PROGRAM

Junwu Tu ShanghaiTech University https://ims.shanghaitech.edu.cn/2018/1110/c4741a35982/page.htm

Биография: Junwu Tu is a Professor at the Insitute of Mathematical Sciences of ShanghaiTech University. He got his bachelor’s degree from Nanjing University in 2005 and Ph.D. from the University of Wisconsin-Madison in 2011. His research centers around homological algebra and its applications in algebraic geometry, symplectic geometry, homological mirror symmetry and data sciences. Recently, he has been working on defining and understanding categorical Gromov-Witten invariants.

Frobenius structures from Calabi-Yau categories.

Primitive forms were introduced by K. Saito in his construction of period mapping in the unfolding space of singularities. The Hodge theoretic structure involved in this construction is known as the semi-infinite Hodge structure introduced by Barannikov and Kontsevich. Following Kontsevich’s proposal in his 1994 ICM address, we shall discuss the appearance of such structures in the categorical contexts, as well as a few open problems in this direction.

Sabir M. Gusein-Zade Lomonosov Moscow State University

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.

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

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.

 The meeting will be held in the form of a webinar on the Zoom platform.

Pre-registration for the event is not required.

Link to the conference:

https://us02web.zoom.us/j/84065324254?pwd=SHV3YnBncS85Tmh4bXhkV29pZHh0dz09

Meeting ID : 840 6532 4254

Passcode：987654