报告题目1：球面上欧拉流的Arnold型稳定性定理

报告人：曹道民，中国科学院数学与系统科学研究院

报告时间：2024年12月14日（周六）9:00-9:40

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：带常角速度自旋的球面上不可压缩流体流动可用不可压缩欧拉方程来描述, 其定常解或旋转解的构造和分类,对一些特殊形式的定常解或旋转解(如纬向流,Rossby-Hauwitz波等)的稳定性研究是重要课题.本报告中报告人将回顾一下相关结果, 并介绍几个报告人和合作者(王国栋,左碧君) 最近关于轨道稳定性结果.

报告人简介：曹道民，1983年6月毕业于湘潭大学数学专业，1989年6月在中国科学院获博士学位。现任中国科学院数学与系统科学研究院研究员、博士生导师。主要从事非线性偏微分方程和非线性分析的研究，独立或与人合作共发表论文160多篇，与人合作在Cambridge University Press出版专著一部。曾获中国科学院青年科学家奖（1999年），曾任中国科学院数学与系统科学研究院应用数学研究所所长。曾主持过中国科学院知识创新工程重要方向性项目《数学物理中的若干重大问题》和中国科学院前沿重点项目《带间断非线性椭圆型方程》等科研项目。现任《应用数学学报》和《数学物理学报》副主编，是《Applicable Analysis》、《Annales Academiae Scientiarum Fennicae，Mathematica》等多种刊物的编委。

报告题目2：Solutions for fractional Schrodinger equations with general potentials

报告人：彭双阶，华中师范大学

报告时间：2024年12月14日（周六）9:40-10:20

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：This talk considers fractional Schrödinger equations with a general potential. Under various assumptions on the potential at infinity, including decay with various rate at infinity, this talk introduces a unified penalization argument and give a complete result on the existence and nonexistence of positive solutions.

报告人简介：彭双阶，华中师范大学教授。曾获得教育部自然科学二等奖和湖北省自然科学奖一等奖, 国家级教学成果奖二等奖。先后主持了国家自然科学基金重点项目、教育部长江学者与创新团队发展计划项目、教育部科学技术重点项目等。共发表学术论文100余篇，其中多篇论文发表在Adv.Math.、J.Math.Pures.Appl.、Proc. London Math.Soc.、Tran. Amer. Math. Soc.、Math.Ann、 Arch. Ratinal. Mech. Anal.、Indiana Univ. Math. J、 Ann.I.H.Poincaré- AN等重要学术期刊上，其研究成果引起了国内外专家的广泛关注，被美国、德国、意大利、澳大利亚等国家的数学家大量引用或推广，并用来解决其它的问题。

报告题目3：The number of positive solutions for $n$-coupled elliptic systems

报告人：刘兆理，首都师范大学

报告时间：2024年12月14日（周六）10:40-11:20

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：We study the number of positive solutions to the $n$-coupled elliptic system

$$

-\Delta u_i=\mu_iu_i^{2^*-1}+\sum_{j=1,\, j\neq i}^n\beta_{ij} u_i^{p_{ij}-1}u_j^{q_{ij}},\ u_i\in\mathscr{D}^{1,2}(\R^N),\ i=1,2,\cdots,n,

$$

where $N\geq3$, $n\geq2$, $\mu_i>0$, $\beta_{ij}>0$, $p_{ij}<2^*$, and $p_{ij}+q_{ij}=2^*$ for $i\neq j\in\{1,2,\cdots,n\}$. We prove new multiplicity and uniqueness results for positive solutions of the system, whether the system has a variational structure or not. In some cases we provide a rather complete characterization on the exact number of positive solutions. The results we obtain reveal that the positive solution set of this system has very different structures in the three cases $p_{ij}<2$, $p_{ij}=2$, and $2<p_{ij}<2^*$. Moreover, when $2<p_{ij}<2^*$, very different structures of the positive solution set can also be seen in the case where $p_{ij}$ close to $2$ and the case where $p_{ij}$ close to $2^*$. Similar results are given for elliptic systems with subcritical Sobolev exponents. This is joint work with Yongtao Jing, Haidong Liu, Yanyan Liu and Juncheng Wei.

