Dr. Catherine Searle PhD

Overview

Catherine Searle is a professor of mathematics in the Department of Mathematics, Statistics, and Physics. After obtaining her PhD in mathematics at the University of Maryland at College Park in 1992 under the direction of Professor Karsten Grove, she started her research and teaching career as an assistant professor at the CINVESTAV-IPN in Mexico City, Mexico. She then worked at the Mathematics Institute of the UNAM in Cuernavaca, Morelos from 1996–2011. She was a visiting professor at Oregon State University from 2012–2014, and then joined the faculty at Wichita State University in 2014, where she was promoted to full professor in 2019.

Catherine Searle works in Differential Geometry with an emphasis on Comparison Geometry. Her research has been focussed on positively and non-negatively curved Riemannian manifolds, which admit “large” isometric group actions, where “large” can be defined in a number of ways. The existence of an isometric group action G on a metric space X leads to information about the space itself and can be used both as a tool to identify the space and as a means to improve the metric on that space. More recently she has been studying isometric group actions in these two contexts, namely, as a tool to identify both Riemannian manifolds and Alexandrov spaces with a lower curvature bound and as a tool to improve the metric on a Riemannian manifold with a G-invariant metric.

Information

Academic Interests and Expertise

Differential Geometry
Alexandrov Geometry
Transformation Groups

Areas of Research Interest

Catherine Searle studies manifolds and singular spaces with curvature lower bounds and symmetries from two different points of view:

(1) using continuous and discrete symmetries to better understand the topology of positively, non-negatively, and almost non-negatively curved Riemannian manifolds and Alexandrov spaces and

(2) finding new examples of Riemannian manifolds of positive Ricci curvature, almost non-negative sectional curvature, and positive intermediate Ricci curvature, using symmetries and topology as tools to do so.

