报告题目1：Logarithmic sub-Laplacian on the Heisenberg group

报告人：窦井波教授，陕西师范大学

报告时间：2026年10月16日（周五）8:30-9:30

报告地点：20-200

报告摘要：In this talk, we present the definition of the logarithmic sub-Laplacian on the Heisenberg group and its basic properties. Based on the first-order Taylor expansion of the fractional sub-Laplacian with respect to the order parameter and group Fourier transformation, we define the logarithmic sub-Laplacian. Moreover, we show some sharp integral inequalities associated with the logarithmic sub-Laplacian. This is joint work with Yahzou Han and Guoqiang Duan.

报告人简介：窦井波，教授，博士生导师。现为陕西师范大学数学与统计学院教授。研究方向是偏微分方程理论及其应用。近年来与多位合作者集中研究最优几何不等式及其椭圆方程解的存在性等问题。在J. Eur. Math. Soc., Adv. Math.，J. Func. Anal.，Inter. Math. Res. Notices, Calc. Var. PDE, J. Diff. Equ.等国际学术期刊上发表学术论文40余篇；主持国家自然科学基金4项，2022年获陕西高校青年创新团队项目。

报告题目2： Global Dynamics and Bifurcation Analysis of a Producer-Consumer Model under Shared Multiple Nutrient Limitations

报告人：纪菊萍副教授，广州大学

报告时间：2026年10月16日（周五）9:30-10:30

报告地点：20-200

报告摘要：The growth of cells and organisms is limited by multiple nutrients, including carbon, nitrogen, and phosphorus. In this talk, we will introduce a producer-consumer model in which the growth of species is limited by the availability of two nutrients. In our model, a significant difference from classical stoichiometric producer-consumer models (the growth of the species follows Liebig's Law of the Minimum) is that the species growth function is smooth and the uptake process of the producer probably takes the longest time. The aim of this work is to first discuss the global dynamical behavior of a producer-consumer model under shared two nutrient limitations with Holling type I functional response, then perform a bifurcation analysis for the model with Holling type II functional response numerically. Our results show that the model with Holling type I functional response has no limit cycles, and the unique interior equilibrium, if it exists, is globally asymptotically stable. Types of bifurcations (saddle-node, Hopf, and transcritical bifurcations) and bistability (node-node, node-cycle bistability) are presented in the model with Holling type II functional response. In addition, several new phenomena are observed in this work.

报告人简介：纪菊萍，广州大学数学与信息科学学院特聘副教授，硕士生导师。2021年博士毕业于加拿大University of New Brunswick。2021年至2023年，在加拿大University of Alberta 从事博士后研究工作。近年来致力于微分方程理论及其在传染病、种群生态学等生物数学领域的应用研究。以第一作者及通讯作者身份在Journal of Mathematical Biology、Journal of Theoretical Biology、Mathematical Biosciences、Bulletin of Mathematical Biology和Journal of Dynamics and Differential Equations等杂志发表SCI论文。主持国家自然科学基金青年基金项目。

报告题目3：Global weak solvability in a chemotaxis-(Navier-)Stokes system with density-suppressed motility

报告人：李中平教授，西华师范大学

报告时间：2026年10月16日（周五）10:30-11:30

报告地点：20-200

报告摘要：This talk investigates the chemotaxis-(Navier-)Stokes system with density-dependent motion in a smooth bounded domain with no-flux/no-flux/Dirichlet boundary conditions. Assuming that the motility function and the chemotactic function satisfy some structural conditions, we prove that the problem possesses a global weak solution.

报告人简介：李中平，西华师范大学数学科学学院副院长、教授，从事非线性偏微分方程和生物数学研究，四川省学术和技术带头人后备人选，四川省数学会常务理事。已在《J. Differential Equations》《Math. Nach.》《Z. angew. Math. Phys.》《数学学报》等国内外知名学术刊物上发表论文40余篇，主持国家自然科学基金项目2项、四川省教育厅重点项目1项，获得四川省数学会首届(2020年度)基础数学奖三等奖。

报告题目4：Spectral Theory for Elliptic Eigenvalue Problems with Interface Transmission Conditions

报告人：苏琳琳副教授，南方科技大学

报告时间：2026年10月16日（周五）11:30-12:30

报告地点：20-200

报告摘要：How does an interface reshape the spectrum of an elliptic operator? We study two classes of eigenvalue problems with transmission conditions across an internal interface, allowing eigenfunctions or their normal derivatives to jump. By constructing suitable weighted variational frameworks, we establish self-adjoint spectral theories, min–max characterizations, parameter dependence, limiting regimes, and Courant-type nodal bounds. We also explain how these interface conditions arise as effective models of thin layers with strong advection. The talk highlights the main ideas behind the proofs and illustrates the theory through explicit one-dimensional examples.

报告人简介：苏琳琳，本科及硕士毕业于清华大学，博士毕业于美国明尼苏达大学。曾在美国伍斯特理工学院任访问助理教授，在奥地利维也纳大学从事博士后研究。2014年加入南方科技大学，历任助理教授、长聘副教授。主要研究偏微分方程与生物数学，关注反应扩散方程的定性研究、特征值问题及其在群体遗传学和生态学中的应用。

邀请人：无穷维动力系统和偏微分方程研究所