| Titel Title: | 黎曼流形上的拟线性偏微分方程研究 |
|---|---|
| Sprecher Speaker: | 孙林林 教授 |
| Zugehörigkeit Affiliation: | 湘潭大学 |
| Datum und Uhrzeit Datetime: | 2026-04-24 10:00 -- 2026-04-24 11:00 |
| Veranstaltungsort Venue: | 数学大楼814 |
| Host Host: | 艾万君 |
| Abstract Abstract: | 本报告将系统介绍黎曼流形上若干重要拟线性偏微分方程的刘维尔型定理研究成果。这些方程与流形的几何结构和分析性质具有深刻的内在联系。报告内容主要基于报告人近期与王友德教授、贺杰博士的合作研究工作。 |
| Persönliches Profil Personal Profile: | 孙林林，湘潭大学数学与计算科学学院教授、博士生导师，武汉大学与德国莱比锡马普所联合培养博士，入选湖北省"楚天学者计划"。2015年获武汉大学博士学位，2015-2017年在中国科学技术大学从事博士后研究，2017-2021年任武汉大学特聘副研究员，2019-2020年在德国莱比锡马克思·普朗克应用数学研究所访问。主要从事微分几何与几何分析研究，研究方向包括几何流、子流形的几何与拓扑等，在《J. Eur. Math. Soc.》、《Adv. Math.》、《Ann. Inst. H. Poincaré Anal. Non Linéaire》、《J. Funct. Anal.》、《J. Differential Equations》、《Calc. Var. Partial Differential Equations》等国际权威期刊发表论文20余篇，主持国家自然科学基金项目两项。 |
Geometry and Analysis Colloquium
Bevorstehender Zeitplan
Vergangener Zeitplan
-
32 -
31 Titel Title: On the Rate of Convergence of Cylindrical Singularity in Mean Curvature Flow Sprecher Speaker: 赵新锐 Zugehörigkeit Affiliation: 耶鲁大学 Datum und Uhrzeit Datetime: 2026-03-04 09:00 -- 2026-03-04 10:00 Veranstaltungsort Venue: online（Zoom）会议号：825 3248 0199 密码：931144 Host Host: Geometry and Analysis Colloquium Abstract Abstract: We prove that if a rescaled mean curvature flow is a global graph over the round cylinder with small gradient and converges at a super-exponential rate, then it must coincide with the cylinder itself. We also show that this result is sharp by constructing local graphical counterexamples with arbitrarily fast super-exponential convergence and rapidly expanding domains. These examples form infinite-dimensional families of Tikhonov-type solutions and show that unique continuation fails for local graphical solutions. Our constructions apply to a broad class of nonlinear equations. This talk is based on joint work with Yigi Huang. Persönliches Profil Personal Profile: Xinrui Zhao is a Gibbs Assistant Professor in the Department of Mathematics at Yale University. He received his Ph.D. from MIT, where he was supervised by Prof. Tobias Colding. His research interests lie in geometric analysis, including mean curvature flow and RCD spaces. -
30 Titel Title: Index and total curvature of minimal surfaces in noncompact symmetric spaces and wild harmonic bundles Sprecher Speaker: 李琼玲 Zugehörigkeit Affiliation: 陈省身数学研究所 Datum und Uhrzeit Datetime: 2024-11-22 15:30 -- 2024-11-22 16:30 Veranstaltungsort Venue: 数学大楼814报告厅 Host Host: 艾万君 Abstract Abstract: We prove two main theorems about equivariant minimal surfaces in arbitrary non-positively curved symmetric spaces extending classical results on minimal surfaces in Euclidean space. First, we show that a complete equivariant branched immersed minimal surface in a non-positively curved symmetric space of finite total curvature must be of finite Morse index. It is a generalization of the theorem by Fischer-Colbrie, Gulliver-Lawson, and Nayatani for complete minimal surfaces in Euclidean space. Secondly, we show that a complete equivariant minimal surface in a non-positively curved symmetric space is of finite total curvature if and only if it arises from a wild harmonic bundle over a compact Riemann surface with finite punctures. Moreover, we deduce the Jorge-Meeks type formula of the total curvature and show it is an integer multiple of for only depending on the symmetric space. It is a generalization of the theorem by Chern-Osserman for complete minimal surfaces in Euclidean n-space. This is joint work with Takuro Mochizuki (RIMS). Persönliches Profil Personal Profile: 李琼玲博士，南开大学陈省身数学研究所的特聘研究员，拥有美国莱斯大学授予的博士学位。她的学术生涯起步于美国数学科学研究所（MSRI），担任Cha-Chern博士后。此后，李博士在美国加州理工学院和丹麦奥胡斯大学的QGM研究所继续她的博士后研究工作。自2019年起，李博士回到南开大学陈省身数学研究所，致力于数学研究。她的研究兴趣集中在高维Teichmüller理论（Higher Teichmüller theory）、Higgs丛（Higgs bundles）以及调和映射（Harmonic maps）等领域。其相关文章发表在GAFA (Geom. Funct. Anal.)、Proc-LMS (Proc. Lond. Math. Soc.)、JDG (J. Differential Geom.)、Math. Ann.、Adv. Math.、CMP (Comm. Math. Phys.)等国际顶尖期刊上。她曾入选国家海外高层次人才计划青年项目、国家重点研发计划青年科学家项目，并荣获德国洪堡资深学者项目的支持。 -
29 Titel Title: Holomorphic curves in Kähler surface Sprecher Speaker: 孙俊 Zugehörigkeit Affiliation: 武汉大学 Datum und Uhrzeit Datetime: 2024-11-10 10:00 -- 2024-11-10 11:00 Veranstaltungsort Venue: 数学大楼814报告厅 Host Host: 艾万君 Abstract Abstract: In this talk, we will introduce two ideas approaching to the existence of holomorphic curves in Kähler surface from geometric analysis viewpoint. The first one is the symplectic mean curvature flow. We will talk about singularity analysis for the flow. The second one is variational method. We will introduce a new family of functionals and study the properties of the critical points of the new functionals as well as the gradient flows. This talk is based on joint work with Xiaoli Han and Jiayu Li. Persönliches Profil Personal Profile: 孙俊，武汉大学数学与统计学院副教授，博士生导师。主要研究方向是几何分析，在Crelle’s Journal，Math Ann.，Calc Var. PDE，IMRN，Adv. Math.，Ann. Inst. H. Poincare Anal. Non Lineaire等数学重要期刊发表论文三十多篇，主持与参与多项国家自然科学基金和湖北省基金。 -