Areas of Teaching Interest

Geometry
Topology
Algebra

Publications

Research Articles

Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds, with I. Beach, H. Contreras-Peruyero, E. Griffin, and R. Rotman, preprint: arXiv. 2509.19620v1 (2025).
On Fixed-Point Sets of Z_2-Tori in Positive Curvature, with A. Bosgraaf and C. Escher, preprint: arXiv.2411.00665 (2024)
Linear bounds for the lengths of geodesics on manifolds with curvature bounded below, with I. Beach, H. Contreras-Peruyero, and R. Rotman, J Geom Anal 35, 217 (2025). https://doi.org/10.1007/s12220-025-02003-6
Positively curved manifolds with discrete abelian symmetries, with L. Kennard and E. Khalili Samani, available at arXiv:2110.13345v2 (2024).
Almost isotropy-maximal manifolds of non-negative curvature, with Z. Dong, and C. Escher, Transactions of the AMS, 377 (2024), 4621--4645.
Positive (p, n)-intermediate scalar curvature and cobordism, with M. Burkemper and M. Walsh, J. Geom. Phys., 181 (2022), https://doi.org/10.1016/j.geomphys.2022.104625.
Odd dimensional GKM manifolds of non-negative curvature, with C. Escher and O. Goertsches, International Math. Research Notices, 2023, Issue 1 (2023), 744–784, https://doi.org/10.1093/imrn/rnab137 (2021).
Positively curved Alexandrov spaces with torus symmetry in dimension 4, with J. Harvey, Documenta Math., 26 (2021), 1889--1927.
Alexandrov Spaces with Integral Current Structure, with M. Jaramillo, R. Perales, P. Rajan, A. Siffert, Communications in Analysis and Geometry, 29 no.1 (2021), pp 115-149, available online at https://dx.doi.org/10.4310/CAG.2021.v29.n1.a4
Torus actions, maximality and non-negative curvature, with C. Escher, J. Reine Angew. Math., 2021, no. 780 (2021), 221--264, doi.org/10.1515/crelle-2021-0035 (2021).
Almost non-negatively curved 4-manifolds with torus symmetry, with J. Harvey, Proceedings of the AMS, 148, no. 11 (2020), 4933–4950.
Non-negatively curved 6-manifolds with almost maximal symmetry rank, with C. Escher, Journal of Geometric Analysis, 29 (2019), 1002--1017.
Orientation and Symmetries of Alexandrov spaces with applications in positive curvature, with J. Harvey, Journal of Geometric Analysis, 27 no. 2 (2017), 1636--1666.
Regularization via Cheeger Deformations, with P. Solorzano, F. Wilhelm, Annals of Global Analysis and Geometry, 48 (2015), 295--303.
How to lift positive Ricci curvature, with F. Wilhelm, Geometry and Topology, 19 (3), 1409--1475 (2015).
An introduction to isometric group actions with applications to spaces with curvature bounded below, Geometry of Manifolds of Non-negative Sectional Curvature, Lecture Notes in Mathematics 2110, DOI 10.1007/978-3-319-06373-7_3, Springer International (2014).
Non-negatively curved 5-manifolds of almost maximal symmetry rank, with F. Galaz-Garcia, Geometry & Topology 18 (2014), 1397–1435.
Initial Structure of Cetyltrimethylammonium Bromide Micelles in Aqueous Solution from Molecular Dynamics Simulations, with G. Fernandez Cata, H. Comas Rojas, A. Perez Gramatges, C. Zicovich-Wilson, L.J. Alvarez, Soft Matter, 7 (2011), 8508--8515.
Cohomogeneity one Alexandrov spaces, with F. Galaz-Garcia, Transformation Groups, 16 no. 1 (2011), 91--107.
Low dimensional manifolds with non-negative curvature and maximal symmetry rank, with F. Galaz-Garcia, Proceedings of the American Mathematical Society, 139 no. 7 (2011), 2559--2564.
Diameters of 3-sphere quotients, with W. Dunbar, S. Greenwald, J. McGowan, Differential Geometry and its Applications, 27 no. 2 (2009), 307--319.
How Tightly Can You Fold a Sphere?, with J. McGowan, Differential Geometry and its Applications, 22 no. 1 (2005), 81--104.
The Hopf Conjecture for Manifolds with Low Cohomogeneity or High Symmetry Rank, with T. Puttmann, Proceedings of the AMS, 130 no. 1 (2002), 163--166.
Global G-Manifold Resolutions and Reductions, with K. Grove, Annals of Global Analysis and Geometry, 18 (2000), 437--446.
Differential Topological Restrictions by Curvature and Symmetry, with K. Grove, Journal of Differential Geometry, 47 (1997), 530--559, Correction, JDG, 49 (1998), 205.
On the Topology of Nonnegatively Curved Simply Connected 4-Manifolds with Continuous Symmetry, with D.G. Yang, Duke Mathematical Journal, 74 no. 2 (1994), 547--556.
Positively Curved Manifolds with Maximal Symmetry Rank, with K. Grove, Journal for Pure and Applied Algebra, 91 (1994), 137--142.
Positively Curved Manifolds with Maximal Symmetry Rank, with K. Grove, Aportaciones Matematicas, serie: Comunicaciones 12, ISBN 968-36-3280-7, 153--156 (1993).
Cohomogeneity and Positive Curvature in Low Dimensions, Mathematische Zeitschrift, vol. 214, no.3, pp. 491--498 (1993), Corrigendum, Math. Z., 226 (1997), 165--167.
Cohomogeneity One Manifolds of Positive Curvature, Aportaciones Matematicas, serie: Notas de Investigacion no. 8, ISBN 968-36-2793-5, 109--110 (1992).
Low-Dimensional Chaotic Attractors for an Unstable, Inhomogeneously-Broadened Single Mode Laser, with A.M. Albano, T.H. Chyba, S. Yong, R.S. Gioggia, N.B. Abraham, Journal Opt. Sci. of America B, 125 (1985), 47--55.
Measurement of Impurities in a Neutral Beam by Laser-Induced Fluorescence, with C.F. Burrell, A.S. Schlachter, R.V. Pyle, Journal Vac. Sci. Technol. A2 (2), 708--709 (1984).
Laser Induced Flourescence as Probe of Fast Impurity Atoms in a Neutral Beam, with C.F. Burrell, A.S. Schlachter, R.V. Pyle, Bulletin American Physical Society, Series II, 28 no.8 (1983), 1119.

Survey Articles

Symmetries of spaces with lower curvature bounds, AMS Notices feature article, April, 2023.

Expository Articles

1. An Introduction to Spherical Orbit Spaces, with J. McGowan, IJMMS, 32 no. 8 (2002), 453--469.

2. Algunos Ejemplos de Espacios Orbitales Esfericos de Cohomogeneidad 2, with J. McGowan, Divulgaciones Matematicas, 9 no. 1 (2001), 1--23.

