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Colloquium: Sebastian Acosta (Baylor College of Medicine and Texas Children’s Hospital)

Tuesday, January 20
4:00 PM
135 TMCB

Title: Inverse Problems and Geometry

Abstract: Geometric notions have played a significant role in understanding inverse problems for partial differential equations (PDE) with applications in mathematical physics, geophysics and medical imaging. Such inverse problems are as follows: For a Riemannian manifold with boundary, find its metric from knowledge of the boundary Cauchy data of all the solutions to a PDE defined on the manifold. Some of the PDEs of interest are Laplace, wave, diffusion, elastic, Maxwell, Schrodinger or Dirac equations. This problem cannot be solved in general; so it is the mathematician’s task to find reasonable conditions under which the problem becomes tractable.