28 Titel Title: Stability of the area preserving mean curvature flow Sprecher Speaker: 李玉巧 Zugehörigkeit Affiliation: 合肥工业大学 Datum und Uhrzeit Datetime: 2024-10-30 15:00 -- 2024-10-30 16:00 Veranstaltungsort Venue: 数学大楼 814 报告厅 Host Host: 艾万君 Abstract Abstract: In this talk, we consider the long-time existence and convergence of the area preserving mean curvature flow of hypersurfaces in space forms under some initial integral pinching conditions. More precisely, we prove that the flow exists for all time and converges exponentially fast to a totally umbilical sphere if the integral of the traceless second fundamental form is sufficiently small. Moreover, we show that starting from a sufficiently large coordinate sphere, the area preserving mean curvature flow exists for all time and converges exponentially to a constant mean curvature surface in asymptotically Schwarzschild spaces. This work is joint with Dr. Yaoting Gui and Pf. Jun Sun. Persönliches Profil Personal Profile: 李玉巧博士，现任职于合肥工业大学数学学院，专攻微分几何领域。她在中国科学技术大学完成了她的最高学历，并在数学领域有着深厚的学术背景。李博士不仅在学术研究上有所建树，还积极参与学术交流，曾在中国科学院数学与系统科学研究院举办的研讨会上发表题为“正质量定理与里奇流”的演讲，详细介绍了正质量定理及其相关问题，特别是里奇流方法的讨论，并分享了她在正质量定理的正则性方面的工作和一些先前的研究结果。相关论文发表在 Ann. Henri Poincaré、J. Math. Phys.、Chinese Ann. Math. Ser. B 等国际一流杂志上。 李玉巧博士的研究成果体现了她在数学领域的专业能力和对学术研究的热情。她的工作不仅推动了微分几何学的发展，也为相关领域的研究提供了宝贵的参考。在教学方面，李博士也致力于培养新一代的数学人才，为学生提供了丰富的知识和启发性的指导。 -
27 Titel Title: Recent progress on the Volume Coniectures for various quantum invariants Sprecher Speaker: Tian Yang Zugehörigkeit Affiliation: Texas A&M University Datum und Uhrzeit Datetime: 2024-07-26 16:00 -- 2024-07-26 17:00 Veranstaltungsort Venue: Room 77201, Jingchunyuan 78, BICMR Host Host: Yiyi Ye Abstract Abstract: In this presentation, I will revisit the volume conjectures associated with various 3-manifold invariants derived from topological quantum field theories (TOFTs). This includes a discussion on the colored Jones polynomials as introduced by Kashaev and Murakami, the Reshetikhin-Turaev invariants, and the Turaev-Viro invariants, which were further developed by Chen and Yang. Additionally, I will introduce recent advancements in this field and explore their implications. Persönliches Profil Personal Profile: **Biography:** Tian Yang is an Assistant Professor in the Department of Mathematics at Texas A&M University. His research delves into the intricate connections between quantum topology, hyperbolic geometry, and knot theory. With a robust academic background, Yang has made significant contributions to the field, as evidenced by his publications in prestigious journals such as Advances in Mathematics, Journal of Topology, Communications in Mathematical Physics, Journal of Differential Geometry, and Quantum Topology. These outlets are testament to his expertise and the impact of his work in the mathematical community. -
26 Titel Title: Complex Spaces, Reflections and the Cyclotomic Hecke Algebras Sprecher Speaker: Mengfan Lyu Zugehörigkeit Affiliation: University of Western Sydney, Australia Datum und Uhrzeit Datetime: 2024-07-08 15:00 -- 2024-07-08 16:00 Veranstaltungsort Venue: Room 78301, Jingchunyuan 78, BICMR Host Host: Wenqiong Li Abstract Abstract: In this talk I will start with the fascinating realms of complex spaces and complex reflection groups. Complex spaces provide a rich playground for investigating symmetries and structures that arise from complex reflections. I will explore the fundamental concepts of complex reflection groups, examining their geometric and algebraic properties. Moreover, I will also introduce the cyclotomic Hecke algebras, which emerge as powerful tools for understanding the symmetries inherent in complex reflection groups. These algebras encode combinatorial and algebraic information about the reflection groups, offering deep insights into their representation theory and geometric properties. Persönliches Profil Personal Profile: -
25 Titel Title: The Minkowski type problems for log-concave functions Sprecher Speaker: 叶德平 Zugehörigkeit Affiliation: Memorial University of Newfoundland Datum und Uhrzeit Datetime: 2024-07-05 10:00 -- 2024-07-05 11:30 Veranstaltungsort Venue: 数学大楼912报告厅 Host Host: 艾万君 Abstract Abstract: There is a great demand for the geometric theory of log-concave functions, due to the facts that the family of log-concave functions resemble those of convex bodies and the Brunn-Minkowski theory of convex bodies has provided rich fundamental results in applications. A major job is to translate the terminologies and notions from convex bodies to their counterparts for log-concave functions. Among the most important are the Minkowski problems, which aim to characterize the geometric measures derived from various variational formulas of functionals on the set of convex bodies. In this talk, I will discuss our recent works on Minkowski type problems for log-concave functions, which can be viewed as functional lifting of related Minkowski type problems for convex bodies. Persönliches Profil Personal Profile: 叶德平教授，2000年本科毕业于山东大学，2000-2003年于浙江大学读研， 2009年博士毕业于美国Case Western Reserve University，现为加拿大纪念大学终身教授，并主持加拿大国家自然科学基金(NSERC) 项目。现任加拿大数学会旗舰杂志Canadian Journal of Mathematics 和 Canadian Mathematical Bulletin的副主编(Associate Editor)， 并于2017年获得JMAA Ames奖。 长期从事凸几何分析，几何和泛函不等式， 随机矩阵，量子信息理论， 和统计学等领域的研究。 已在 Comm. Pure Appl. Math.，Adv. Math., J. Funct. Anal., Math. Ann., CVPDE等国际著名杂志（数学类， 数学物理类，和统计类） 上发表论文40篇。 -