Awards and Honors

Scholars Walk honoree, 2025
Nominated for Wichita State University Distinguished University Professor, 2021.
Academia Mexicana de Ciencias
(Mexican Academy of Sciences--by nomination only), since 2010.
Sistema Nacional de Investigadores, Level I (National System of Researchers-by election only), 1993--2012.

Grants

Research Grants:

PI for NSF grant Curvature, Topology, and Symmetry, DMS#2506633 for $200,000.00, 2025-2028
PI for Simons Foundation Travel Grant for Mathematicians #SFI-MPS-TSM-00012804 for $35,000.00, 2025-2030
PI for continuing NSF grant Curvature and Symmetry, DMS #2204324 for $261,767.00, 2022-2025
PI for NSF grant Curvature and Symmetry, DMS #1906404 for $248,098.00, 2019-2022
PI for NSF grant Lower Curvature Bounds, Topology and Symmetries, DMS #1611780 for $150,000.00, 2016-2019
PI for Simons Collaboration Grant for Mathematicians #355508, Lower curvature bounds and symmetries, 2015--2018

Other Grants:

SLMath Semester-long Program in New Frontiers in Curvature: Flows, General Relativity, Minimal Submanifolds, and Symmetries: Co-organizer with A. Fraser, L.-H. Huang, R. Schoen, L. Wang, and G. Wei, Fall 2024.
Co-PI and co-organizer with Ghazal Gheshnizjani, Raquel Perales, and Tracy Payne, Women in Geometry III Workshop, Banff International Research Station (BIRS), September 24--29, 2023.
Lead organizer with A. Fraser, L.H. Huang, and L. Wang, MSRI Summer School: Topics in Geometric Flows and Minimal Submanifolds Summer 2023..
Co-PI for NSF grant DMS #1856652 for Symmetry and Geometry on the Southern Great Plains, co-organized with M. Jablonski, 2019.
co-PI for NSF grant DMS #1856293 for Collaborative Research: Midwest Geometry Conference, co-organized with D. Auckley, I. Blank, Y.-J. Lin, X.H. Nguyen, P. Stinga, and S. W. Wei, 2019.
co-PI and co-organizer with M. Fraser, E. Stanhope, and G. Wei, Women in Geometry II Workshop, Banff International Research Station, Casa Matematica Oaxaca (CMO-BIRS), June 23--28, 2019.
Co-PI for BIRS Research in Teams: Finding New Examples of Almost Non-negative Curvature, Research in Teams, with P. Sol\'orzano and F. Wilhelm, 2016.
Co-PI for NSF Grant DMS #1630367 for the Smoky Great Plains Geometry Conference August 18--21, 2016, with R. Bettiol-Ghini, J. McGowan, C. Plaut and M. Walsh, 2016.
PI for NSF grant DMS #150268 for the Smoky Great Plains Geometry Conference, co-organized with C.Plaut, M. Walsh, and L. Wilkins, 2015.
PI for NSF grant DMS #1408592 funding the Smoky Cascade Geometry Conference, co-organized with C. Plaut and L. Wilkins.
Co-PI and co-organizer for BIRS 5-Day Workshop: Women in Geometry, with A. Fraser and E. Stanhope, 2013.
PI for CONACyT project \#82471, Geometr\'ia Riemanniana Global (Global Riemannian Geometry), 2009--2011.The grant was awarded for approximately $22, 000 US dollars over a three-year period and covered travel related costs and fellowships for my masters and PhD students.
Co-PI for UNAM DGAPA project IN-115408. PAPIIT is an internal grant program of the UNAM exclusively for researchers of the UNAM, 2008--2010. The grant was awarded for approximately \$44, 000 over a three-year period. The grant covered travel costs, computer purchases and fellowships for my undergraduate students.
co-PI in four consecutive CONACyT projects #28491-E, \#37558-E, #SEP-CO1-46274 and #106923, Estructuras Geom\'etricas Distinguidas, II, III, IV and V, 1999--2013. The last grant awarded was for approximately $113,000.00 US dollars over a three-year period. The grant only coverstravel related costs for 12 researchers and 6 PhD students listed as participants in the project.