Abstract:  Beginning with the Manhattan project during World War II, Los Alamos has pioneered the field of precision high explosives.  A brief overview of high explosives and detonation propagation experiments and theory will be presented.  Mathematical models and the resulting computational challenges will be discussed.  Some resultant advanced computational methods will be described.  One such recently devised algorithm, the Runge-Kutta-Legendre (RKL) method for explicit efficient integration of parabolic and mixed parabolic/hyperbolic partial differential equations, will be discussed in detail.  RKL computational examples from a broad range of science and engineering fields will be presented. Short Bio:  I received my B.S. in mechanical engineering from the University of Notre Dame in 1991, and my M.S. (1993) and PhD (1996) in Theoretical and Applied Mechanics from the University of Illinois.  I have been a scientist at Los Alamos National Laboratory since 1997.  I have made contributions to several aspects of detonation theory and also contributed to the broader field of computational fluid dynamics.  Some of the methods I've developed or co-developed over the years: Level Set methods for detonation propagation, The Ghost Fluid Method, Mapped Weighted Essentially Non-Oscillatory schemes, Level Set Tracking of discontinuities for conservation laws, Runge-Kutta-Legendre time integration.  I have also taught a course in Level Set Methods at Cambridge University (2012) and at Notre Dame (2010). Host:  Prof. Frederic Gibou