24 Titel Title: 复旦2024 算术几何研讨会 Sprecher Speaker: 曹 阳（山东大学） 扶 磊（清华大学） 刘若川（北京大学） 刘一峰（浙江大学） 欧阳毅（中国科学技术大学） 秦厚荣（南京大学） 申 旭（中国科学院数学与系统科学研究院） 田一超（中国科学院数学与系统科学研究院） 肖 梁（北京大学） 许 宾（四川大学） 徐 飞（首都师范大学） 赵 斌（首都师范大学） 朱艺航（清华大学） Zugehörigkeit Affiliation: Datum und Uhrzeit Datetime: 2024-06-14 08:30 -- 2024-06-16 12:15 Veranstaltungsort Venue: TBA Host Host: 陈猛、陈苗芬、李志远、任汝飞、王海宁、吴泉水 Abstract Abstract: 报告人：曹阳 题目：Rational points on Rost’s norm varieties 摘要： In motivic cohomology theory, Rost’s norm varieties are used to construct a weak version of splitting varieties for cohomological elements. I will talk about its rational points over number fields and some other fields. 报告人：扶磊 题目：An effective version of Deligne's equi-distribution theorem 摘要：In his work on the Weil conjecture, Deligne deduces an equi-distribution theorem for the images of Frobenii in the space of conjugacy classes of the monodromy group for a pure lisse sheaf. Using the Weyl integration formula, the Weyl character formula and tools from harmonic analysis, we prove an effective version of Deligne's equidistribution theorem. This is a joint work with Wen-Ching Li, Yuk-Kam Lau and Ping Xi. 报告人：刘一峰 题目：An Iwasawa bipartite Euler system for Rankin-Selberg motives 摘要： We construct a bipartite Euler system for hermitian Rankin-Selberg motives over the Iwasawa algebra, and explain its consequences in the anticyclotomic Iwasawa main conjecture for those motives. This is a joint work with Yichao Tian and Liang Xiao. 报告人：刘若川 题目：Towards a p-adic analogue of λ-connections 摘要：The notion of flat λ-connections was originally suggested by Deligne as the interpolation of usual flat connections and Higgs fields. In an ongoing joint work with Zekun Chen, Yupeng Wang and Xinwen Zhu, we are extending this theory to a p-adic context. Precisely, for a smooth rigid analytic variety X over a p-adic local field with good reduction, we define a functor from the small p-adic etale local systems over X to integrable connections over the base change of X to the Robba ring. This functor is expected to interpolate the p-adic Simpson and p-adic Riemann-Hilbert functors developed by Xinwen Zhu and myself. Additionally, we will explore some potential applications of this theory. 报告人：欧阳毅 题目：Isogeny-based cryptosystems and structure of isogeny graphs 摘要： Supersingular elliptic curve Isogeny-based cryptography is one route for post-quantum cryptography. In this talk, we shall explain the mathematical problems on isogeny computation and the cryptosystems based on those problems. We’ll then focus on the study of the isogeny graphs of supersingular elliptic curves and of superspecial abelian surfaces. We will explain several results about the local structure of these graphs. This is based on joint works with Zheng Xu, Songsong Li and Zijian Zhou. 报告人：秦厚荣 题目：The Lang-Trotter Conjecture for CM elliptic curves 摘要： Let 𝐸 be a CM elliptic curve defined over ℚ and 𝑟 a fixed integer. For a prime 𝑝, let 𝑎𝑝 be the Frobenius trace of 𝐸 at 𝑝. Define 𝜋𝐸,𝑟(𝑛)=♯{𝑝≤𝑛∣𝑎𝑝=𝑟}. The Lang-Trotter predicts that 𝜋𝐸,𝑟(𝑛)∼𝑐𝐸,𝑟𝑛√/log(𝑛), where 𝑐𝐸,𝑟 is a constant defined by using information from the Galois representation of 𝐸. We explain how to compute the Lang-Trotter constant 𝑐𝐸,𝑟 and show that the Hardy-Littlewood conjecture implies the Lang-Trotter conjecture. 报告人：申旭 题目：Bruhat-Tits buildings and p-adic period domains 摘要： Bruhat-Tits buildings are key tools to study the structure and representations of reductive groups over non-archimedean local fields. In 2010, Rémy-Thuillier-Werner constructed embeddings of BT buildings into the Berkovich spaces associated to suitable flag varieties (generalizing the work of Berkovich for split groups), and defined compactifications of BT buildings by taking closure inside these Berkovich flag varieties. We show that, in the setting of a local Shimura datum, the RTW embedding factors through the associated p-adic period domain (as a Berkovich space, defined using Fargues-Fontaine curve, which is still mysterious beyond the fully Hodge-Newton decomposable case). This brings the question to compare these two p-adic candidates of symmetric spaces: topological and combinatorial vs p-adic analytic. We will compare the boundaries of the BT buildings and non basic Newton strata. Moreover, we will discuss some applications to cohomology and smooth representations. This is joint work in progress with Ruishen Zhao. 报告人：田一超 题目：Level raising on unitary Shimura varieties of even rank 摘要： In this talk, I will explain an analogue of Ribet’s level raising on the Shimura varieties attached to a unitary group of even rank. The proof is based on a detailed study of the nearby cycle sheaf of some etale local system on the unitary Shimura variety. The whole result is one of the key geometric ingredients on my recent joint work with Yifeng Liu and Liang Xiao on the anti-cyclotomic Iwasawa main conjecture for Rankin--Selberg motives. 报告人：许宾 题目：Gamma factors for representations of finite groups of Lie type 摘要： Gamma factor is an important invariant in the representation theory of p-adic groups, and it also has a finite field analog. In the first part of this talk, we will recall the Gamma factors associated to tensor product representations of general linear groups over finite fields, as well as its relation to some arithmetic objects such as Gauss sums and Kloosterman sums. Then we will introduce an approach to study the Gamma factors associated to the representations of classical groups twisted by general groups over finite fields in a special case. 