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Invariant Manifold for Random Dynamic Systems

At the invitation of the school of mathematics science of Nanjing Normal University, Professor Kening Lu, Professor of Birmingham University, USA, conducted online academic exchange in the school of mathematics of our university on the morning of June 27, 2020, and made the title of "Invariant Manifold for Random Dynamic Systems" in conference room 505 of the Xingjian building . Professor Hongjun Gao of the school of mathematics science presided over the report meeting, and some teachers of the school of mathematics science, masters and doctoral students of Applied Mathematics participated in the report meeting.

Professor Kening Lu, professor and doctoral supervisor of the Department of Mathematics, Brigham Young University, USA. In 2017, he was awarded the first "Zhang Zhifen Mathematics Achievement Award", and in 2005 he was awarded China National Outstanding Youth Science Fund (Category B). His research interests include infinite-dimensional dynamic systems, nonlinear partial differential equations, and stochastic partial differential equations. Since 1992, he has been continuously supported by the National Natural Science Foundation of America. He has been invited to make conference reports at important international academic conferences. He is the editors-in-chief of "J. Differential Equations", and editorial board of the internationally renowned academic journals, and he has published more than 80 academic papers, many of which have been published in world-class mathematics journals.

At the beginning of the lecture, Professor Lu first expounded the development history of the stochastic dynamic system, and introduced the concept of invariant sets through a simple example. Then Professor Lu introduced the work done by scholars related to local theoretical stability, instability, and central manifold of stochastic dynamic systems. Then Professor Lu introduced the general hyperbolic invariant manifold, and intuitively showed the characteristics of the hyperbolic invariant manifold. Finally, Professor Lu showed us the practical application of invariant manifolds through an example of energy gathering to the boundary.

At the end of the talk, the students and teachers here put forward their own questions about the contents of the talk, and Professor Lu gave the answers with more details. The seminar had a complete success in the warm applause of teachers and students.