I will present a recent result, joint with Maria Gordina and Laurent Saloff-Coste, showing that there is a uniform volume doubling constant for all left-invariant Riemannian geometries on the compact Lie group SU(2). This implies uniformity in a wide variety of functional inequalities for this family of geometries, including eigenvalue bounds for the Laplacian, heat kernel estimates, and more. Classical estimates based on curvature are not available in this setting, since there is no uniform lower bound on the Ricci curvatures of these metrics. A key idea in the proof is to study the size and shape of metric balls by a careful analysis of the Campbell--Baker--Hausdorff--Dynkin--Strichartz formula. We conjecture that the same uniform doubling result holds for every compact connected Lie group.
A preprint is available at https://arxiv.org/abs/1708.03021
Uniform volume doubling for left-invariant geometries on SU(2) Sponsored by the Meyer Fund
Mar. 01, 2018 2pm (MATH 350)
Functional Analysis
Karen Strung (Radboud Universiteit, Netherlands)
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Results from the Elliott classification program can be used to translate theorems of optimal transport into calculations of the distance between unitary orbits of normal elements in well-behaved -algebras. In particular, in certain simple Jiang-Su stable -algebras with real rank zero and trivial , the distance between full-spectrum unitaries can be computed in terms of spectral data. This talk is based on joint work with Bhishan Jacelon and Alessandro Vignati.
Unitary Orbits via Transportation Theory Sponsored by the Meyer Fund