报告人：徐飞 题目：Integral Springer theorem for quadratic bundles over affine curves under base change of odd degree 摘要： The classical Springer theorem says that a quadratic form f is represented by another g over a field k if and only if f is represented by g over a finite extension of odd degree. Arithmetic version of this result has been established for indefinite integral quadratic forms over number fields. In this talk, we will extend this result over general Dedekind domains. This is a joint work with Yong Hu and Jing Liu. 报告人：赵斌 题目： Refined spectral halo for eigencurves 摘要： Coleman-Mazur-Buzzard-Kilford conjecture predicted that over the boundary of the weight space, the eigencurve is a disjoint union of rigid analytic spaces which are finite flat over the weight space. This conjecture has been proved by the work of Liu-Wan-Xiao and Diao-Yao. In this talk, I will explain a joint work in progress with Yongquan Hu and Liang Xiao on a refinement of this conjecture and how it can be used to determine the p-adic slopes of all the crystabelline lifts of a reducible (local) mod p Galois representation. The new ingredient is a universal principal series type theory that interpolates classical principal series types. 报告人：朱艺航 题目： Zeta Functions of Shimura Varieties: Past, Present, and the Near Future 摘要： I will first recall the general expectations of Shimura, Langlands, and Kottwtiz on the shape of the zeta function of a Shimura variety, or more generally its étale cohomology. I will then report on some recent progress which partially fulfills these expectations, for Shimura varieties of unitary groups and special orthogonal groups. Finally, I will give a preview of some foreseeable developments in the near future. Persönliches Profil Personal Profile: -
23 Titel Title: The Loewner-Nirenberg Problem in Cones Sprecher Speaker: 韩青 Zugehörigkeit Affiliation: 美国圣母大学 Datum und Uhrzeit Datetime: 2024-06-07 10:30 -- 2024-06-07 11:30 Veranstaltungsort Venue: 数学大楼912报告厅 Host Host: 唐春雷 Abstract Abstract: Loewner and Nirenberg discussed complete metrics conformal to the Euclidean metric and with a constant scalar curvature in bounded domains in the Euclidean space. The conformal factors blow up on boundary. The asymptotic behaviors of the conformal factors near boundary are known in $C^2$-domains. In this talk, we discuss asymptotic behaviors near vertices of cones. We will prove that solutions on finite cones are well-approximated by the solution in the corresponding infinite cone. To derive optimal estimates, we need to study a class of elliptic operators over spherical domains. These operators are singular on boundary. We will study the eigenvalue problem with the homogeneous Dirichlet boundary value and investigate boundary behaviors of the eigenfunctions. Persönliches Profil Personal Profile: 韩青，美国圣母大学数学系终身教授。美国纽约大学库朗数学研究所博士，美国芝加哥大学博士后。获美国Sloan Research Fellowship. 韩青教授长期致力于非线性偏微分方程和几何分析的研究，在等距嵌入、Monge-Ampere方程、调和函数的零点集和奇异集、退化方程等方面做出了一系列原创性的重要研究成果。 -
22 Titel Title: Recent progress on the Type IIA flow Sprecher Speaker: 张享文 Zugehörigkeit Affiliation: University of California, Irvine Datum und Uhrzeit Datetime: 2024-06-03 14:00 -- 2024-06-03 15:00 Veranstaltungsort Venue: Room 106, SCMS Host Host: TBA Abstract Abstract: Geometric flows have been proven to be powerful tools in the study of many important problems arising from both geometry and theoretical physics. In this talk, we will discuss the progress on the so- called Type IIA flows, introduced in a joint work with Fei, Phong and Picard, aiming to study the Type IIA equations from the flux compactifications of superstrings. Persönliches Profil Personal Profile: -
21 Titel Title: Regularity theory of biharmoinc mappings and unsolved problems Sprecher Speaker: 向长林 Zugehörigkeit Affiliation: 三峡大学/三峡数学研究中心 Datum und Uhrzeit Datetime: 2024-05-31 09:30 -- 2024-05-31 11:30 Veranstaltungsort Venue: 数学大楼912 Host Host: 艾万君 Abstract Abstract: This talk is to report the regularity theory of biharmonic mappings, including those different approaches developed by several famous mathematicians. In particular, I will discuss the quantitative differentiation approach developed by J. Cheeger, A. Nabor and their collaborators in the recent ten years. This new approach can be efficiently attack the singular set of many geometric mappings and also their flow (such as harmonic mapping flow, mean curvature flow, Ricci flow). As a consequence the global regularity of those geometric objects are obtained. Persönliches Profil Personal Profile: 向长林，2015年博士毕业于芬兰于韦斯屈莱大学，现为峡大学三峡数学研究中心特聘教授。目前主要研究几何型偏微分方程组正则性与奇点集理论及其在几何映照理论中的应用。研究主要成果发表在 Trans. Amer. Math. Soc., Calc.Var. Partial Differential Equations, Int.Math. Res. Not.,J.Differential Equations, J. Lond. Math. Soc.等国际知名数学期刊上。主持国家自然科学基金青年项目一项。 -
