math-request@lists.uni-hamburg.de

The topic for our working seminar is Koszul Duality. If you want to give a talk in the working seminar, send an email to us. The first three talks are based on the book Algebraic Operads by Loday and Vallette. A fourth talk will be given by Julian Holstein on Koszul duality in the curved context.

1. Basics on operads and cooperads: Some background on symmetric sequences, classical definition of an operad and the one using partial compositions, algebras over operads (examples!), cooperads. Based on Chapter 5 of Loday-Vallette.
2. What is Koszul duality for operads?: Define what a quadratic operad is and introduce its Koszul dual (co)operad. What is the Koszul dual of the operad Com? What happens for Ass? (Chapter 7, sections 1,2 and parts of 6)
3. Bar and cobar construction: Define the bar construction of a quadratic operad and the cobar construction of a quadratic cooperad and explain their role in Koszul duality (Chapter 7.3 with background from earlier parts)