Algebraický seminář
Matthew Habermann (Univ. Hamburg): Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities
Abstract: Invertible polynomials are a class of hypersurface singularities which are defined in an elementary way from square matrices with non-negative integer coefficients. Berglund—Hübsch mirror symmetry posits that the polynomials defined by a matrix and its transpose should be mirror as Landau—Ginzburg models, and an extension of this idea due to Berglund and Henningson postulates that this equivalence should respect equivariant structures. In this algebraically orientated talk, I will begin by giving some background and context for the problem, and then explain of my recent work proving conjecture in the first non-trivial dimension; that of curves. They key input is detailed calculations in categories of graded matrix factorisations, as well as a model for the orbifold Fukaya--Seidel category in this context which takes inspiration from the crepant resolution conjecture.
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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.