20 Titel Title: 二聚体模型会变分法 Sprecher Speaker: 钟晓 Zugehörigkeit Affiliation: 赫尔辛基大学(芬兰) Datum und Uhrzeit Datetime: 2024-05-10 10:00 -- 2024-05-10 11:00 Veranstaltungsort Venue: Tencent: 596-402-870 Host Host: 袁显宝(三峡大学理学院院长) Abstract Abstract: TBA Persönliches Profil Personal Profile: 钟晓，芬兰科学与人文院院士，赫尔辛基大学数学与统计系教授，曾任教育部长江学者讲座教授。本科毕业于中国科技大学，在中科院武汉数学物理研究所获得硕士学位，1998年博士毕业于芬兰于韦斯屈莱大学，师从芬兰著名数学家Tero Kilpelǎinen，2009年-2016年任芬兰于韦斯屈莱大学教授。因卓越学术成就，于2011年获得芬兰科学与人文学院的Vaisala奖(芬兰最有影响力的数学物理方向奖励)。 钟晓老师的主要研究方向是偏微分方程和几何函数论。在偏微分方程解的正则性方面取得突出成绩，独立解决DeGiorgi提出的多个退化椭圆方程解的连续性公开猜测。在度量空间上的分析领域，与合作者证明Poincare不等式的开端点性质，成果发表在国际顶顶尖期刊《Annals of Mathematics》上，为度量测度空间上的一阶微积分提供了公理性基础。近期，与合作者在二聚体理论研究上做出了突破性贡献。 -
19 Titel Title: Tian’s Stabilization Problem - Algebraic Meets Complex & Convex Geometry Sprecher Speaker: Yanir A. Rubinstein Zugehörigkeit Affiliation: University of Maryland Datum und Uhrzeit Datetime: 2024-05-08 09:00 -- 2024-05-08 10:00 Veranstaltungsort Venue: Zoom: 817-5226-6172 | 303016 Host Host: Chu JianChun Abstract Abstract: Coercivity thresholds are a central theme in geometry. They appear classically in the Yamabe problem (constant scalar curvature in a conformal class), in the Nirenberg problem (prescribed curvature on the 2-sphere), and in numerous problems on determining best constants in Sobolev embeddings and related functionals inequalities. In 1980's Aubin and Tian introduced the first such thresholds in the Kahler-Einstein problem and their study has been a central and still very active field. In 1988 Tian observed that these thresholds have quantum versions and he posed the so-called Stabilization Problem: do the equivariant quantum thresholds become constant (and hence equal to the classical thresholds)? Cheltsov conjectured that these invariants coincide with the algbero-geometric log canonical thresholds (lct), and this was verified by Demailly (2008). The best result so far has been Birkar's theorem (2019) that shows that the quantum lcts are constant along a subsequence in the absence of group actions. In joint work with Chenzi Jin (PhD student at UMD) we offer a new approach and solve Tian's problem in the toric case. Surprisingly, the equivariant lcts are constant already from the first quantum level. For more general Grassmannian lcts we offer counterexamples to stabilization and determine when it holds. The key new ideas are understanding the effect of finite group actions on these invariants, and relating these thresholds to support and gauge functions from convex geometry. Time permitting I will discuss extensions and generalizations to other invariants, e.g., the Fujita-Odaka stability thresholds. Persönliches Profil Personal Profile: Rubinstein received his doctorate from M.I.T. in 2008. He then held positions at Johns Hopkins University and Stanford University before accepting a tenured position at the University of Maryland in 2012 where he has been since. His research has spanned problems originating from geometric analysis, algebraic geometry, microlocal analysis, complex and convex analysis, and numerical analysis. He has led initiatives for the development and expansion of Research Experiences for Undergraduates (REUs) and has edited a volume on ``Directions for Mathematics REUs" in 2016. In 2023 he received the University of Maryland Grand Challenges award and in 2024 the Do Good award for increasing the participation of underrepresented minorities and women in STEM. He is a Sloan Fellow (2013) and a Simons Fellow (2024). -
18 Titel Title: Regularity of Viscosity Solutions of the $\sigma_k$-Loewner-Nirenberg Problem Sprecher Speaker: 熊金钢 Zugehörigkeit Affiliation: 北京师范大学 Datum und Uhrzeit Datetime: 2024-01-19 15:30 -- 2024-01-19 17:30 Veranstaltungsort Venue: Tencent: 524-811-965 Host Host: 李刚 Abstract Abstract: I will talk about a joint work with Yanyan Li and Luc Nguyen about the regularity of viscosity solutions to the $\sigma_k$-Loewner-Nirenberg problem in bounded domains, $k\ge2$. When the domains' boundaries have more than one connected components, we show that viscosity solutions are not $C^1$. However, the Lipschitz regularity was known. On the other hand, we establish smoothness of the viscosity solutions near the boundaries. Persönliches Profil Personal Profile: 熊金钢，北京师范大学教授、博导。研究领域为非线性分析——变分法、椭圆与抛物型偏微分方程，解决Berryman和Holland 1980年提出的快速扩散方程正则性猜想，被菲尔茨奖得主论文评价称“ingenious”&“remarkable”; 解决Monge-Ampère方程、Yamabe方程以及奇异调和映照中的若干长期未解的奇点结构问题; 开启非局部Nirenberg问题等临界非线性问题的研究。迄今在国际期刊 Amer. J. Math., J. Eur. Math. Soc., J. Reine Angew. Math.，Proc. London Math. Soc. 等发表论文近 40 篇，获国家优秀青年科学基金和国家杰出青年科学基金资助。 -
17 Titel Title: The $\sigma_2$-Curvature Equation on a Compact Manifold with Boundary Sprecher Speaker: Wei Wei Zugehörigkeit Affiliation: Nanjing University Datum und Uhrzeit Datetime: 2023-12-13 09:00 -- 2023-12-13 10:00 Veranstaltungsort Venue: Zoom: 878 0965 2245 | 837865 Host Host: 北京大学数学学院 Abstract Abstract: We first establish local $C^2$ estimates of solutions to the $\sigma_2$-curvature equation with nonlinear Neumann boundary condition. Then, under assumption that the background metric has nonnegative mean curvature on totally nonumbilic boundary, for dimensions three and four we prove the existence of a conformal metric with a prescribed positive $\sigma_2$-curvature and a prescribed nonnegative boundary mean curvature. The local estimates play an important role in the blow up analysis in the latter existence result. This is a joint work with Xuezhang Chen. Persönliches Profil Personal Profile: Wei Wei is currently an assistant professor at Nanjing University. She obtained her Ph.D. at University of Science and Technology of China in 2019 under the supervision of Professor Xian Ma. Her research focuses on fully nonlinear elliptic equations and geometric analysis. -
