# Real Curves, Open Strings, and A-infinity Algebras

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

## 5 thoughts on “Real Curves, Open Strings, and A-infinity Algebras”

1. David Ben-Zvi says:

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

2. jim stasheff says:

The requested URL was not found on this server. The link on the referring page seems to be wrong or outdated. Please inform the author of that page about the error.

Error 404
math.berkeley.edu
Sun Sep 30 18:18:17 2007
Apache/2.0.61 (FreeBSD) PHP/4.4.7 with Suhosin-Patch mod_fastcgi/2.4.2 DAV/2 mod_ssl/2.0.61 OpenSSL/0.9.7e-p1

3. A.J. Tolland says:

I think this must have been a problem with the http server. I’m currently able to download the notes from home.

I did change the location of the notes about a week ago, so if you had an outdated link saved, that could explain the problem. But clicking on the link should work.

Anyways, please let me know if the problem continues.