Research
Interests
My research interests are in global Riemannian geometry and global analysis. In particular, I am interesting in finding connections between geometric and topological information of spaces using symmetry or variational methods.
In my recent projects, I focus on:
lower curvature bounds (e.g. positive or non-negative sectional curvature, Ricci curvature, or intermediate Ricci curvature),
isometric Lie group actions (e.g. torus symmetry, symmetric spaces, homogeneous spaces),
geometric inequalities and extremum problems (e.g. relative isoperimetric problem, Bang's affine-invariant plank problem).
I am also interested in synthetic notions of curvature on singular spaces, convergence of spaces with curvature bounds, and stability of minimal submanifolds.
Publications and Preprints
Positive intermediate Ricci curvature with maximal symmetry rank, with Lee Kennard, Journal of Geometric Analysis, 34(129), 2024. DOI: 10.1007/s12220-024-01575-z.
On the relative isoperimetric problem for the cube, with Gregory R. Chamber, preprint, arXiv:2302.04382, Feb 2023, submitted.
A note on the affine-invariant plank problem, with Gregory R. Chambers, preprint, arXiv:1604.00456, Jul 2021, submitted.
Torus actions on manifolds with positive intermediate Ricci curvature, Journal of the London Mathematical Society ,106(4):3792–3821, 2022. DOI: 10.1112/jlms.12674
Infinite families of manifolds of positive kth-intermediate Ricci curvature with k small, with Miguel Domínguez-Vázquez and David González-Álvaro, Mathematische Annalen, 386:1979--2014, 2023. DOI: 10.1007/s00208-022-02420-w
Local symmetry rank bound for positive intermediate Ricci curvatures, Geometriae Dedicata 216(23), 2022. DOI: 10.1007/s10711-022-00686-7
Dissertation
Positive intermediate Ricci curvature with symmetries, University of California, Riverside, June 2020. [errata]
Presentations
Research Seminars & Conferences:
Mar 2024: Department Colloquium, Trinity University.
Feb 2024: Geometry and Topology Seminar, Durham University.
Jan 2024: Department Colloquium, Bowdoin College.
Jan 2024: Geometry and Topology Seminar, University of Waterloo.
Jan 2024: JMM AMS Contributed Papers Session.
Nov 2023: Topology/Geometry Zoom Seminar, University of Oregon. [slides]
Nov 2023: Lefschetz Geometry & Geometric Analysis Seminar, Clark University.
Aug 2023: Workshop on Curvature and Global Shape, Universität Münster. [notes]
Apr 2023: Upper New York State Geometric Analysis Workshop, Cornell.
Mar 2023: Midwest Geometry Conference, KSU.
Feb 2023: CUNY Geometric Analysis Seminar.
Jan 2023: JMM AMS Special Session: New Developments in Diff. Geom. and Top.
Apr 2022: JMM MSRI Special Session: Metric geometry and topology.
Mar 2022: UC Berkeley Differential Geometry Seminar.
May 2021: AMS Special Session, Western Sectional Meeting, SFSU.
Sep 2020: University of Oregon Topology/Geometry Zoom Seminar.
Aug 2020: 2020 Virtual Workshop on Ricci and Scalar Curvature.
Mar 2020: University of Oklahoma Geometry & Topology Seminar.
Jan 2020: JMM AMS Special Session on Diff. Geom. and Global Analysis, Denver, CO.
Nov 2019: Syracuse University Geom. and Top. Seminar.
Nov 2019: AMS Special Session, Western Sectional Meeting, UCR.
Oct 2018: Felix Klein Seminar, Univ. of Notre Dame.
May 2018: Math Connections conference.
Apr 2018: Graduate Student Topology and Geometry Conference.
UCR Seminars & Courses:
The Connectivity Principle - UC Riverside Differential Geometry Seminar, May 2019.
Grove-Shiohama diameter sphere theorem - UC Riverside Riemannian Geometry course, March 2018.
Fundamental equations of Riemannian submersions - UC Riverside Riemannian Geometry course, February 2018.
Deformations and Non-negative Curvature - UC Riverside Math Grad Seminar, December 2017.
Morse theory and distance functions - UC Riverside Math Grad Seminar, January 2017.
Metric structure of Cheeger deformations - Oral exam presentation, January 2017.
What is comparison geometry? - UC Riverside Math Grad Seminar, October 2016.
Hausdorff and Gromov-Hausdorff distance - UC Riverside Comparison Geometry course, January 2016.
Milnor's proof of the fundamental theorem of algebra - UC Riverside Geometry Group meeting, April 2015.
Nets and filters - UC Riverside Graduate Seminar, April 2015.
Links to my pages on other platforms
Cajun Geometer - a WordPress blog
Recommended resources made by others
List of Women Geometers - Never let organizers claim that "there are no women in geometry." - compiled and maintained by Catherine Searle
Virtual seminar on geometry with symmetries - virtual research seminar on the topic of Lie group actions in Riemannian geometry
Open problems in non-negative sectional curvature - list compiled by Martin Kerin at the Workshop on Manifolds with Non-negative Sectional Curvature held at the American Institute of Mathematics in 2007