Publications

Articles

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

2. Positively curved manifolds with discrete abelian symmetries, with L. Kennard and E. Khalili Samani, available at arXiv:2110.13345  (2021).

3. Almost isotropy-maximal manifolds of non-negative curvature, with Z. Dong, and C. Escher,  Transactions of the AMS, 377 (2024), 4621--4645. 

4. 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.

5.  Odd dimensional GKM manifolds of non-negative curvature, with C. Escher and O. Goertsches, International Math. Research Notices, https://doi.org/10.1093/imrn/rnab137 (2021).

6.  Positively curved Alexandrov spaces with torus symmetry in dimension 4, with J. Harvey, Documenta Math., 26 (2021), 1889--1927.

7.  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

8.  Torus actions, maximality and non-negative curvature, with C. Escher, J. Reine Angew. Math., doi.org/10.1515/crelle-2021-0035 (2021).

9. Almost non-negatively curved 4-manifolds with circle symmetry, with J. Harvey, Proceedings of the AMS, 148, no.  11 (2020),  4933–4950.

10. Non-negatively curved 6-manifolds with almost maximal symmetry rank, with C. Escher, Journal of Geometric Analysis,  29 (2019), 1002--1017.

11.  Orientation and Symmetries of Alexandrov spaces with applications in positive curvature, with J. Harvey, Journal of Geometric Analysis,  27 no. 2 (2017),  1636--1666. 

12.  Regularization via Cheeger Deformations, with P. Solorzano, F. Wilhelm, Annals of Global Analysis and Geometry, 48 (2015), 295--303.

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

14.  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).

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

16.  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. 

17.   Cohomogeneity one Alexandrov spaces, with F. Galaz-Garcia, Transformation Groups, 16 no. 1 (2011), 91--107.

18.  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. 

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

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

21.   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. 

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

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

24.   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. 

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

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

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

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

29.   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.  

30.   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). 

31.  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.

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.