Research Activity

The geometry and topology group at UConn covers a broad spectrum of research directions including

• Differential Geometry: complex geometry, foliation theory, infinite-dimensional geometry, and Riemannian, sub-Riemannian, and pseudo-Riemannian geometryGeometric Analysis: geometric flows, geometric partial differential equations, heat kernel analysis, and mathematical general relativity
• Geometric and Functional Inequalities (on manifolds and metric measure spaces): RCD spaces, Sobolev inequalities, isoperimetric inequalities, curvature dimension inequalities
• Geometric Topology: applications of computational topology to computer animation, scientific visualization, and engineering design
• Interconnections with other fields: algebra and number theory, algebraic geometry, analysis, mathematical physics, numerical analysis, and probability

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