报告人简介：刘兆理，首都师范大学二级教授，博士生导师。非线性分析专家，教育部特聘教授，获得过教育部高校自然科学二等奖，当前主持国家自然科学基金重点项目。主要研究方向为非线性分析，在临界点理论以及椭圆型方程解的存在性、多重性、变号性等方面做出了多项有意义的研究工作，在研究解的变号性方面系统地发展了下降流不变集方法。出版专著一部，在Adv. Math., Comm.Math. Phy., J. Fun.Anal., Math. Zeit. JDE., Ann. MInst. H. Poincar e-Anal. non Lin e aire, Comm. PDE等SCl核心期刊上发表学术论文多篇，其研究成果已被他人多次引用，国际上有多位数学家，包括多位科学院院士，在他们的工作中采用刘兆理教授的研究方法，并称刘兆理教授的工作是开创性工作。

报告题目4：Some new results on normalized solutions of Schrodinger equations and systems

报告人：张志涛，中国科学院数学与系统科学研究院

报告时间：2024年12月14日（周六）11:20-12:00

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：We introduce some new results on normalized solutions, especially for normalized solutions of mass subcritical Schrodinger equations in exterior domains; normalized solutions to p-Laplacian equations with combined nonlinearities; normalized solutions to Schrodinger systems etc.

报告人简介：张志涛，中国科学院数学与系统科学研究院二级研究员、博士生导师，华罗庚数学首席研究员，中国科学院大学岗位教授，江苏大学数学科学学院院长。长期从事非线性泛函分析研究，出版Springer专著一部，科学出版社出版合著《拓扑与变分方法及应用》。多次应邀在重要国际会议上作大会报告，多次应邀访问美国、法国、德国、澳大利亚的著名大学，曾担任中国数学会副秘书长，担任Springer期刊Partial Differential Equations and Applications 主编和4个国际刊物编委，主持国家重点研发计划，主持、参加多项国家自然科学基金（重点）项目。在 Journal of Functional Analysis，Annales de l'Institut Henri Poincare Analyse Non Lineaire，J. Differential Equations，Calculus of Variations and PDE, Transactions of the American Mathematical Society等国际著名刊物发表论文近百篇。

报告题目5：The classification of critical points of Heat kernel on tori and applications to elliptic equation and minimization problem on lattice

报告人：邹文明，清华大学

报告时间：2024年12月14日（周六）14:00-14:40

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In this talk, I will report the critical points of the Heat kernel on two-dimensional flat tori. Using methods related to theta functions, we determine that the Heat kernel exhibits four and six critical points on rectangular and hexagonal tori, respectively. Furthermore, on a rhombic torus, the number of critical points of the Heat kernel depends on the geometry of torus. We have also established a connection between the Heat kernel, linear elliptic equations with singularity, and particle energy. This connection allows us to recover partial results of the Green function and provides a positive answer to the conjecture regarding Mueller-Ho conjecture. An intriguing finding of our study is that all three functions exhibit uniform critical points on rectangular and hexagonal tori. (jointly with C.G. Long and J. C.Wei)

报告人简介：邹文明，清华大学数学科学系教研系列长聘教授、教育部数学专业教学指导委员会委员、中国数学会非线性分析专业委员会副主任；曾任清华大学数学科学系主任。1998年在中国科学数学研究所获得博士学位；1998-1999年在瑞典Stockholm大学进行博士后研究；2001-2004年在美国加州(Irvine) 大学访问助理教授和讲师，英文授课三年。目前担任《中国科学-数学》、《Advances in Nonlinear Analysis》和《Minimax Methods》 等刊物编委。 在Springer-New York出版英文专著二部，系统地建立了新的临界点理论；在许多核心问题上取得了突破。发表SCI论文160余篇，发表刊物包括Math Ann; ARMA;  Adv in Math; JMPA; ComPDE; AIHP; TransAMS; JFA；SIAM-JMA; Ann.Scuola Normale-Pisa等等。

报告题目6：On the minimal number of closed geodesics on Finsler spheres

报告人：段华贵，南开大学

报告时间：2024年12月14日（周六）14:40-15:20

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In this talk, we will introduce the problem about the optimal number of closed geodesics on Finsler spheres. Recently it has been proved that for every Finsler metric on certain positively-curved spheres of dimension $n$, there exist at least $n$ prime closed geodesics, which solved a conjecture of Katok and Anosov for such spheres when $n$ is even, which is a joint work with Dong Xie.

