## Real Curves, Open Strings, and A-infinity Algebras September 20, 2007

Posted by A.J. Tolland in Category Theory, homological algebra, mathematical physics.

Kevin Costello gave a talk last week in one of Peter Teichner’s many seminars, explaining $A_\infty$-algebras with a view towards his papers on topological string theory. It was the sort of talk that might have interested a lot of people, so (with Kevin’s permission), I’m posting my .pdf scanned notes here. I’ve added some physics interpretation that Kevin didn’t make explicit.

Defining $A_\infty$-algebras

Kevin also gave a shorter talk (in a different Teichner seminar) about his characterization of the homotopy type of a moduli space of genus zero open string worldsheets. My notes here are less detailed, but maybe someone will enjoy them.

The Homotopy Type of a Certain Moduli Space of Open String Worldsheets

1. The Infinite Seminar » A infinity at the Secret Blogging Seminar - September 20, 2007

[...] AJ Tolland links to some seminar notes from a seminar by Peter Teichner on A ∞-algebras in topological string theory. September 21, 2007, Mathematics, A-infinity, [...]

2. This week in the arXivs… « It’s Equal, but It’s Different… - September 21, 2007

[...] Real Curves, Open Strings, and A-infinity Algebras [...]

3. David Ben-Zvi - September 21, 2007

Thanks for the notes AJ!

For people seeking more Costellian inspiration (which I usually am), check out the recent streaming video of his lecture “Topology in two dimensions and Frobenius algebras” at
http://www.math.utexas.edu/~benzvi/GRASP.html
and notes from five other related talks (on topological field
theory, renormalization in the BV formalism, rational homotopy theory etc) at
http://www.math.utexas.edu/~benzvi/notes.html

4. jim stasheff - September 30, 2007

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