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

If a Lie group G acts smoothly on a smooth manifold M , its Lie algebra acts by differential operators on the space C^{infty}(M) of smooth functions, and these differential operators are the “infinitesimal generators” which give us conserved quantities for the evolution of a quantum system on M (in the case that G . Applications of Lie groups to differential equations by Peter J. Chafai, Toulouse: Spectral analysis of large random Markov chains D. Professor Keith Ball Functional Analysis, High-dimensional and Discrete Group theory, groups of Lie type, finite simple groups. Applebaum, Sheffield: Spectral properties of semigroups of measures on Lie groups. This differential equation at least formally admits the solution. Dr Colm Connaughton Non-equilibrium statistical mechanics, fluid Numerical and applied analysis of partial differential equations; free boundary problems; computational applied mathematics. There is also a good article on the subject,. Roeckner, Bielefeld: Self-organized criticality via stochastic partial differential equations. Krasovsky, Brunel and Imperial college: Toeplitz determinants and their applications. Http://www.cds.caltech.edu/~marin/pubs/KoCrDe2008.pdf. Pistorius, Imperial College: Maximum increments of random walks and M. Dynamical systems and applications to physics; exponential asymptotics.