报告人简介：段华贵，教授，博士生导师，南开大学数学科学学院副院长，教育部重点实验室副主任，南开大学百名青年学科带头人。主要研究方向为非线性分析与动力系统，近年来，在哈密顿系统的周期轨道和微分几何中的闭测地线等方面取得系统性的研究成果，论文发表在《Adv. Math.》《Calc. Var. & PDE》《J. Diff. Equ.》《J. Diff. Geom.》《J. Funct. Anal.》《Math. Z.》等国际学术期刊上。

报告题目7：Morse index, topological degree and local uniqueness of multi-spikes solutions

报告人：严树森，华中师范大学

报告时间：2024年12月14日（周六）15:40-16:20

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：We consider multi-spike positive solutions to the Lane-Emden problem in any bounded smooth planar domain, and investigate the related linearized eigenvalue problem. By obtaining estimates for its eigenvalues and sharp descriptions of the asymptotic behavior of the corresponding eigenfunctions, we compute the Morse index of each k-spikes solution and the total degree of all the k-spikes solutions concentrating at a non-degenerate critical points of the K-R function. As a consequence, we prove the local uniqueness of such solutions.

报告人简介：严树森，华中师范大学数学与统计学院教授、博导。1990年毕业于中国科学院系统科学研究所。主要从事非线性椭圆偏微分方程的研究，特别是在非线性椭圆问题爆破解的存在性及相关性质取得了系列具有国际影响的成果。解决了相关领域国际知名数学家提出的猜想：如，在20世纪八十年代由Lazer和McKenna对Ambrosetti-Prodi型椭圆问题提出的猜想、非紧椭圆问题无穷多解的存在性、著名的Chern-Simons方程解的个数、流体力学中涡补丁问题解的存在性和局部唯一性等。在Comm. Pure Appl. Math.，Comm. Math. Phy.，Adv. Math. J. Math. Pures Appl. 等国际权威数学期刊发表学术论文100多篇。

报告题目8：Estimates for stress concentration between two adjacent rigid inclusions in stationary Stokes/Navier-Stokes flow

报告人：李海刚，北京师范大学

报告时间：2024年12月14日（周六）16:20-17:00

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：Particles suspending in complex fluids usually result in complicated flow behavior. It is vitally important to study the stress enhancements in the narrow region between two rigid particles. In this talk, we will show the pointwise upper bounds of the gradient and the second-order partial derivatives for the stationary Stokes/Navier-Stokes flow as the distance between two rigid particles approaches to zero in a bounded domain in dimension two and three. The optimality of these blow-up rates is demonstrated by establishing the corresponding lower bounds.

报告人简介：李海刚，北京师范大学数学科学学院教授、博士生导师。主要从事材料科学中的偏微分方程理论研究，在复合材料中的Babuska问题、流-固模型的悬浮问题等方面取得一系列进展，在Adv Math、ARMA、JMPA、JFA、AIHP-NL、SIMA、TAMS、CV&PDEs等国际权威数学杂志发表论文30余篇。

报告题目9：Navier-Stokes equations on the generalized phase spaces

报告人：洪桂祥，哈尔滨工业大学

报告时间：2024年12月14日（周六）17:00-17:40

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：The noncommutative partial differential equations, such as the time-dependent Bogoliubov-de Gennes (BdG) equation, sometimes referred to as the generalized Hartree–Fock equation or the Hartree–Fock–Bogoliubov equation, have arisen naturally in the theory of effective evolution equations. Recently, there have appeared a lot of works in this direction such as noncommutative Burgers equations, quantum Laplace equations, quantum Fokke-Planck equations, noncommutative Schrodinger equations, and quantum wave equations etc. However, the Lp theory has not been implemented successfully in most of the previously mentioned work; this is due to the fact that the Lp theory is the core of noncommutative analysis which has been neglected by the PDE community. In this talk, we shall present the study of the Navier-Stokes equation on the phase spaces by developing the noncommutative analysis techniques. This is based on joint work with Deyu Chen, Liang Wang and Wenhua Wang.

报告人简介：洪桂祥，哈尔滨工业大学教授。他专注于调和分析、非交换分析及其在非交换几何和量子信息中的应用，为这一前沿领域的建立和发展做出重要贡献，已在《Duke Mathematical Journal》《Memoirs of the American Mathematical Society》《Advances in Mathematics》等顶级期刊发表论文30余篇。其研究方向涵盖经典与非交换调和分析、量子概率论、非交换遍历理论和泛函分析，尤其在非交换鞅论、非交换遍历论等方面取得突破，解决了若干公开问题。

报告题目10：Harmonic Analysis Methods in Harmonic Maps and Its Applications

报告人：李嘉禹，中国科学技术大学

报告时间：2024年12月15日（周日）8:15-8:55

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In the talk we will review compactness results and regularity theorems related to harmonic maps by the methods in harmonic analysis. We will review Sacks-Uhlenbeck blow-up methods, H´elein regularity theorem, Evens and Bethuel partial regularity, Lin theorem, Rivi`ere estimates, and our results in this field.

