Non-commutative analogue of the Berglund-Hübsch-Henningson duality and symmetries of orbifold invariants of singularities

• 主讲人：Sabir M. Gusein-Zade (Lomonosov Moscow State University)
• 举办方： Beijing-Moscow Mathematics Colloquium
• 时间： 2022-12-23 17:00 - 2022-12-23 18:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/9E311B9B60E51416E32FC149EA494B27
Valid Until: 2027-01-31 23:59

 

Abstract: The first regular construction of (conjecturally) mirror symmetric orbifolds belongs to Berglund, Hübsch and Henningson. The Berglund-Hübsch-Henningson- (BHH- for short) duality is a duality on the set of pairs (f,G) consisting of an invertible polynomial group and a subgroup G of diagonal symmetries of f. Symmetries of (orbifold) invariants of BHH-dual pairs are related to mirror symmetry. There were prooved symmetries for the orbifold Euler characteristic, orbifold monodromy zeta-function, and orbifold E-function. One has a method to extend the BBH-duality to the set of pairs (f,G^, where G^ is the semidirect product of a group G of diagonal symmetries of f and a group S of permutations of the coordinates preserving f. The construction is based on ideas of A.Takahashi and therefore is called the Berglund-Hübsch-Henningson-Takahashi- (BHHT-) duality. Invariants of BHHT-dual pairs have symmetries similar to mirror ones only under some restrictions on the group S: the so-called parity condition (PC). Under the PC-condition it is possible to prove some symmetries of the orbifold invariants of BHHT-dual pairs.

The talk is based on joint results with W.Ebeling.

 

Bio: Sabir Medzhidovich Gusein-Zade is a Professor at the Department of Higher Geometry and Topology of Lomonosov Moscow State University. He graduated from the Faculty of Mechanics and Mathematics of MSU in 1974 and defended his PhD thesis under the supervision of Sergei Novikov in 1975. In 1991, Gusein-Zade became Doctor of Physical and Mathematical Sciences. Gusein-Zade has been the faculty of the Department of Higher Geometry and Topology since 1996. His scientific interests include the theory of singularities and the topology of algebraic spaces. Prof. Gusein-Zade is the author of more than 120 publications on pure and applied mathematics (including 4 monographs). He is also the editor of the Moscow Mathematical Journal and has been the Secretary of the Moscow Mathematical Society since 1996.