Mathematics Colloquia and Seminars

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I discuss my current research in the area of General Relativity and Shock Wave Theory. Jeff Groah and I were the first to establish the Glimm scheme of shock wave theory could be implemented in General Relativity, and the resulting shock wave solutions of the Einstein equations appeared “singular” at shock waves in the coordinate systems in which the Glimm analysis was feasible. Recently Moritz Reintjes and I have established that these “singularities” can always be removed by coordinate transformation. The coordinate transformations are determined by a new system of elliptic PDE’s we named the RT-equations. The elliptic RT-equations thus regularize non-optimal solutions of the hyperbolic Einstein equations. I will discuss the problems I am working on in General Relativity and Shock wave theory, with an emphasis on this new result.