The main focus of my research is the geometry and topology of Riemannian manifolds with either non-negative or positive sectional curvature, often under an additional symmetry assumption. As the Bott Conjecture asserts that such manifolds are rationally elliptic, I am also interested in related questions in rational homotopy theory.
Publications
- (with J. DeVito and F. Galaz-García) Manifolds that admit a double disk-bundle decomposition, Indiana Univ. Math. J. (2023), PDF
- (with F. Galaz-García and M. Radeschi) Torus actions on rationally elliptic manifolds, Math. Z. (2021), PDF
- (with S. Goette and K. Shankar) Highly connected 7-manifolds and non-negative sectional curvature, Ann. of Math. (2020), PDF
- (with S. Goette and K. Shankar) Fake lens spaces and non-negative sectional curvature, Proceedings of the Australian-German Workshop on Differential Geometry in the Large, Cambridge Univ. Press (2020), PDF
- (with J. Harvey and K. Shankar) Semi-free actions with manifold orbit spaces, Documenta Math. (2020), PDF
- (with S. Goette and K. Shankar) Non-negative curvature and the linking form, Oberwolfach Rep. (2018), Geometrie
- (with F. Galaz-García, M. Radeschi and M. Wiemeler) Torus orbifolds, slice-maximal torus actions and rational ellipticity, Int. Math. Res. Not. IMRN (2018) PDF
- (with S. Goette and K. Shankar) Non-negative sectional curvature on exotic 7-spheres, Oberwolfach Rep. (2016), Geometrie
- (with F. Galaz-García) Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension, Math. Z. (2014) PDF
- A note on totally geodesic embeddings of Eschenburg spaces into Bazaikin spaces, Ann. Glob. Anal. Geom. (2013) PDF
- (with K. Shankar) Riemannian submersions from simple, compact Lie groups, Münster J. of Math. (2012) PDF
- On the curvature of biquotients, Math. Ann. (2012) PDF
- Some new examples with almost positive curvature, Geom. Top. (2011) PDF
- (with J.-H. Eschenburg) Almost positive curvature on the Gromoll-Meyer sphere, Proc. Amer. Math. Soc. (2008) PDF
- (with D. Wraith) Homogeneous metrics on spheres, Irish Math. Soc. Bull. (2003) PDF
Preprints
- (with S. Goette and K. Shankar) Highly connected 7-manifolds, the linking form and non-negative sectional curvature, PDF
In preparation
- (with D. Corro and F. Galaz-García) Smooth 2-torus actions on the 5-sphere
- (with J. DeVito and F. Galaz-García) Obstructions to double disk-bundle decompositions
- (with J. DeVito) Rational spheres and double disk-bundles