报告题目：Virasoro symmetries of bihamiltonian hierarchies and Dubrovin-Zhang polynomiality conjecture

报告人：王哲，清华大学

时间：2022年1月11日（星期二）下午14:30-16:00

                      1月18日（星期二）下午14:30-16:00

                      1月20日（星期四）下午14:30-16:00

腾讯会议 ID：572 283 2445 ，会议密码：123456

摘要：Dubrovin-Zhang theory is a framework of studying the 2D topological field theory (2DTFT) via the theory of bihamiltonian integrable hierarchies. Given the genus zero part of a 2DTFT, Dubrovin constructed a Frobenius manifold as its geometrical model and a corresponding bihamiltonian integrable hierarchy that controls the genus zero partition function of the 2DTFT. In order to extend this construction to higher genera, Dubrovin and Zhang constructed a unique deformation of the genus zero integrable hierarchy that satisfies some axioms and nowadays it is called the Dubrovin-Zhang hierarchy. Many properties of this deformed integrable hierarchy have been studied in last two decades, however the polynonmiality of the second hamiltonian structure remains unproved, which is one of the most important properties conjectured by Dubrovin and Zhang. In this series of seminars, I will talk about our proof of the polynonmiality of the bihamiltonian structure of the Dubrovin-Zhang hierarchy by developing the theory of variational bihamiltonian cohomologies and the theory of super tau-covers. This is a joint work with Si-Qi Liu and Youjin Zhang.