I am currently a Doctoral-stream Master's in Mathematics Student at the University of Toronto. I am working in the field of geometric analysis. Currently I am studying geometric measure theory under the supervision of Professor Yevgeny Liokumovich. I am primarily interested in optimal/canonical objects and geometric rigidity problems.
Geometric analysis is primarily the study of geometric and topological questions through analytic methods. This in many ways starts with the foundation of differential geometry, through Riemann's original proof that a shape is locally flat if and only if a certain partial differential equation holds locally. The use of modern analytic techniques date back to at least the mid 1940's with Hodge discovering that there is an equivalence between solutions of the Laplacian on forms, which is a specific PDE, and the holes in a shape. There has been a great amount of recent work done by many individuals in areas including geometric elliptic PDEs such as Monge-Ampere equations, geometric flows such as the Ricci flow, and geometric measure theory and the study of minimal surfaces.
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