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Deformation Theory Seminar

Monday, July 11, 2022 - 2:00pm

Dasha Poliakova

U Copenhagen


University of Pennsylvania

Upcoming: 7/25 Chris Eliot 8/15 Kate Ponto

When algebras, or operads, or colored operads are Koszul dual, there are some numeric consequences for their Poincare-Hilbert series, which I will explain. Polytopes are a source of Koszul self-dual algebras, namely their incidence algebras. In some cases such an algebra can be upgraded to a Koszul self-dual colored operad, equipping the (contractible) complex of cellular chains with the newly defined structure of an integrated A-infinity coalgebra. In some (more interesting) cases, this upgrade is yet to be constructed (by further development Laplante-Anfossi's methods). This has applications in the study of operadic diagonals and weak monoidality.
The talk will be largely based on joint work with Sergey Arkhipov arXiv:2112.13743.