Research

Research Interests

Differential Geometry and Geometric Analysis. In particular, Lie group actions on manifolds and the Ricci flow on cohomogeneity one manifolds.

Publications and Preprints

  1. Prescribing Ricci curvature on a Product of Spheres [with T. Buttsworth]
    Ann. Mat. Pura Appl., to appear. arXiv:2010.05118
  2. Diagonalizing the Ricci tensor
    J. Geom. Anal., to appeararXiv:1912.12686
  3. Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature [with R. G. Bettiol]
    Comm. Anal. Geom., 27 (2019), no. 3, 511–527. arXiv:1606.00778
  4. Making Matrices Better : Geometry and topology of polar and singular value decomposition [with D. DeTurck, A. Elsaify, H. Gluck, B. Grossmann, J. Hoisington, J. Zhang]
    Notices Amer. Math. Soc., 64 (2017), no. 8, 876–886. arXiv:1702.02131 Published version