### Research interest

Foliations on Riemannian manifolds.

Isometric Lie group actions on Riemannian manifolds.

Manifolds with positive/non-negative curvature.

Closed geodesics/Immersed minimal surfaces in Riemannian manifolds.

### published articles

*Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces*(with R. Mendes and C. Gorodski), to appear in**Calc. Var. PDEs**(2019)*.*[arXiv]*Singular Riemannian foliations and their quadratic basic polynomials*(with R. Mendes), to appear in**Transf. Groups**(2019). [arXiv]Virtual immersions, and a characterization of symmetric spaces

*(with R. Mendes),***Ann. Glob. Anal. Geom.**() 55 (2019), no 1, 43–53. [arXiv]*AGAG**A slice theorem for singular Riemannian foliations, with applications**(with R. Mendes),***Trans. AMS**371 (2019), no 7, 4931–4949. [arXiv]A note on the Petersen-Wilhelm Conjecture

*(with D. Gonzalez-Alvaro)*,146 (2018), no. 10, 4447–4458. [arXiv]*Proc. Amer. Math. Soc.*Metrics on spheres all of whose geodesics are closed

*(with B. Wilking)*,**Invent. Math.**210 (2017), no. 3, 911–962. [arXiv]Closure of singular foliations: the proof of Molino’s Conjecture

*(with M. Alexandrino)*,**Compos. Math.**153 (2017), no. 12, 2577-2590. [arXiv]Torus orbifolds, rational ellipticity and non-negative curvature

*(with M. Kerin, F. Galaz-Garcia and M. Wiemeler)*,**Int. Math. Res. Not.**18 (2018), 5786–5822. [arXiv]Smoothness of isometric flows on orbit spaces and Molino’s conjecture

*(with M. Alexandrino)*,**Transf. Groups 22**(2017), no. 1, 1–27. [arXiv]Algebraic nature of singular Riemannian foliations in spheres

*(with A. Lytchak)*,**J. Reine Ang. Math. (Crelle)**744 (2018), 265–273. [arXiv]On homogeneous composed Clifford foliations

*(with C. Gorodski)*,**Münster J. Math.**9 (2016), 35–50. [arXiv]Mean curvature flow of singular Riemannian foliations

*(with M. Alexandrino)*,**J. of Geom. Anal.**26 (2016), no. 3, 2204–2220. [arXiv]Singular Riemannian foliations and applications to positive and nonnegative curvature

*(with F. Galaz-Garcia)*,**J. Topol.**8 (2015), no. 3, 603–620. [arXiv]Differentiable classification of 4-manifolds with singular Riemannian foliations

*(with J. Ge)*,**Math. Ann.**363 (2015), no. 1-2, 525–548. [arXiv]Clifford algebras and new singular Riemannian foliations in spheres,

**Geom. Funct. Anal. (GAFA)**24 (2014), no. 5, 1660–1682. [arXiv]Isometries between leaf spaces

*(with M. Alexandrino)*,**Geom. Dedicata**174 (2015), no. 1, 193–201. [arXiv]

### Preprints

Low dimensional singular Riemannian foliations in spheres. [arXiv]

Torus actions on rationally elliptic manifolds: rank and rigidity

*(with M. Kerin and F. Galaz-Garcia)*. [arXiv]Generalized immersions and minimal hypersurfaces in compact symmetric spaces

*(with R. Mendes)*. [arXiv]Odd dimensional orbifolds with all geodesics closed are covered by manifolds (with M. Amann and C. Lange). [arXiv]

Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem (with R. Mendes)