武汉大学数学与统计学院05月19日——05月25日学术报告通知一览

05.20

Multi-solitons and blow-up of Hartree equations

报告人：吴雨桐（耶鲁大学）

报告时间：2026年05月20日 10:00--11:00

报告地点：数学与统计学院A644报告厅

报告摘要:

I will present a series of papers in which we constructed multi-soliton solutions to the Hartree equation in the $L^2$-subcritical (3D) and $L^2$-critical (4D) settings. In these solutions, the soliton centers evolve according to an effective N-body system. This work generalized and improved the 2009 result of Krieger–Martel–Raphaël, which constructed two-soliton solutions for the three-dimensional Hartree equation. In four dimensions, our results further imply the existence of multi-point pseudo-conformal blow-up via the pseudo-conformal symmetry.

05.22

图上的分数阶拉普拉斯算子

报告人：杨云雁 教授（中国人民大学）

报告时间：2026年05月22日 09:00--10:00

报告地点：数学与统计学院A446报告厅

报告摘要:

在这个报告中，我先介绍图的基本概念，包括有限图与局部有限图，然后引入分数阶拉普拉斯算子的定义，阐述此类算子的一些分析性质，并讨论若干涉及分数阶拉普拉斯算子的非线性方程解的存在性问题。该内容基于我近期与我的博士生张梦杰、清华大学林勇教授合作的研究成果。

报告人简介：

杨云雁，中国人民大学教授，博士生导师，获教育部2008年度新世纪优秀人才支持计划，主要研究流形上的偏微分方程，图上的分析，目前已（合作）发表学术论文80余篇，部分发表在J. Functional Analysis, Calc. Var. PDE, J. Differential Equations。

05.22

Ricci flow of graphs and its applications in real-world networks

报告人：赵亮 教授 （北京师范大学）

报告时间：2026年05月22日 10:10--11:10

报告地点：数学与统计学院A446报告厅

报告摘要:

We first introduce the theoretical framework of Ollivier Ricci curvature and the curvature flow on graphs. Next, we briefly present several recent advances at the intersection of graph geometry and real-world problems. In particular, we introduce the Geometric Evolution Graph Convolutional Network (GEGCN), a novel framework that enhances graph representation learning through explicit modeling of geometric evolution on graph structures. Extensive experiments demonstrate that GEGCN achieves excellent performance on classification tasks across various benchmark datasets, including homophilic/heterophilic graphs, filtered graphs, and large-scale graphs.

The report is based on collaborative works with Ma Jicheng, Tian Yulu, Yang Yunyan and Zhao Juan.

报告人简介：

赵亮，北京师范大学数学科学学院，教授, 博士生导师。研究方向为非线性分析及其在交叉领域的应用，已在JMPA、CVPDE、JDE、PRE、Sci. China Math.等期刊发表论文30余篇，含多篇ESI高被引论文，出版专著或教材7部。

05.22

TWIST DYNAMICS IN THE SPATIAL ISOSCELES THREE-BODY PROBLEM

报告人：胡锡俊  教授（山东大学）

报告时间：2026年05月22日 10:30--11:30

报告地点：数学与统计学院A644报告厅

报告摘要:

We study dynamical constraints arising from Embedded Contact Homology (ECH) in the spatial isosceles three-body problem. For energies below the critical level, the dynamics on the energy surface is identified with a Reeb flow on the tight three-sphere. We obtain quantitative estimates for the Euler orbit, including monotonicity of its transverse rotation number and a strict inequality comparing its action with the contact volume. Combined with the ECH classification of Reeb flows on the tight three-sphere with two simple periodic orbits, these estimates rule out the two-orbit scenario, thus forcing every compact energy surface below the critical level to have infinitely many periodic orbits. The result admits a dynamical interpretation via disk-like global surfaces of section bounded by the Euler orbit. In this setting, the rotation number and the contact volume define a non-trivial twist interval which encodes the relative winding of periodic orbits.

This talks based on joint works with  Lei Liu, Yuwei Ou, Zhiwen Qiao, Pedro A. S. Salomão, and Guowei Yu.

05.22

针对复杂概率模型的近似贝叶斯推断

报告人：汪时嘉 助理教授（上海科技大学数学科学研究所）

报告时间：2026年05月22日 15:00--16:00

报告地点：数学与统计学院A349报告厅

报告摘要:

近似贝叶斯计算（Approximate Bayesian computation，简称ABC）是一类用于处理似然函数不可得或难以计算的问题的贝叶斯推断算法。它通过从模拟模型中生成的合成数据来逼近后验分布。然而，对于复杂模型而言，ABC的计算量非常大。在本报告中，我将介绍一些先进的近似贝叶斯计算方法，旨在克服这些计算瓶颈。

报告人简介：

汪时嘉博士是上海科技大学数学科学研究所的助理教授、研究员、博士生导师。 先后于武汉大学获得硕士学位、加拿大西蒙佛雷泽大学获得统计学博士学位，2019—2023年在南开大学任教。研究兴趣主要包括贝叶斯统计、统计机器学习以及进化生物学等。现担任 Statistics and Computing 编委（Associate Editor）。

05.24

The high-order energy-preserving method for the long-time dynamics

报告人：宋怀玲 教授（湖南大学）

报告时间：2026年05月24日 15:00--16:00

报告地点：数学与统计学院A644报告厅

报告摘要:

The numerical methods are provided for the long-time dynamics Double Sine-Gordon equation (DSGE), while the nonlinearity is characterized by β/εwith small parameter ε\in(0,1] and interaction parameterβ\in(0,+∞). In comparison to the Sine-Gordon equation, DSGE has many properties of solitons as well as its own unique new features. In this talk, a family of novel energy-preserving schemes are presented for numerically solving the DSGE. These schemes are constructed by using an auxiliary variable in the integrating factor Runge-Kutta (IFRK) method. In virtue of the auxiliary variable, the proposed method is high-order accurate, preserves the original discrete energy through the solution of only one scalar equation per time step, while the previous energy-preserving schemes for long-time dynamics are usually implicit. Meanwhile, the improved uniform error bounds are proved. Numerical experiments demonstrate that our schemes exhibit superior long-time energy conservation and accuracy, with excellent performance in simulating the solitons dynamics of both DSG and SG equations.

报告人简介：

宋怀玲，湖南大学数学学院教授，博士生导师，从事数学理论、计算方法和高效数值算法的教学和科研工作。本科与博士均毕业于山东大学，主要研究兴趣包括相场模型、相场耦合模型、非局部模型和多孔介质两相流问题的高阶数值方法的建立以及模型约化与应用等。相关研究成果发表在Computer Methods in Applied Mechanics and Engineering、Journal of Computational Physics、Journal of Scientific computing、Communications in Computational Physics等计算数学国际期刊，主持了包括国家自然科学基金，天元数学交流项目，湖南省面上项目等。