Abstract for the talk on 22.04.2021 (15:15 h)

Leipzig seminar on Algebra, Algebraic Geometry and Algebraic Topology

Pedro Tamaroff (MPI MIS, Leipzig)
The Diamond Lemma through homotopical algebra
22.04.2021, 15:15 h, only video broadcast

The Diamond Lemma is a result indispensable to those studying associative (and other types of) algebras defined by generators and relations. In this talk, I will explain how to obtain a new approach to this celebrated result through the homotopical algebra of associative algebras: we will see how every multigraded resolution of a monomial algebra leads to "its own" Diamond Lemma, which is hard-coded into the Maurer-Cartan equation of its tangent complex. For the reader familiar with homotopical algebra, we hope to provide a conceptual explanation of a very useful but perhaps technical result that guarantees uniqueness of normal forms through the analysis of "overlapping ambiguities". For a reader familiar with Gröbner bases or term rewriting theory, we hope to offer some intuition behind the Diamond Lemma and at the same time a framework to generalize it to other algebraic structures and optimise it. This is joint work with Vladimir Dotsenko (arXiv:2010.14792).

If you want to participate in this video broadcast please register using this special form. The (Zoom) link for the video broadcast will be sent to your email address one day before the seminar.

13.04.2021, 13:23