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Applications of Lie groups to differential equations Peter J. Olver
Publisher: Springer-Verlag

Section VIII covers Lie groups and their applications. Dynamical systems and applications to physics; exponential asymptotics. Preferred qualifications: research interests which are compatible with the need and interests of the department, including combinatorics, complex dynamics, differential equations, functional analysis, Lie groups, numerical analysts, and (Tel: 765-285-8640; Fax: 765-285-1721; Email: amohammed@bsu.edu --insert “Mathematics Position” in the subject line) Review of completed applications will begin December 15, 2012, and will continue until the position is filled. Here differential geometry is developed. ABSTRACT : In this lecture , I plan to make a historical review of the infinite-dimensional Lie groups , more properly called now "pseudo-groups" after Ehresmann . There is also a good article on the subject,. Olver 108 Holomorphic Functions and Integral Representations in Several Complex Variables, R. Applications of Lie groups to differential equations by Peter J. 107 Applications of Lie Groups to Differential Equations, Peter J. Http://www.cds.caltech.edu/~marin/pubs/KoCrDe2008.pdf. The book contains exercises and plenty of worked examples. Erlangen Program and Discrete Differential Geometry ABSTRACT : It is remarkable that the revolutionary ideas of Klein and Lie in geometry and differential equations have had so little influence in the teaching of mathematics at the university level up to the present time. Professor Keith Ball Functional Analysis, High-dimensional and Discrete Group theory, groups of Lie type, finite simple groups. Topics include: Lie groups & Lie algebras, differential geometry (vector fields, Riemannian metrics, covariant derivatives, geodesics, Killing vector fields), Lie groups and differential equations and the calculus of variations. Within this section general relativity is briefly discussed as is Noether's theorem. Dr Colm Connaughton Non-equilibrium statistical mechanics, fluid Numerical and applied analysis of partial differential equations; free boundary problems; computational applied mathematics.