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Speaker: Shibing Chen (University of Science and Technology of China) Abstract: In this talk, I will discuss the optimal partial transport problem, in which free boundaries arise. The problem was first investigated by Caffarelli and McCann [Annals 2010], where they established the interior C^{1,\alpha} regularity of the free boundary but left open the higher-order regularity …

SIMIS Seminar on Geometric Analysis and PDEs: Free boundaries in optimal transportation Read More »

报告人：张磊（中国科学技术大学） 摘要：我们将首先讨论代数几何中的一些正性的概念，从分析和代数两个角度，然后介绍典范层的正向层的一些正性结论以及证明思想，然后介绍这些结论在代数簇分类中的一些应用。 时间: 2024-05-11, 周六 15:00 地点: 上海市杨浦区伟成路62号创智天地企业中心3号楼6层 Zoom Meeting No.: 423 317 8953Password: SIMIS 组织者: 胡森

Speaker：韦勇（中国科学技术大学） Abstract：The locally constrained inverse curvature flow in space forms was introduced by Brendle, Guan and Li and is a powerful tool to prove the Alexandrov-Fenchel inequalities. In the first part of the talk, we show that h-convexity is preserved by Brendle-Guan-Li’s flow in hyperbolic space and as applications we prove some optimal geometric inequalities …

Locally constrained inverse curvature flows and applications Read More »

4月29日至5月3日，在清华三亚国际数学论坛（TSIMF）举行了“逻辑、认知与数学哲学”交叉学科研讨会。此次研讨会由清华大学逻辑学研究中心与上海数学与交叉科学研究院（SIMIS）联合主办，旨在聚集逻辑、哲学、数学和认知科学领域的专家学者，共同探讨学科交叉的前沿话题。 研讨会历时三天，每天上午举行专题报告，下午则分组进行针对性讨论。会议涉及模态逻辑、数学哲学以及逻辑与认知科学、博弈论、图论、域理论等领域的交叉。 4月30日上午的议程包括快速会晤环节和两场报告。在快速会晤环节，与会者介绍自己的研究背景和兴趣，为深入的跨学科交流做准备。第一场报告由清华大学哲学系石辰威博士主讲“模态逻辑”，第二场报告由美国得克萨斯大学休斯顿健康科学中心健康数据科学与人工智能系的张国强教授以线上形式主讲“时态组合逻辑”。下午的小组讨论分别是由清华大学金岳霖教授、新西兰奥克兰大学教授谢立民（Jeremy Seligman）主导的“数独解题思路的洞见”、中国政法大学哲学系付小轩博士主导的“偏好逻辑研究”、以及中国科学院哲学研究所和中国科学院大学人文学院副教授李大柱主导的“分体论研究”。 5月1日上午举行了两场报告，上海数学与交叉科学研究院教授、美国密歇根大学安娜堡分校心理学系与统计学系教授张俊主讲“论闭包算子”、闽南师范大学数学与统计学院的孙文博士主讲“论知识空间”。下午的小组讨论分别是由张俊教授主导的“邻域语义学与认知科学”，和由高万霆（Valentin Goranko）与刘奋荣主导的“逻辑、图论与博弈论”。 5月2日上午举行了三场报告，北京雁栖湖应用数学研究院教授吴杰主讲“超图的嵌入同调”、武汉大学哲学学院副研究员谢凯博主讲“论因果推理的逻辑”、华东师范大学软件学院教授陈仪香主讲“稳定域的逻辑进路”。下午的小组讨论主要围绕因果推理、域理论的最新进展、拓扑语义等问题展开。 此次会议邀请来自美国、瑞典、新西兰等国家和地区的专家学者以及国内高校和科研机构的师生近20人参会。与会者充分发挥自己的专业特长，就交叉学科的前沿研究问题展开了热烈而深刻的讨论，有效促进了交叉学科研究的深入发展。 鸣谢：本次研讨会得到了清华三亚国际数学论坛领导及管理团队的大力支持。与会者对负责后勤保障的叶莉女士表示特别感谢。 撰稿人：王威 Announcement: IMIS-TSIMF INTERDISCIPLINARY SERIES: International Workshop on Logic, Cognition, and Philosophy of Mathematics

Speaker: 来米加教授（上海交通大学） Abstract: Hamilton’s pinching conjecture asserts that if a three dimensional manifold satisfies a Ricci pinching condition (, for some small ), then M must be compact unless it is flat. This conjecture was recently proved by Lee and Topping. In this talk, I will first talk about the origin of this conjecture, which is a …

SIMIS Seminar on Geometric Analysis and PDEs: Hamilton’s pinching condition and conformal deformation Read More »

Speaker: Alexander Ochirov (SPST, ShanghaiTech University) Abstract: I will review some recent developments in massive higher-spin theory, namely, Zinoviev’s massive gauge symmetry and the new chiral-field approach. I will discuss the applications of massive higher-spin scattering amplitudes to classical gravitational dynamics of rotating black holes, in particular, the so-called gravitational Compton amplitude. Time: 16:00 ~ …

SIMIS Seminar on Field Theory and String Theory: From massive higher spins to Kerr black holes Read More »

Speaker: Rui-Dong Zhu (Soochow University) Abstract: Various kinds of integrability structures have been found in supersymmetric gauge theories, while we still have limited understanding on the connection among them. In this talk, I will explain an efficient method, called the rational Q-system, to find all the physical solutions to the Bethe ansatz equation in spin …

SIMIS Seminar on Field Theory and String Theory: Bethe/Gauge correspondence, rational Q-system and beyond Read More »

Speaker: Kilar Zhang (Shanghai University) Abstract: The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence offers an efficient analytical approach to calculate the QNM frequencies, which was only available numerically before. This is based on the fact that both sides are characterized by Heun-type equations. We find that a similar duality exists between Seiberg-Witten theory and …

SIMIS Seminar on Field Theory and String Theory: The Applications of String Dualities on Black Hole Superradiance and Neutron Star Equation of States Read More »

Speaker: Lingjie Du (School of Physics Nanjing University, China) Abstract: Gravitons are hypothetical neutral spin-2 bosons[1]. In the fractional quantum Hall (FQH) state at filling factor v = 1/3, a chiral graviton mode is predicted as quantum of metric fluctuations under a new quantum geometry description [2,3,4], which could be described by the corresponding Fierz-Pauli …

SIMIS Seminar on Field Theory and String Theory: Chiral graviton modes in quantum Hall liquids Read More »

Speaker: Professor Mikhail Khovanov (Columbia University) Abstract: We recall how the Jones polynomial of links lifts to a link homology theory which is functorial under link cobordisms in 4-space. Extending this homology theory to tangles relates the theory to a variety of categories in representation theory and geometry. Another extension, to a categorification of the …

SIMIS-Fudan Colloquium: Link homology theories and their ramifications Read More »