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A-infinity algebras and matrix factorisations

Banff International Research Station for Mathematical Innovation and Discovery

I will give a general introduction to A-infinity algebras and their triangulated categories of modules, with a focus on an important class of concrete examples coming from algebraic geometry, specifically, from isolated hypersurface singularities. Since Dyckerhoff identified the DG-endomorphism algebra of the generator of the homotopy category of matrix factorisations in his thesis, it has been possible to (in principle) apply the general method of minimal models to produce the associated A-infinity algebra. I will describe a good choice of homotopy retract which makes such calculations tractable, and sketch the yoga of Feynman diagrams that computes the A-infinity algebra associated to a given singularity.

Mathematics; Category theory; homological algebra; Algebraic structures

video/mp4

Author affiliation: University of Melbourne

2016-12-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60045

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/