时间： 2018 年6月10日，星期日
地点： 精正楼2楼报告厅
9:45-10:45 XiaomengXu (MIT)
Title: An introduction to Stokes phenomenon andits applications
Abstract: This talk will include a general introductionto a linear differential system with singularities, and its relation withsymplectic geometry, Yang-Baxter equations, integrable hierarchy andtopological field theories.
11:10-12:10 YoulinLi (Shanghai Jiao Tong University)
Title: Contact (+1)-surgeries along Legendriantwo-component links
Abstract: In this talk, we prove that the contactOzsv/'ath-Szab/'o invariant of a contact 3-manifold vanishes if it can beobtained from the standard contact 3-sphere by contact (+1)-surgery along a Legendrian two-componentlink L=L_1/cup L_2 with the linking number of L_1 and L_2 being nonzero and L_2satisfying /nu^{+}(L_2)=/nu^{+}(/overline{L_2})=0. We also give a sufficientcondition for the contact 3-maniold obtained from the standard contact 3-sphereby contact (+1)-surgery along aLegendrian two-component link being overtwisted. This is joint work with FanDing and Zhongtao Wu.
14:00-15:00 XiaojunChen (Sichuan University)
Title: Calabi-Yaualgebras and the shifted noncommutative symplectic structure
Abstract: The notionof Calabi-Yau algebras was introduced by Ginzburg in 2007 and has widely beenstudied since then. In this talk, we show that for a Koszul Calabi-Yau algebra,there is a shifted bi-symplectic structure on the cobar construction of itsco-unitalized Koszul dual coalgebra,
and hence its DGrepresentation scheme have a shifted symplectic structure. Joint with F. Eshmatov.
15:30-16:30 JianghuaLu (The University of Hong Kong)
Title: Generalized Bruhat Cells and Completeness ofHamiltonian Flows of Kogan-Zelevinsky Integrable Systems
Abstract: Let G beany connected and simply connected complex semisimple Lie group, equipped witha standard holomorphic multiplicative Poisson structure. We show that theHamiltonian
flows of all theFomin-Zelevinsky twisted generalized minors on every double Bruhat cell of G arecomplete in the sense that all the integral curves of their Hamiltonian vectorfields are defined on the set of all complex numbers. It follows that theKogan-Zelevinsky integrable systems on G have complete Hamiltonian flows,generalizing the result of Gekhtman and Yakimov for the case the general lineargroups.