16 Titel Title: Boundary behaviors of solution to elliptic equations and their applications on some Minkowski problems Sprecher Speaker: 陈正茂 Zugehörigkeit Affiliation: 广西师范大学 Datum und Uhrzeit Datetime: 2023-12-12 10:00 -- 2023-12-12 11:00 Veranstaltungsort Venue: Tencent: 828-817-524 Host Host: 向长林 Abstract Abstract: In this talk, we will introduce some Minkowski type problems associated to Potential Theory and discuss the a priori bounds, existence, uniqueness and regularity to these problems mentioned above. The core elements are boundary behaviors of gradient of solution to some elliptic equations, such as the BMO regularity and VMO regularity. Persönliches Profil Personal Profile: 陈正茂，博士。广西师范大学专任教师。主要从事位势理论及其应用的研究。 -
15 Titel Title: On the classification of entire solutions to the critical p-Laplace equation Sprecher Speaker: 欧乾忠 Zugehörigkeit Affiliation: 广西师范大学 Datum und Uhrzeit Datetime: 2023-12-12 08:30 -- 2023-12-12 09:30 Veranstaltungsort Venue: Tencent: 828-817-524 Host Host: 向长林 Abstract Abstract: In this talk, we will focus on the classification of positive entire solutions to the critical $p$-Laplace equation. Note that for the subcritical case, the equations have no positive solutions by the well known works of Gidas-Spruck [CPAM1981] and Serrin-Zou[ACTA2002]. While for the critical case, there are nontrivial 2-parameters family of solutions and which are classified by Caffarelli-Gidas-Spruck [CPAM1989] for $p=2$ and by J. Vetois [JDE2016] (for $1<p<2$) . Then by exploiting the method of integral estimate we obtain the same classification results for $(n+1)/3<p<n$ . Persönliches Profil Personal Profile: 欧乾忠，广西师范大学数学与统计学院教授。2008年于华东师范大学获得博士学位，之后曾到中国科学技术大学、香港中文大学等访问研究。主要研究领域为椭圆偏微分方程及其几何应用，椭圆偏微分解的凸性与刘维尔定理方面取得了一系列研究成果。学术论文发表在CPAM，TAMS，Adv.Math.，JGA等学术期刊。主持国家自然科学基金地区科学基金2项、国家自然科学基金重点专项项目子课题1项。 -
14 Titel Title: Weak compactness of nematic liquid flows in dimension two Sprecher Speaker: 黄涛 Zugehörigkeit Affiliation: 美国韦恩州立大学 Datum und Uhrzeit Datetime: 2023-11-17 08:30 -- 2023-11-17 11:30 Veranstaltungsort Venue: Tencent: 779-526-012 Host Host: 湖北省数学与交叉学科创新引智基地三峡数学研究中心 Abstract Abstract: For any bounded smooth domain in dimension two，we established the convergence of weak solutions of the Ginzburg-Landau type nematic liquid crystal flows to a weak solution of the simplified Ericksen-Leslie system as the parameter tends to zero for both uniaxial and biaxial cases. This is based on the compensated compactness property of the Ericksen stress tensors, which has been obtained by applying the Pohozaev type argument to the Ginzburg-Landau type nematic liquid crystal flows. Persönliches Profil Personal Profile: 黄涛，现任职于美国韦恩州立大学，博士师从著名数学家王长友老师，在液晶方程与调和映照流、双调和映照流等研究领域做出了系统而杰出的工作。 -
13 Titel Title: Asymptotic Plateau problem via equidistant hyperplanes Sprecher Speaker: 洪寒 Zugehörigkeit Affiliation: 北京交通大学 Datum und Uhrzeit Datetime: 2023-11-15 10:00 -- 2023-11-15 11:00 Veranstaltungsort Venue: Tencent: 621 998 208 Host Host: 周恒宇 Abstract Abstract: In this talk, we are going to discuss the asymptotic Plateau problem. Firstly, we recall some classical results by Anderson and Guan-Spruck as well as some remaining open questions. The solution of APA is classically approximated by compact solutions with boundary sitting on horo-spheres when it is interpreted as solutions to a fully nonlinear PDE. Then we discuss new ideas to get solutions of APA approximated by the shape of cylindrical graphs whose boundaries rest upon equidistant hyperplanes. Through this procedure, we establish an alternative method for constructing solutions to the asymptotic Plateau problem. The resulting solution may differ from the classical ones, particularly in cases where uniqueness cannot be assured. This is a joint work with Haizhong Li and Meng Zhang. Persönliches Profil Personal Profile: 洪寒博士2021年博士毕业于加拿大英属哥伦比亚大学，师从陈竞一和Ailana Fraser教授。2021-2023年间在清华大学丘成桐数学科学中心做博士后，合作导师为吴云辉和李海中教授。现就职于北京交通大学数学与统计学院。他的研究方向是微分几何与几何分析，主要集中在极小曲面，谱理论等研究。研究成果发表在Crelle, CVPDE, IMRN，JGA等杂志上。 -
12 Titel Title: On the Solvability of General Inverse $\sigma_k$ Equations Sprecher Speaker: Chao-Ming Lin Zugehörigkeit Affiliation: Ohio State University Datum und Uhrzeit Datetime: 2023-11-15 09:00 -- 2023-11-15 10:00 Veranstaltungsort Venue: Zoom: 892 7039 8293 | 511067 Host Host: Wenqiong Li Abstract Abstract: In this talk, first, I will introduce general inverse equations in Kähler geometry. Some classical examples are the complex Monge–Ampère equation, the J-equation, the complex Hessian equation, and the deformed Hermitian–Yang–Mills equation. Second, by introducing some new real algebraic geometry techniques, we can consider more complicated general inverse equations. Last, analytically, we study the solvability of these complicated general inverse equations. Zoom: https://us02web.zoom.us/j/89270398293?pwd=UnhVbWZSbHdCd255RE9PcitERFFXZz09 Persönliches Profil Personal Profile: Chao-Ming Lin is currently a Zassenhaus Assistant Professor at the Ohio State University under the mentorship of Bo Guan. He obtained his Ph.D. at University of California-Irvine in 2023 under the supervision of Zhiqin Lu and Xiangwen Zhang. His research focuses on differential geometry, geometric analysis, and real algebraic geometry. -
