Factorisation homology seminar

General information

This is the official website for the factorisation homology, organised together with Alba Sendón Blanco and taking place between Universiteit Utrecht and Vrije Universiteit.

Place: the talks will alternate between UU and VU, see the PDF file below for the exact room for each day.
Time: the talks will happen weekly on Friday, from 3 PM until 5 PM. Ideally, each talk should consist of two parts of 45 minutes each, with a break in the middle and the remaining time left for questions.
Prerequisites: some knowledge of category theory and differential topology will be assumed. Topics such as higher categories and operads will be covered in the first few talks.

If you have any questions about the seminar or want to give one of the talks, please send an email to either Alba (a.sendon.blanco@vu.nl) or you can also send me (m.lourencohenriquesbarata@uu.nl) an email.

Brief description

Factorisation homology was first introduced in 2008 in the PhD thesis of John Francis, and since its birth it has had a rising importance in homotopy theory, as well as all the many areas it naturally connects to, such as TQFTs, differential topology and derived algebraic geometry, just to name a few. The intent of this seminar is to get acquainted with the basics of factorisation homology, and perhaps understand some the instances where this theory appears in other places in mathematics.

The plan of the seminar is to learn the basics about factorisation homology by going through this article by Ayala-Francis.

Talks of the seminar

Here is a quick description of the talks of the seminar, in case you would be interested in giving one of the talks. See also this file for some more details and references. The general plan is to cover this article by Ayala-Francis, which is referenced below as [AF].

Lecture 1 (Inbar Klang, VU, NU09-A46 Maryam, October 18): This talk will be an introduction/overview about factorisation homology. See here for Inbar's notes.
Lecture 2 (Sven van Nigtevecht, UU, Minnaert 0.14, October 25): This talk will serve as an introduction to infinity-categories. See here for Sven's notes.
Lecture 3 (Miguel Barata, VU, Maryam NU09-A46, November 1): This talk will serve as an introduction to operads. See here for Miguel's notes.
Lecture 4 (Alba Sendón Blanco, UU, KBG 228, November 8): In this talk one should try to cover the contents of section 2 of [AF], which is about how to correctly set up the language of differential topology within the context of higher categories. See here for Alba's notes.
Lecture 5 (Miguel Barata, VU, Maryam NU09-A46, November 15): In this talk one should cover Section 3 of [AF] except for 3.3. Here one should introduce the central notions of factorisation homology and factorisation algebras, and discuss some of the main properties of these constructions. See here for Miguel's notes.
Lecture 6 (Guy Boyde, UU, BBG 169, November 22): In this talk one should do some examples of factorisation homology, for instance the factorisation homology over 1-dimensional manifolds (Section 3.3 of [AF]) with the identification of factorisation homology over $S^1$ of an associative algebra with its Hochschild homology. One should also cover some of the examples in Section 5. See here for Alba's notes on this talk.
Lecture 7 (Remy van Dobben de Bruyn, VU, Maryam NU09-A46, November 29): In this talk one should try to cover the material in Section 4 of [AF] about non-abelian Poincaré duality. See here for Remy's notes.
December 6: This is talk is cancelled due to the DDTG seminar in Utrecht.
Lecture 8 (Niall Taggart, UU, BBG 077, Decemeber 13): In this talk one should try to go through Sections 6 and 7 of [AF] on the relation between Goodwillie calculus and filtrations on factorisation homology. See here for Niall's notes.

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