RESEARCH

RESEARCH INTEREST

  • Differential Geometry

  • Metric Foliations

  • Geometric Analysis


  • Geometric and Differential Topology

  • Group Actions

  • Geometric Group Theory

PUBLICATIONS

  1. Yamabe problem in the presence of singular Riemannian Foliations (with Juan Carlos Fernández and Raquel Perales)
    arXiv:2202.13109 [math.AP], to appear in Calc. Var. Partial Differential Equations.

  2. Core reduction for singular Riemannian foliations in Positive Curvature (with Adam Moreno) arXiv:2011.05303 [math.DG], to appear in Ann. Global Anal. Geom., 2022.

  3. Torus actions on Alexandrov 4-spaces (with Jesús Núñez-Zimbrón, and Masoumeh Zarei) arXiv:1902.09402 [math.DG], in J. Geom. Anal. 32, 214, 2022.

  4. Short survey on the existence of slices for the space of Riemannian metrics (with Jan-Bernhard Kordaß) arXiv:1904.07031 [math.DG], in Contemporary Mathematics, vol. 75, "Mexican Mathematicians in the World: Trends and Recent Contributions", pp. 65-84, 2021.

  5. Bundles with even-dimensional spherical space form as fibers and fiberwise quarter pinched Riemannian metrics (with Martin Günther, Karla Garcia, and Jan-Bernhard Kordaß), arXiv:2004.02518 [math.GT] Proc. A. M. S., vol. 149, (12), pp. 5407-5416, 2021.

  6. Integral foliated simplicial volume and circle foliations (with Caterina Campagnolo) arXiv:1910.03071 [math.GT], in J. Topol. Anal., 2020.

  7. Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions (with Fernando Galaz-Garcia), arXiv:1609.06125 [math.DG] in Proc. A. M. S., vol. 148, (7), pp. 3087–3097, 2020.


PREPRINTS

  1. A-Foliations of codimension two on compact simply-connected manifolds
    arXiv:1903.07191 [math.DG].

IN PREPARATION

  1. Smooth 2-torus actions on the 5-sphere, andnonnegative curvature (with Fernando Galaz-Garica and Martin Kerin).

  2. Myres-Steenrod theorem for metric submetries and applications to singular Riemannian foliations (with Fernando Galaz-Garcia).

SELECTED TALKS

  • 2022 - "Symmetry-preserving solutions to the Yamabe Problem", at the Virtual Seminar of Geometry with Symmetries, Darthmouth College-University of Queensland-Universidad Nacional del Sur (US-Australia-Argentina).

  • 2022 - “Reduction of singular Riemannian foliations and how to detect boundary of the leaf space”, at the Workshop on Geometry of Spaces with Upper and Lower Curvature Bounds of the Thematic Program on Nonnsmooth Riemannian andLorenzian Geometry, Fields Institute (Canada).

  • 2021 - "Quarter pinched spherical space forms bundles and Ricci flow”at the Young Geometers Meeting, Københavns Universitet (Denmark).

  • 2021 - "Singular Riemannian foliations and topological rigidity" at the Modern Techniques in Riemannian geometry, UNAM–Durham University (Online).

  • 2020 - “Foliated simplicial volume and circle foliations" at the Workshop on Simplicial volumes and bounded cohomology, Universität Regensburg (Germany).

  • 2019 - “Manifolds with singular Riemannian foliations by aspherical leafs" at Ibero- American Geometry Meeting, Universidad de Granada (Spain).

  • 2019 - “Manifolds with singular Riemannian foliations by aspherical leafs" at SPP 2026-Geometry at Infinity Conference, Münster (Germany).

  • 2018 - “Ricci positive curvature in Manifolds with large torus actions" at Mexican Mathematicians in the World: Perspectives and Recent Contributions IV, held at BIRS’ Casa Matemática Oaxaca (Mexico).

  • 2018 - "Ricci positive curvature in Manifolds with large torus actions" at the Graduate Student Topology and Geometry Conference, University of Illinois at Chicago (US).

  • 2018 - “Manifolds with singular Riemannian foliations by aspherical leafs" at the Felix Klein Seminar, Notre Dame University (US).

  • 2017 - “Ricci positive curvature in Manifolds with large torus actions" at the 2017 Dual meeting between the Royal Spanish Mathematical Society (RSME) and the Mexican Mathematical Society (SMM), Valladolid (Spain).

  • 2017 - “Ricci positive curvature in Manifolds with large torus actions" at the 2017 Workshop on Curvature and Global Shape, Universität Münster (Germany).