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.

Speaker: Prof. CHEN Yifei, Associate Research Fellow, Academy of Mathematics and Systems Science, Chinese Academy of SciencesVenue: Lecture Hall, Institute of Advanced Mathematics, No.7 East Teaching Building, Zijingang CampusAbstract:Singularities play an important role in the Minimal Model Program (MMP), which aims to birationally classify algebraic varieties. In this talk, I will introduce main conjectures of singularities in MMP, as well as some recent progress in the direction, including a joint work with Caucher Birkar for Shokurov's Conjecture.

Speaker: Dr. XU Qing, Financial Policy Expert of Sustainable Development Goals, United Nations Development Agency in ChinaScan the QR code to join the online meeting on Dingtalk.

Speaker: Prof. WU Hao, YAU Mathematical Sciences Center, Tsinghua UniversityVenue: Room 200-9, Run Run Shaw Business Administration Building, Yuquan CampusAbstract:Two-dimensional Gaussian free field (GFF) is a natural 2D time analogue of Brownian motion. It is also known as free bosonic field in physics literatures, and it is the building block in conformal field theory, quantum gravity and statistical physics. In this talk, we focus on estimates of crossing probability in GFF. Such crossing probability is a delicate quantity for GFF. We will introduce discrete GFF (dGFF) and metric graph GFF (mGFF). Both objects converge to continuum GFF as distributions. However, the crossing probabilities in dGFF and in mGFF are distinct. To derive the scaling limits of crossing probabilities in dGFF and in mGFF, we will introduce Schramm Loewner evolution (SLE). It turns out that the crossing probability in dGFF converges to the so-called pure partition functions of multiple SLEs, and that the crossing probability in mGFF converges to the "fusion" of pure partition functions.  This talk is based on joint works with J. Ding (UPenn), M. Wirth (UPenn), and with M. Liu (Tsinghua).  Contact Person: Su Zhonggen（suzhonggen@zju.edu.cn, Tel：0571-87953676）