Research Centre: Department of Mathematics
Speaker: Pedro Tamaroff (Trinity College, Dublin)
Title: Minimal models for monomial algebras
In 1985, David Anick came up with a combinatorial construction of "chains'' which can be used to compute various homological invariants of an associative algebra from a ``nice'' presentation of such an algebra by generators and relations. In particular, for algebras with monomial relations, his construction produces those invariants directly.
In this talk, I will explain how to compute a rich algebraic structure on Anick chains leading to the explicit formula for a "minimal model'' for any monomial algebra. A minimal model is a replacement of an algebra by a differential graded algebra with the same homological properties. This computation relies on algebraic discrete Morse theory and on homotopy transfer formulas; those are formulas perfectly suited for homological computations where underlying chain complexes are of combinatorial nature. Prior knowledge of these techniques is not required: they will be explained along the way.
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When & where
3.00pm - 4.00pmTuesday 13th November 2018