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Real Curves, Open Strings, and A-infinity Algebras
Kevin Costello gave a talk last week in one of Peter Teichner’s many seminars, explaining -algebras with a view towards his papers on topological string theory. It was the sort of talk that might have...
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Koszul algebras and Koszul duality
One of the famous theorems that tend to crop up in undergraduate algebra classes is the Artin-Wedderburn theorem, which says Theorem. Any semi-simple ring is a product of matrix algebras over division...
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(Anton Geraschenko) The Salamander lemma
[I'm happy to introduce Anton, our very first guest blogger.] A couple of years ago, George Bergman gave me a copy of a fun preprint that he never got around to preparing for publication. A scan of it...
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Derived categories bleg
Is the following theorem true, and if so, where is the reference? Theorem? Let be a triangulated category with finite homological dimension, and let be a finite set of objects which generate and whose...
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Hypertoric varieties and Koszul duality
So, on Wednesday, I gave a talk with the above title at IAS, about work in progress with Tom Braden, Tony Licata, and Nick Proudfoot. I was hoping to get David Nadler to blog it for me, but he was...
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Reference Hunt I
Does anyone know where the following useful facts were first proved? A lot of papers just say, "It is known that…" and I’d like to give proper attribution in some future work. Let A be an abelian...
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Hall algebras and Donaldson-Thomas invariants I
I would like to tell you about recent work of Dominic Joyce and others (Bridgeland, Kontsevich-Soibelman, Behrend, Pandaripande-Thomas, etc) on Hall algebras and Donaldson-Thomas invariants. I don’t...
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The Witt group, or the cohomology of the periodic table of n-categories
A very popular topic at the Modular Categories conference was the a generalization of the Witt group which is being developed by Davydov, Mueger, Nikshych, and Ostrik. What is this Witt group? Well...
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A hunka hunka burnin’ knot homology
One of the conundra of mathematics in the age of the internet is when to start talking about your results. Do you wait until a convenient chance to talk at a conference? Wait until the paper is ready...
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When fine just ain’t enough
If you use sheaves to study differential geometry, one of the basic lemmas you’ll want is the following: Let be a smooth manifold and let be a sheaf of modules over . (For example, might be the sheaf...
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