报告题目：Recent progress on the mathematical theory of the inertial spin model

报 告 人：Seung-Yeal Ha 教授（韩国首尔国立大学）

报告时间：2026年4月22日（星期三）09:00—10:00

报告地点：见好就收才是赢太阳9728114（小报告厅）      

校内联系人：董久刚 教授         联系方式：84708351-8318

报告摘要：In this talk, we discuss recent progress on the flocking estimates for the inertial spin(IS) model on the three-dimensional Euclidean space, and high-dimensional generalization of the three-dimensional one. For two-dimensional case, it reduces to the inertial Kuramoto model for synchronization. For quantitative flocking estimates, we derive a system of differential inequalities for relative kinetic and spin energies, and explicitly obtain exponential flocking under the proposed frameworks. We also introduce a high-dimensional inertial spin model which generalizes the inertial spin model on three-dimensional Euclidean space and study its emergent behaviors. For the generalization of the IS model to the high-dimensional Euclidean space, we replace the cross product by the multiplication via skew-symmetric matrix, and identify a new set of constants of motions which are conserved along the proposed model. We provide two frameworks leading to the collective behaviors of the high-dimensional IS model leading to qualitative and quantitative emergent dynamics in terms of system parameters and initial data.

报告人简介：Professor Seung Yeal Ha is a professor at the Department of Mathematical Sciences, Seoul National University in Korea since 2003. He received a B.S. degree with Summa cum Laude from Seoul National University in 1997 and Ph.D. degree from Stanford University in 2001. Ha’s primary research interests are applied nonlinear analysis such as hyperbolic conservation laws, the kinetic theory of gases and collective dynamics of many-body interacting systems, application of flocking theory to finance and sociology. He has received numerous honors and awards including 14th Presidential Young Scientist Award in 2010, 17th Korea Science Prize in 2017 and KSIAM-Kumkok prize in 2023. He has given several distinguished lectures in the past such as a plenary talk at 1st Asian Mathematics Conference in 2013, and invited talk at ICM 2014, and a plenary talk at HYP 2014 (the largest conference in the hyperbolic problems) and keynote lecture at 32nd International Symposium on Rarefied Gas Dynamics in 2022. He is currently a member of the Korean Academy of Science and Technology.