## 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).