报告人简介：李嘉禹，中国科学技术大学杰出讲席教授、中法中心主任、国家基金委创新群体带头人、国家级人才特聘教授。2001年至2004年担任中德几何分析伙伴小组组长。2004年至2009年担任国际理论物理中心（ICTP）研究员，负责几何与分析国际合作方面的工作。学术刊物《中国科学》，《数学学报》等杂志编委，《JPDE》主编。曾任中国数学会常务理事、国家自然科学基金委员会“数学天元基金领导小组”成员。

报告题目11：Periodic solution for Hamiltonian type system

报告人：郭玉霞，清华大学

报告时间：2024年12月15日（周日）8:55-9:35

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In this talk , I will talk about the periodic solution for Hamiltonian systems. We give a direct method to prove the existence and nonexistence of solutions which are periodic in its first k variables.

报告人简介：郭玉霞，清华大学数学系教授，博士生导师。1999年北京大学博士毕业，先后在中国科学院、葡萄牙里斯本大学、加拿大纽芬兰大学做博士后。主要从事非线性泛函分析及其在偏微分方程中的应用等方面的研究工作。2003至2004年德国洪堡基金学者。曾应邀先后访问美国、澳大利亚、意大利、新加坡、日本等国家，与国内外著名专家学者有着广泛深入的合作研究。先后主持完成国家自然科学基金项目5项，独立完成其他国家级项目2项。目前作为主要成员参与自然科学基金重点项目两项。发表SCI学术论文70余篇。部分研究成果发表在Comm. Pure. Appl. Math., Jour. Diff.Equa., Comm. Parl. Diff.Equa. Cal. Var. PDE. Jour.Func. Anal，SIAM J. Contr. Opt.等国际权威数学期刊上。

报告题目12：Weak Diffusive Stability Induced by High-order Spectral Degeneracies

报告人：吴启亮，美国俄亥俄大学

报告时间：2024年12月15日（周日）9:35-10:15

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：The Lyapunov stability of equilibria in dynamical systems is determined by the interplay between the linearization and nonlinear terms. In this talk, we present our recent results on the case when the spectrum of the linearization is diffusively stable with high-order spectral degeneracy at the origin. Roll solutions at the zigzag boundary of the Swift-Hohenberg equation are shown to be nonlinearly stable, serving as examples that linear decays weaker than the classical diffusive decay, together with quadratic nonlinearity, still give nonlinear stability of spatially periodic patterns. The study is conducted on two physical domains: the 2D plane and the infinite 2D torus. Linear analysis reveals that, instead of the classical $t^{-1}$ diffusive decay rate, small perturbations of zigzag stable roll solutions decay with slower algebraic rates ($t^{-3/4}$ for the 2D plane; $t^{-1/4}$ for the infinite 2D torus) due to the high-order degeneracy of the translational mode at the origin in the Bloch-Fourier spaces. The nonlinear stability proofs are based on decompositions of the neutral translational mode and the faster decaying modes, and fixed-point arguments, demonstrating the irrelevancy of the nonlinear terms.

报告人简介：吴启亮，美国俄亥俄大学副教授，博士生导师。其主要研究方向包括非线性动力学和模式形成。在J. Math. Pures Appl.，Proc. Amer. Math. Soc.，J. Differential Eqns.，J. Math. Biol.，J. Dyn. Diff. Eqns.，Discrete Contin. Dyn. Syst.等刊物上发表多篇论文。也曾获美国国家自然科学基金资助。

报告题目13：On a semilinear equation with logarithmic Laplacian operator

报告人：周风，华东师范大学

报告时间：2024年12月15日（周日）10:30-11:10

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In this talk, we present some basic results about the logarithmic Laplacian operator which has been investigated in various directions: the eigenvalues estimates, semilinear problems, application to the analysis of the L\’evy Flight. In particular, we discuss our recent work on the classification of the positive solutions, and the existence and nonexistence of positive solutions to the critical semilinear problem involving the logarithmic Laplacian. This is based on joint work with HY Chen.

