Research

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

1. Weyl's Law for singular Riemannian foliations, with applications to invariant theory (with S. Lin and R. Mendes), accepted in Geometry & Topology (2025). [arXiv] 

2. Rational ellipticity of G-manifolds from their quotients (with E. Khalili Samani), Compositio Math  161 (2025), 244–256 [arXiv].

3. On the topology of leaves of singular Riemannian foliations (with E. Khalili Samani), Rev. Mat. Iberoam. 40 (2024), no. 1, 111-128. [arXiv]

4. On the structure of Besse convex contact spheres (with M. Mazzucchelli), Trans. AMS 376 (2023), 2125-2153. [arXiv]

5. Maximality of Laplacian algebras, with applications to invariant theory (with R. Mendes), Annali di Matematica Pura ed Applicata 202 (2023), 1011–1031. [arXiv]

6. How highly connected can an orbifold be? (with C. Lange), Rev. Mat. Iberoam. 39 (2023), no. 6, pp. 2171–2186. [arXiv]

7. Polar foliations on symmetric spaces and mean curvature flow (with X. Liu), Journal für die reine und angewandte Mathematik (Crelles Journal) (2022), no. 791, 135-155.

8. Odd dimensional orbifolds with all geodesics closed are covered by manifolds (with M. Amann and C. Lange), Math. Ann. 380 (2021), 1355–1386. [arXiv]

9. Virtual immersions and minimal hypersurfaces in compact symmetric spaces (with R. Mendes), Calc. Var. PDEs 192 (2020). https://doi.org/10.1007/s00526-020-01854-x. [arXiv]

10. Torus actions on rationally elliptic manifolds: rank and rigidity (with M. Kerin and F. Galaz-Garcia), Math. Z 297 (2021), 197-221. [arXiv]

11. Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem (with R. Mendes), Geom. Funct. Anal. (GAFA) 30 (2020), 536-573. [arXiv]

12. Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces (with R. Mendes and C. Gorodski), Calc. Var. PDEs 58 (2019). https://doi.org/10.1007/s00526-019-1552-x. [arXiv]

13. Singular Riemannian foliations and their quadratic basic polynomials (with R. Mendes), Transf. Groups 25 (2019), no. 1, 251-277. [arXiv]

14. Virtual immersions, and a characterization of symmetric spaces (with R. Mendes), Ann. Glob. Anal. Geom. (AGAG) 55 (2019), no 1, 43–53. [arXiv]

15. A slice theorem for singular Riemannian foliations, with applications (with R. Mendes), Trans. AMS 371 (2019), no. 7, 4931–4949. [arXiv]

16. A note on the Petersen-Wilhelm Conjecture (with D. Gonzalez-Alvaro), Proc. Amer. Math. Soc. 146 (2018), no. 10, 4447–4458. [arXiv]

17. On the Berger conjecture for manifolds all of whose geodesics are closed (with B. Wilking), Invent. Math. 210 (2017), no. 3, 911–962. [arXiv]

18. Closure of singular foliations: the proof of Molino’s Conjecture (with M. Alexandrino), Compos. Math. 153 (2017), no. 12, 2577-2590. [arXiv]

19. 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]

20. Smoothness of isometric flows on orbit spaces and applications (with M. Alexandrino), Transf. Groups 22 (2017), no. 1, 1–27. [arXiv]

21. Algebraic nature of singular Riemannian foliations in spheres (with A. Lytchak), J. Reine Ang. Math. (Crelle) 744 (2018), 265–273. [arXiv]

22. On homogeneous composed Clifford foliations (with C. Gorodski), Münster J. Math. 9 (2016), 35–50. [arXiv]

23. Mean curvature flow of singular Riemannian foliations (with M. Alexandrino), J. of Geom. Anal. 26 (2016), no. 3, 2204–2220. [arXiv]

24. Singular Riemannian foliations and applications to positive and nonnegative curvature (with F. Galaz-Garcia), J. Topol. 8 (2015), no. 3, 603–620. [arXiv]

25. Differentiable classification of 4-manifolds with singular Riemannian foliations (with J. Ge), Math. Ann. 363 (2015), no. 1-2, 525–548. [arXiv]

26. Clifford algebras and new singular Riemannian foliations in spheres, Geom. Funct. Anal. (GAFA) 24 (2014), no. 5, 1660–1682. [arXiv]

27. 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]

• Isoparametric foliations and bounded geometry (with M. Krannich and A. Lytchak). [arXiv]

• Positive curvature and rational ellipticity in cohomogeneity three (with E. Khalili Samani). [arXiv]