学术报告

题目：Moving Frames and Their Applications

报告人：Prof. Peter J. Olver (SIAM Fellow, AMS Fellow, Head of School of Mathematics, University of Minnesota)

校内联系人: 张超(84708351-8136); 校外联系人:李玮(大连海洋大学, wwli1230@163.com)

时间：2015年7月31日（周五）14：30－15：30

地点：创新园大厦A1101

报告摘要：The classical method of moving frames was developed by Elie Cartan into a powerful tool for studying the geometry of submanifolds under certain geometrical transformation groups. In this talk, I will present a new foundation for moving frame theory based on equivariant maps. The method is completely algorithmic, and applies to very general Lie group actions and even infinite-dimensional pseudo-groups.  It has led to a wide variety of new applications, ranging over classical differential geometry, differential equations, the calculus of variations, geometric flows, image processing, invariant numerical algorithms, invariant theory, and elsewhere.  The talk will survey the key ideas, and present some of the principal applications.

报告人简介：Peter J. Olver received his Ph.D. from Harvard University in 1976 under the guidance of Prof. Garrett Birkhoff. After being a Dickson Instructor at the University of Chicago and a postdoc at the University of Oxford, he has been on the faculty of the School of Mathematics at the University of Minnesota since 1980, and a full professor since 1985. As of July, 2008, he has been serving as the Head of the Department. He has supervised 20 Ph.D. students to date, as well as mentoring 21 postdocs and visiting students.

His research interests revolve around the applications of symmetry and Lie groups to differential equations. Over the years, he has done research in fluid mechanics, elasticity, quantum mechanics, mathematical physics, Hamiltonian mechanics, the calculus of variations, differential geometry, classical invariant theory, computer vision, and geometric numerical methods. He is the author of over 130 papers in refereed journals, and was named a "Highly Cited Researcher" by Thomson-ISI in 2003.  He is the author of 5 books, including the definitive text on applications of Lie groups to differential equations, which was published in 1986, translated into Russian, and also republished in China. His most recent book is an undergraduate text on partial differential equations, published by Springer in 2014.