11 Titel Title: A class of functionals with duality Sprecher Speaker: 汪徐家 Zugehörigkeit Affiliation: 澳大利亚国立大学 Datum und Uhrzeit Datetime: 2023-11-14 14:30 -- 2023-11-14 15:30 Veranstaltungsort Venue: Tencent: 715-345-467 Host Host: 陕西师范大学数学与统计学院、基础数学研究中心 Abstract Abstract: We introduce a class of functionals subject to a duality restriction. The functional is of the form $J(U,V)= \int_U f(x)dx - \int_V g(y)dy$, where $f$, $g$ are given non-negative functions. This model includes the Minkowski problem in the sphere and Kantorovich's dual functional in optimal transport as special cases. The Euler equations of the functionals are of Monge-Ampere type. In this talk, I will report some new results on the functionals, which were obtained in collaboration with Qiang Guang and Qi-Rui Li. Persönliches Profil Personal Profile: 汪徐家，澳大利亚科学院院士，澳大利亚国立大学教授。汪教授主要从事非线性椭圆抛物方程理论及其应用的研究，取得了一系列深刻的结果。解决了陈省身的仿射Bernstein问题猜想和Monge的原始最优运输问题。他曾在Ann. of Math.，Acta Math., J. Amer. Math. Soc., Invent. Math., Duke Math. J. 等国际重要的数学专业学术期刊上发表论文120余篇。 -
10 Titel Title: Thurston norms, $L^2$-norms, geodesic laminations and Lipschitz maps Sprecher Speaker: 韩肖垄 Zugehörigkeit Affiliation: 清华大学 Datum und Uhrzeit Datetime: 2023-11-10 10:00 -- 2023-11-10 11:00 Veranstaltungsort Venue: Tencent: 116 321 129 Host Host: 周恒宇 Abstract Abstract: For closed hyperbolic 3-manifolds $M$, Brock and Dunfield prove an inequality on the first cohomology bounding the ratio of the geometric $L^2$-norm to the topological Thurston norm. Motivated by Dehn fillings, they conjecture that as the injectivity radius tends to $0$, the ratio is big O of the square root of the log of the injectivity radius. We prove this conjecture for all sequences of manifolds which geometrically converge. Generically, we prove that the ratio is bounded by a constant, by showing that any least area closed surface is disioint from the thin part. We then study the connection between the Thurston norm, best Lipschitz circle-valued maps, and maximal stretch laminations, building on the recent work of Daskalopoulos and Uhlenbeck, and Farre, Landesberg and Minsky. We show that the distance between a level set and its translation is the reciprocal of the Lipschitz constant, bounded by the topological entropy of the pseudo-Anosov monodromy if $M$ fibers. Persönliches Profil Personal Profile: 韩肖垄，清华大学博士后，伊利诺伊大学香槟分校博士，主要研究兴趣为双曲几何，低维流形等。 -
9 Titel Title: Fill-in with nonnegative scalar curvature Sprecher Speaker: 王文龙 Zugehörigkeit Affiliation: 南开大学 Datum und Uhrzeit Datetime: 2023-11-09 09:00 -- 2023-11-09 10:00 Veranstaltungsort Venue: Tencent: 590-8644-3073 Host Host: 重庆理工大学数学中心 Abstract Abstract: We will first introduce the notion "fill-in with nonnegative scalar curvature" and the motivation of this problem both from geometry of compact manifold with boundary and quasi-local mass in the general relativity. Then we will review some questions raised by Gromov and some results in this direction. This talk is based on some joint work with Yuguang Shi, Guodong Wei and Jintian Zhu. Persönliches Profil Personal Profile: 王文龙,南开大学副教授.研究方向是几何分析,特别是与数量曲率有关的几何问题和几何流自相似解的刚性.在 Crelle, Math.Ann., Int. Math. Res. Not., Math Z. 等期刊发表过论文. -
8 Titel Title: The Sigma-2 Equation in Dimension Four Sprecher Speaker: Ravi Shankar Zugehörigkeit Affiliation: Princeton University Datum und Uhrzeit Datetime: 2023-11-08 09:00 -- 2023-11-08 10:00 Veranstaltungsort Venue: Zoom: 836 3199 0429 | 072570 Host Host: Wenqiong Li Abstract Abstract: The sigma-2 equation is the remaining equation in the Monge-Ampere / sigma-n family to be understood. It unclear whether solutions are smooth inside their domains. With Yu Yuan, we confirm the interior regularity in dimension four. In higher dimensions, we find an interior estimate under a weak condition. The dimension two case is by Heinz in the 1950’s, and dimension three is by Warren and Yuan in the 2000’s. Our method is pointwise and combines several overlooked ingredients from the past two decades. The idea is to propagate partial regularity using a three-sphere inequality. The method also gives new pointwise proofs of the Monge-Ampere and special Lagrangian equation results. https://us02web.zoom.us/j/83631990429?pwd=TDRNdkMwekI4YWtWR0dDTi9vcllsUT09 Persönliches Profil Personal Profile: Ravi Shankar is an instructor at Princeton University. He obtained his PhD at the University of Washington in 2021 under the supervision of Gunther Uhlmann and Yu Yuan. His recent research focuses on aspects of fully nonlinear elliptic PDEs. -
7 Titel Title: 关于四维 Yang-Mills 连络的爆破分析 Sprecher Speaker: 殷浩 Zugehörigkeit Affiliation: 中国科学技术大学 Datum und Uhrzeit Datetime: 2022-10-17 14:00 -- 2022-10-17 15:30 Veranstaltungsort Venue: Tencent: 678-905-872 Host Host: 艾万君 Abstract Abstract: 报告四维流形上能量有界的杨-米尔斯(Yang-Mills)连络的爆破现象。通过在杨-米尔斯联络的能量集中点附近的脖子区域上选择合适的规范，研究连络形式的渐近展开，由此证明弱极限连络和泡泡联络之间的一个曲率等式。进一步启发了杨-米尔斯场等相关几何偏微分方程的紧性现象的研究。 Persönliches Profil Personal Profile: 殷浩，中国科学技术大学数学科学学院副教授。主要从事调和映射和 Yang-Mills 联络相关问题的紧性研究。主持国家自然科学基金科研项目4项。在J. Funct. Anal., Calc. Var. Partial Differential Equations, Comm. Anal. Geom. 等国际知名杂志上发表研究论文十余篇。 -
