Catherine Searle

Catherine Searle, Professor

Differential Geometry; PhD in Mathematics, University of Maryland at College Park, 1992

Contact

Email: searle@math.wichita.edu
webpage: https://sites.google.com/site/catherinesearle1/home
Phone: 316 978-3965
Office: 351 Jabara Hall

Research

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.

Selected Publications

1. Almost non-negatively curved 4-manifolds with circle symmetry, with J. Harvey, available at arXiv:1907.06702 (2019).

2. Almost torus manifolds of non-negative curvature, with Z. Dong, and C. Escher, available at arXiv:1811.01493v1 (2018).

3. Positively curved Alexandrov spaces with circle symmetry in dimension 4, with J. Harvey, available at arXiv:math.DG/1805.09362v1 (2018).

4. Alexandrov Spaces with Integral Current Structure, with M. Jaramillo, R. Perales, P. Rajan, A. Siffert, accepted for publication in Communications in Analysis and Geometry, available at arXiv:1703.08195 (2017).

5. Non-negatively curved 6-manifolds with almost maximal symmetry rank, with C. Escher, Journal of Geometric Analysis, doi.org/10.1007/s12220-018-0026-2 (2018).

6. Torus actions, maximality and non-negative curvature, with C. Escher, available at arXiv:math.DG/1506.08685v3 (2016).

7. Orientation and symmetries of Alexandrov spaces with applications in positive curvature, with J. Harvey, Journal of Geometric Analysis, 27 (2) , 1636--1666 (2017).

8. Regularization via Cheeger Deformations, with P. Solorzano, F. Wilhelm, Annals of Global Analysis and Geometry, doi:10.1007/s10455-015-9471-3, pp. 1--9 (2015).

9. How to lift positive Ricci curvature, with F. Wilhelm, Geometry and Topology, 19 (3), pp. 1409-1475 (2015).

10. 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).

11. Non-negatively curved 5-manifolds of almost maximal symmetry rank, with F. Galaz-Garcia, Geometry & Topology 18 pp. 1397–1435 (2014).

12. 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, vol. 7, pp. 8508--8515 (2011).

13. Cohomogeneity one Alexandrov spaces, with F. Galaz-Garcia, Transformation Groups, Vol. 16, No. 1, pp. 91--107 (2011).

14. Low dimensional manifolds with non-negative curvature and maximal symmetry rank, with F. Galaz-Garcia, Proceedings of the American Mathematical Society, Volume 139, Number 7, pp. 2559--2564 (2011).

15. Diameters of 3-sphere quotients, with W. Dunbar, S. Greenwald, J. McGowan, Differential Geometry and its Applications, vol 27, no. 2, pp. 307--319 (2009).

16. How Tightly Can You Fold a Sphere?, with J. McGowan, Differential Geometry and its Applications, v. 22, no. 1, pp. 81--104 (2005).

17. The Hopf Conjecture for Manifolds with Low Cohomogeneity or High Symmetry Rank, with T. Puttmann, Proceedings of the AMS, vol. 130, no. 1, pp. 163--166 (2002).

18. Global G-Manifold Resolutions and Reductions, with K. Grove, Annals of Global Analysis and Geometry, vol. 18, pp 437--446 (2000).

19. Differential Topological Restrictions by Curvature and Symmetry, with K. Grove, Journal of Differential Geometry, vol 47, pp. 530--559 (1997), Correction, JDG, vol. 49, p. 205 (1998).

20. On the Topology of Nonnegatively Curved Simply Connected 4-Manifolds with Continuous Symmetry, with D.G. Yang, Duke Mathematical Journal, vol. 74, no. 2, pp. 547--556 (1994).

21. Positively Curved Manifolds with Maximal Symmetry Rank, with K. Grove, Journal for Pure and Applied Algebra, vol. 91, pp. 137--142 (1994).

22. Positively Curved Manifolds with Maximal Symmetry Rank, with K. Grove, Aportaciones Matematicas, serie: Comunicaciones 12, ISBN 968-36-3280-7, pp. 153--156 (1993).

23. Cohomogeneity and Positive Curvature in Low Dimensions, Mathematische Zeitschrift, vol. 214, no.3, pp. 491--498 (1993), Corrigendum, Math. Z., vol 226, pp. 165--167 (1997).

24. Cohomogeneity One Manifolds of Positive Curvature, Aportaciones Matematicas, serie: Notas de Investigacion no. 8, ISBN 968-36-2793-5, pp. 109--110 (1992).

25. 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, vol.125, pp. 47--55 (1985).

26. 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), pp. 708--709 (1984).

27. 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, v. 28, no.8, p. 1119 (1983).

Expository Articles

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

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