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Geometric Analysis and Partial Differential Equations Seminar
June 7, 2013 @ 10:30 am - 11:30 pm
Mr Lashi Bandara (The Australian National University)
Geometry and the Kato square root problem
Since the resolution of the Kato square root problem on Euclidean space in 2002, there have been a number of developments in the understanding of versions this problem on manifolds and Lie groups. There have been a number of positive results for uniformly elliptic divergence form operators, for perturbations of the inhomogeneous Hodge-Dirac operator, and in the setting of Lie groups, uniformly sub-elliptic operators. I will talk about these results, their connection to PDE, and in particular, possible connections to geometric flows.