报告人简介：周风，华东师范大学数学科学学院教授，博士生导师。1993年获得巴黎第六大学数学博士学位，师从H. Brezis教授。2004年至2012年任华东师范大学数学系系主任。入选上海市曙光计划、上海市优秀学科带头人计划，主持国家“数学创新引智”计划。研究领域为非线性偏微分方程，主要研究几何、数学物理中若干非线性偏微分方程解的性态及相关问题。研究成果发表在Comm. Pure Appl. Math., J. Funct. Anal.,  Ann. I.H.P.，Calc. Var. PDEs., J. Differential Equations等国际著名数学期刊上。

报告题目14：F-functional and entropy for Fujita equation

报告人：王克磊，武汉大学

报告时间：2024年12月15日（周日）11:10-11:50

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In 2013, in their work on mean curvature flow, Colding and Minicozzi introduced a quantity, now called Colding-Minicozzi entropy. This entropy plays an important role in many subsequent works on MCF. In a recent joint work with Juncheng Wei and Ke Wu, we introduce a similar entropy for Fujita equation. In this talk, I’ll discuss this notion and some applications of it to the blow up problem for Fujita equation.

报告人简介：王克磊，武汉大学教授、博士生导师，主要研究椭圆与抛物型偏微分方程，特别是偏微分方程的奇异扰动理论及相关的自由边界问题等；曾荣获第十一届钟家庆数学奖，入选国家级人才计划。王克磊教授在非线性偏微分方程的几何与定性性质，尤其是与几何测度论问题相关的奇性分析问题的研究中取得了若干具有国际影响力的研究结果，在Comm. Pure Appl. Math., J. Eur. Math. Soc., Trans. Amer. Math. Soc., Adv. Math., J. Differential Equations等数学期刊上发表学术论文四十余篇，并在Springer出版社出版一本英文专著。

报告题目15：A compactness result for invariant minimal hypersurfaces

报告人：Paolo Piccione，University of São Paulo，浙江师范大学

报告时间：2024年12月15日（周日）11:50-12:30

报告地点：金华雷迪森广场酒店三楼通济2厅

报告摘要：In this talk, I will introduce the Hsiang-Lawson construction of minimal hypersurfaces through the lens of equivariant geometry. I will then present a compactness result for cohomogeneity one invariant minimal hypersurfaces. As an application of these concepts, I will demonstrate the existence of multiple minimal spheres in elongated ellipsoids. Joint work with R. Bettiol (CUNY), D. Corona and F. Giannoni (Camerino).

报告人简介：Paolo Piccione, Graduated in Mathematics from the University of Rome La Sapienza (Italy, 1987), and Ph.D. in Mathematics from Pennsylvania State University (USA, 1994), holds a Livre Docência at the University of São Paulo (1998). Served for three consecutive terms (2017-2023) as the President of the Brazilian Mathematical Society, and currently holding the position of Full Professor (MS-6) at the University of São Paulo. A full member of the Brazilian Academy of Sciences since May 2012, and a member of the Executive Committee of the International Mathematical Union (IMU) for a second term (2023-2025), as well as a member of the Special Committee on Work Regimes (CERT) at USP, and part of the Coordination of Area - Mathematics and Statistics at Fapesp. Admitted to the National Order of Scientific Merit in the rank of Commander, in the field of Mathematical Sciences, in 2018.

He has served as a member of the Advisory Board in Mathematics for the Brazilian Ministry Of Science and Technology, President of the Research Committee of the Institute of Mathematics and Statistics of the University of Sao Paulo (USP), member of the Research Council of USP, and member of the Sectoral Assessment Committee (CAS) for Mathematics and Statistics at the University of São Paulo. His mathematical specialty is Differential Geometry, primarily engaged in the following topics: Calculus of Variations and Geometric Variational Problems, Bifurcation Theory, Global Riemannian and Lorentzian Geometry, Morse Theory, Symplectic Geometry, and Hamiltonian Systems. He coordinates the Fapesp Thematic Project Algebraic, Topological, and Analytical Techniques in Differential Geometry and Geometric Analysis. Since March 2017, he has held the status of Researcher 1A of the Brazilian National Committee for Research.

His contributions to the Brazilian Mathematical Society (SBM) encompass participation in the Evaluation Committee for the IMPA-SBM Journalism Prize, coordination of the SBM Prize Jury, and involvement in the editorial committees of the journals: Revista Matemática Universitária (Chief Editor), Matemática Contemporânea (Associate Editor), and the SBM Newsletter.