Семинар Международной лаборатории кластерной геометрии: А. А. Басалаев. 11.05.2023 скачать в хорошем качестве

Семинар Международной лаборатории кластерной геометрии: А. А. Басалаев. 11.05.2023

Hodge diamonds of the Landau-Ginzburg orbifolds Landau-Ginzburg orbifolds are the pairs (f,G) with f being the quasihomogeneous polynomial with complex coefficients and only isolated ciritical points, G being the subgroup in the group of linear symmetries of f. Such objects became popular in the context of mirror symmetry. In particular in the search of the Calabi-Yau varieties with the Hodge diamonds differing by a "rotation". The bridge to the Landau-Ginzburg orbifolds is then given by the following observation. If the reduced weights of f sum up to 1, one can define a Calabi-Yau variety as the zero set {f = 0}/G. In this talk we will explain the role of Landau-Ginzburg orbifolds in mirror symmetry and show how one can work in mirror symmetry (as described above} from the point of view of singularity theory. All necessary definitions will be given, the talk should be accessible for the 3rd year bachelor students.