Algebraický seminář
Matt Booth (Imperial College London): Nonsmooth Calabi—Yau structures for algebras and coalgebras
Abstract: I'll talk about a generalised notion of Calabi-Yau structure for dg co/algebras, before explaining why this `nonsmooth Calabi—Yau' condition is Koszul dual to a symmetric Frobenius condition. The proof boils down to a comparison of various types of linear duality functors across Koszul duality. There are also twisted and one-sided versions of this statement, the latter saying that Gorenstein and Frobenius are Koszul dual properties. This leads to a surprising example: the ring k[[x]] of formal power series, equipped with its natural topology, is a pseudocompact Frobenius algebra. As an application of the above theory, we obtain a new characterisation of Poincaré duality spaces, which for simply connected spaces recovers Félix-Halperin-Thomas's notion of Gorenstein space. This talk is based on joint work with Joe Chuang and Andrey Lazarev.
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