6 Titel Title: Signature and Toledo invariants for flat unitary bundles over surfaces with boundary Sprecher Speaker: 万学远 Zugehörigkeit Affiliation: 重庆理工大学 Datum und Uhrzeit Datetime: 2022-07-14 09:30 -- 2022-07-14 11:00 Veranstaltungsort Venue: Tencent: 616-496-230|202207 Host Host: 艾万君 Abstract Abstract: This talk deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems, due to Meyer and Atiyah, to Burger-lozzi-Wienhard’s Toledo invariant. To measure the difference, we extend Atiyah-Patodi-Singer’s rho invariant, initially defined on $U(p)$, to discontinuous class functions, first on $U(p,q)$, and then on other classical groups via embeddings into $U(p,q)$. This work is joint with Prof. Inkang Kim and Prof. Pierre Pansu. Persönliches Profil Personal Profile: 万学远博士，重庆理工大学数学科学研究中心特聘教授。2016 年博士毕业于南开大学，2017- 2021 年先后在瑞典查尔姆斯理工大学和韩国高等研究院做博士后。目前主要从事复几何的相关研究，研究结果发表在 JMPA, JAG, Compositio, Tran. AMS, Math. Ann. 等国际著名数学期刊。 -
5 Titel Title: Analysis of Yang-Mills-Higgs-Dirac model Sprecher Speaker: 吴瑞军 Zugehörigkeit Affiliation: 北京理工大学 Datum und Uhrzeit Datetime: 2022-07-05 09:00 -- 2022-07-05 10:30 Veranstaltungsort Venue: Tencent: 289-224-876|202207 Host Host: 艾万君 Abstract Abstract: We will describe a nonlinear model involving the sigma models and the gauge theory. This can be seen as a gauged Dirac-harmonic map model, which will be located on a fiber bundle with compact fibers. After a description of the model, we emphasize on the blowup analysis and the bubbles. Persönliches Profil Personal Profile: 吴瑞军，北京理工大学教授，获中科院数学与系统科学研究院以及Max-Planck研究所双博士学位。先后在Max-Planck、De Giorgi Center of SNS、 SISSA从事博士后研究工作。主要研究兴趣为与Dirac算子有关的变分问题和方程。相关研究工作发表在Comm. Math. Phys. , Trans. AMS., Calc. Var. PDE., J. Differential Equations, J. Geom. Phys., 等杂志上。 -
4 Titel Title: Transverse $\mathcal{F}$-entropy for Riemannian foliations and its application Sprecher Speaker: Dexie LIN Zugehörigkeit Affiliation: College of Mathematics and Statistics of Chongqing University Datum und Uhrzeit Datetime: 2022-06-29 10:00 -- 2022-06-29 11:30 Veranstaltungsort Venue: Tencent: 520-642-524|202206 Host Host: 艾万君 Abstract Abstract: In this talk, we introduce some basic notions of Riemannian foliations and given an entropy functional on Riemannian foliation, we also give some properties of this functional. In application, we give a necessary condition for codimension 4 Riemannian foliation admitting the transverse Einstein metric by using the entropy and basic Seiberg-Witten equations. Persönliches Profil Personal Profile: Dexie LIN, who got the Ph.D of The University of Tokyo in 2020 September. His main interest is about the Seiberg-Witten equations and low dimensional manifold geometry. The related results are published on Proc. Amer. Math. Soc. and Topology Appl. etc. -
3 Titel Title: Topics in the uniqueness of floating bodies Sprecher Speaker: 张宁 Zugehörigkeit Affiliation: 华中科技大学 Datum und Uhrzeit Datetime: 2022-06-23 09:00 -- 2022-06-23 10:30 Veranstaltungsort Venue: Tencent: 825-526-905|202206 Host Host: 艾万君 Abstract Abstract: In this talk, I will present a couple of recent results related with the uniqueness of floating bodies. Persönliches Profil Personal Profile: 张宁，华中科技大学副研究员，博士生导师。2017 年毕业于加拿大阿尔伯塔大学获博士学位，美国国家数学科学研究所博士后，肯特州立大学博士后。主要研究领域涵盖凸几何、几何分析、黎曼几何和概率相关方向。部分成果发表在 Trans. Amer. Math. Soc., J. Func. Anal., CVPDE 等学术期刊上。 -
2 Titel Title: Regularity of subelliptic harmonic maps with values into metric spaces of nonpositive curvature Sprecher Speaker: 桂耀挺 Zugehörigkeit Affiliation: Max Planck Institute for Mathematics in the Sciences Datum und Uhrzeit Datetime: 2022-06-21 15:00 -- 2022-06-21 16:30 Veranstaltungsort Venue: Tencent: 590-939-207|202206 Host Host: 艾万君 Abstract Abstract: We present a result of Holder continuity of a harmonic map from a domain of a sub-Riemanian manifold into a locally compact manifold with nonpositive curvature, and more generally into a non-positively curved metric space in the Alexandrov sense. This is a joint work with Prof. Jost and Prof. Li-Jost. Persönliches Profil Personal Profile: Gui Yaoting, obtain his doctorate degree from USTC in June 2022. His main interest is nonlinear analysis on manifolds, especially in the analysis on singular space, such as conical manifolds and degenerate elliptic operator. He visits the Max Planck Institute from 2022.03 to 2022.07, and he has been offered a postdoc fellowship in BICMR. -
1 Titel Title: A Liouville’s theorem for some Monge-Ampère type equations Sprecher Speaker: 韦韡 Zugehörigkeit Affiliation: 南京大学 Datum und Uhrzeit Datetime: 2022-06-21 08:30 -- 2022-06-21 10:00 Veranstaltungsort Venue: Tencent: 807-884-844|202206 Host Host: 艾万君 Abstract Abstract: In this talk we study a Monge-Ampère type equation that interpolate the classical 2-Yamabe problem in conformal geometry and the 2-Hessian equation in dimension 4.This is a joint work with Hao Fang and Biao Ma. Persönliches Profil Personal Profile: 韦韡，现南京大学助理研究员。博士毕业于中国科学技术大学，上海数学中心博士后。曾获得博士后创新人才计划。在 Adv.Math, J.Funct. Anal., Calc. Var.等杂志发表过文章。