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Scalar Curvature and Singularities

KIDD 364

Speaker: Mark Wash

A central theme in modern geometry concerns the relationship between the curvature and topology of a smooth manifold. One popular measure of curvature is the scalar curvature, and a well-studied problem is that of determining whether a given smooth manifold admits a Riemannian metric whose scalar curvature is strictly positive (PSC-metric). In the case of manifolds admitting such metrics one can ask about the topology of the space of all PSC-metrics on the underlying manifold. Over the last couple of decades many interesting results, showing non-trivial topology of this space, have been obtained. In this talk, we consider the analogous problems for manifolds with various kinds of singularities and present some recent results. This is based on joint work with Boris Botvinnik. Read more.


Numerical Solution of Double Saddle-Point Systems

TBA

Speaker: Chen Greif

Double saddle-point systems are drawing increasing attention in the past few years, due to the importance of multiphysics and other relevant applications and the challenge in developing efficient iterative numerical solvers. In this talk we describe some of the numerical properties of the matrices arising from these problems. We derive eigenvalue bounds and analyze the spectrum of preconditioned matrices, and it is shown that if Schur complements are effectively approximated, the eigenvalue structure gives rise to rapid convergence of Krylov subspace solvers. A few numerical experiments illustrate our findings. Read more.


TBD

Kidder 350

Speaker: Weinan Wang

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TBD

Speaker: Daniel Eceizabarrena

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TBD

Speaker: Sara Pollock

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