Speaker: SU Yucai, Professor of the School of Mathematical Science, Tongji UniversityVenue: Room 200-9, Run Run Shaw Business Administration Building, Yuquan CampusAbstract:The Virasoro-like algebra, a natural generalization of the well-known Virasoro algebra, is a Lie algebra closely related to Block type or Cartan type Lie algebras. In this talk, we present some results on Quasifinite representations of the Virasoro-like algebra. Contact: WU Zhixiang(wzx@zju.edu.cn)

Speaker: LI Wenwei, Beijing International Center for Mathematical ResearchVenue: Room 211, Run Run Shaw Science Building, Yuquan CampusAbstract:The metaplectic covering Mp(2n) of Sp(2n) plays a pivotal role in various aspects of representation theory and arithmetics. In order to harness the full power of Arthur's methods in this setting, we need a stable trace formula for Mp(2n). Thus far, only the elliptic terms have been stabilized. In this talk, I will report an ongoing work on the full stabilization, which will hopefully grant access to the whole genuine discrete automorphic spectrum of Mp(2n), for general n. This is based on the techniques of Arthur and Moeglin-Waldspurger, who worked with linear reductive groups or their twisted analgoues.Contact: GAO Fan(gaofan@zju.edu.cn)

Speaker: Prof. JIANG Shidong, New Jersey Institute of Technology, USAAbstract: A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand side singularities，such as 1/|r|^\alpha with \alpha close to 1，can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.Tencent meeting ID: 431 602 349Contact: LAI Jun(laijun6@zju.edu.cn)

Reporter: GENG Zhiyuan, Postdoc Fellow, Basque Center for Applied MathematicsVenue: Room 314, Ouyang chunmei buildinngAbstract:Liquid crystal droplets are of great interest from physics and applications. They are important in the studies of topological defects, both in a bulk and on a surface, in understanding of anisotropic surface energies and anchoring conditions of liquid crystals. In this lecture I will talk about a two-dimensional free boundary problem motivated by a liquid crystal droplet model. The problem occurs when droplets of nematic liquid crystals are dispersed in an isotropic polymeric medium. Determining the shape of the droplet and the equilibrium configuration of the liquid crystals leads to a shape optimization problem that minimizes both the elastic energy inside the droplet and the nematic-isotropic interfacial energy on the surface. I will discuss the existence result and decribe some properties of the free boundary. These results are joint work with Fanghua Lin. Link: https://meeting.tencent.com/s/YMkyFfmyp1ayTecent Meeting ID：173 711 908 Contact: WANG Wei(wangw07@zju.edu.cn)

Speaker: TONG Jiajun, Hedrick Assistant Adjunct Professor，UCLAVenue: Room 314, Ouyangchunmei Buiding, Yuquan CampusAbstract: We study a two-phase tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal cells into the exterior vacuum. Instead of considering evolution of cell densities, our focus will be on the dynamics of two moving interfaces in the model that separate the tumor, the normal tissue, and the exterior vacuum. We will discuss well-posedness results on the interface evolution starting from a nearly radial initial configuration, under an assumption which is in line with the well-known Rayleigh-Taylor condition. We will briefly discuss possible ill-posedness scenarios when these conditions are violated, as well as implications of our results on further analysis of the tumor growth models. This is joint work with Inwon Kim. Tencent meeting ID: 932 901 393 https://meeting.tencent.com/s/UNQTSFVy19bFContact: WANG Wei, wangw07@zju.edu.cn

Speaker: Thomas Szanto, Associate Professor, Department of Communication, University of Copenhagen

Speaker: HUA Zheng, associate professor, The University of Hong KongVenue: Room 200-9, Run Run Shaw Business Administration Building, Yuquan CampusAbstract: Given a semi-simple collection of rational curves on a smooth quasi-projective 3-fold, its multipointed noncommutative deformation is represented by a negatively graded DGA \Gamma. The finite dimensionality of the cohomology of \Gamma seems to relate to contractibility of the collection of rational curves. For CY 3-folds, \Gamma is a bimodule 3CY DG algebra. If we further assume contractibility then H^0\Gamma is isomorphic to the contraction algebra of Donovan and Wemyss. And the cluster category of \Gamma is dg-equivalent to the singularity category of the contracted space. In some sense the CY algebra \Gamma links the deformation theory of the exceptional fibres and the singularity theory of the contracted space. In this talk I will present a joint work with Bernhard Keller, where we prove that the derived Morita type of the contraction algebra together with a canonical class in its 0-th Hochschild homology defined via CY structure determines the analytic type of the singularity of the contracted space.Contact: yufei@zju.edu.cn

Speaker: LUO Li, Associate Professor, School of Mathematical Sciences, East China Normal UniversityVenue: Lecture hall, first floor, Institute for Advanced Mathematics, Zijingang CampusAbstract:As generalizations of quantum groups, the i-quantum groups have recently drawn considerable attention because of its application in Kazhdan-Lusztig theory due to Bao and Wang. In this talk, we will introduce some developments on the study of i-quantum groups. Precisely, we will establish the geometric Schur-Weyl duality and Howe duality for i-quantum groups, and give the Beilinson-Lusztig-MacPherson realization for i-quantum groups and their canonical basis. The talk is based on a series of joint work with WANG Weiqiang, FAN Zhaobin, LI Yiqiang, LAI Junru, CUI Weideng.

Speaker: Dr. YIN ZhenyuTencent meeting: 283 554 834Abstract:This work deals with the response of caisson foundations in sand for offshore wind turbines submitted to combined monotonic and cyclic loadings. First, the failure process and failure envelope (or bearing capacity diagram) of a caisson foundation in sand under combined monotonic loadings is numerically investigated. A Combined Lagrangian-Smoothed Particle Hydrodynamics (CLSPH) method is adopted to consider large deformation. A recently developed critical state model for sand (SIMSAND) is then introduced and combined with the CLSPH method. Different parameters affecting the shape and size of the failure envelope are considered, such as soil density and stiffness, friction strength, grain breakage, geometry and aspect ratio of the foundation. An analytical formula is introduced to describe the 3D failure surface reproducing the numerical results. Based on the proposed analytical formula, a macro-element for the caisson foundation in sand submitted to monotonic and cyclic loadings is finally developed within the framework of hypoplasticity. Validation is provided through comparison with experimental results.