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  4. Minimal models for monomial algebras

Nov

13

Tuesday

Minimal models for monomial algebras

3.00pm

Seminars

Staff, Students, Academics

Research Centre: Department of Mathematics

Speaker: Pedro Tamaroff (Trinity College, Dublin)

Title: Minimal models for monomial algebras

Abstract:

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

Tait Building City, University of London Northampton Square London EC1V 0HB United Kingdom
C300 Tait Building City, University of London Northampton Square London EC1V 0HB United Kingdom