Department of Mathematics

Homotopical and Higher Algebra

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Professor Damien Calaque
Assistant Claudia Scheimbauer, Mathieu Anel
Time Tue 3-5
Place HG G19.2
Requirements Students are required to give one or two talks, depending on the subject and length.
Meetings We will meet once approximately 2 weeks before the talk, usually on Monday afternoons ("office hours") in Damien Calaques office HG G 28.3. Furthermore, you can ask questions to Claudia or Mathieu.
First meeting Tue, Sept. 18, 3-5.
Talks will be distributed at the first meeting! Please contact the organizers beforehand if you are unavailable on this day.


The ultimate goal for this Seminar is to understand the statement of the cobordism hypothesis after Baez-Dolan and Lurie. This will serve as a pretext for introducing several important notions and concepts from higher category theory and homotopy theory.

Overview of the semester

A detailed outline of the talks can be found here.

Week Date Speaker Notes (if available)
Week 1 Sept. 25 Merlin The symmetric monoidal category nCob and nTFTs.
Week 2 Oct. 2 Daniel, Julian Duality in monoidal categories, Presentation of 1Cob by generators and relations.
Week 3 Oct. 9 Thomas 2TFTs and Frobenius algebras.
Week 4 Oct. 16 Rade, Damien Extending down TFTs, Bicategories.
Week 5 Oct. 23 Claudio, Florian Symmetric monoidal bicategories.
Week 6 Oct. 30 summary session  
Week 7 Nov. 6 Ivan, Camilo 2-dualizable objects.
Week 8 Nov. 13 Daniel, Julian Model categories, Models for \infty-groupoids.
Week 9 Nov. 20 Adrian Models for (\infty,1)-categories and Quillen equivalences
Week 10 Nov. 27 Merlin, Florian The (\infty, 1)-category 1Cob_\infty.
Week 11 Dec. 4 Rade, Claudia n-fold Segal spaces, The n-fold complete Segal space Bord_n.
Week 12 Dec. 11 Paul Symmetric monoidal structures on higher categories.
Week 13 Dec. 18 Mathieu, Damien Around fully dualizable objects in (\infty,n)-categories.

Warning: There are some errors in the talks on Bord_n and its symmetric monoidal structure which will be corrected in an article in preparation by the organizers.


Main references
Other references
Origin of the subject
On the 2-dimensional case
On bi- and higher categories
On homotopy theory
On category theory

If you read french, there are some interesting lecture notes from a workshop on Lurie's and Baez-Dolan's work in Paris, which are available here


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