Ralf Holtkamp, email: holtkamp at math.uni-hamburg.de


Since the 1990's, operads became a widely used tool, with applications in algebra, topology, differential geometry, and mathematical physics. An operad encodes all operations which can be performed on some type of algebra, say, and all the ways to compose these operations. The first three examples of algebraic operads are associated to the classical types of algebras: associative algebras, commutative algebras, and Lie-algebras. The theory of operads allows to go beyond the classical types. Strong homotopy algebras and other types of algebras with infinitely many different operations like A-infinity-algebras appear in the context of operads. And even for the classical types of algebras, operadic theorems have brought new insights and results.

In a first part of this lecture course, an introduction to the theory of operads will be given. In particular, we are going to present the Koszul duality for operads.

In the second part, depending on the interest of the participants, we may treat

  • (Co)Homology theories

  • Generalized bialgebras

  • Infinity-algebras

  • Operads in 2d CFT

Aim/Prerequisites: This course is mainly aimed at Masters students in Mathematics or Mathematical Physics. A basic knowledge of algebra is necessary, some familiarity with topology and/or homological algebra would be helpful. In any case, if you think this course might be something for you but you are not sure that you will be able to follow, please send me an e-mail about your interest and knowledge.


Algebraic Operads, J.-L.Loday, B.Vallette (Leitfaden)
Operads in Algebra, Topology and Physics, M. Markl, S.Shnider, J.Stasheff, AMS (2002).



Time and Place:

Lectures Tuesdays 8:30–10:00am, Geom H3; Tutorials Tuesdays 4:00pm, Geom H4.