Research Publications & Preprints

On the minimum spanning tree distribution in grids, preprint 2024.

Spanning Tree Bounds for Grid Graphs, The Electronic Journal of Combinatorics, Vol. 31, Issue 1 (2024).  (Supported by this Jupyter Notebook and this Jupyter Notebook)

On Pull-backs of the Universal Connection, Canadian Mathematical Bulletin, Vol. 65, No. 4 (2022), 845-859.

Clustering and Expected Seat-Share for District Maps, Communications in Statistics -- Theory and Methods, 51:22 (2022), 7751-7766 (Supported by this Jupyter Notebook)  

Measuring Political Gerrymandering, Amer. Math. Monthly, Vol 126 (2019), No. 7, 579-592.

Radially Symmetric Connections over Round Spheres, Proc. Amer. Math. Soc. 2018.

On the Mathematics of the Free-Choice Paradigm, with Peter Selinger.

A Note on Quasi-Positive Curvature Conditions, with Megan Kerr, Differential Geometry and its Applications, Vol. 34 (2014), 63-79.

Rigidity for Odd-Dimensional Souls, Geometry and Topology, Vol. 16, issue 2 (2012) 957-962.

Metrics with Nonnegative Curvature on S2xR4, Annals of Global Analysis and Geometry, Vol. 42, No. 1 (2012), 61-77.

Totally Geodesic Foliations and Doubly Ruled Surfaces in a Compact Lie Group, with Marius Munteanu, Proc. Amer. Math. Soc., Vol. 139, No. 11 (2011), 4121-4135.

Homogeneous metrics with nonnegative curvature, with Lorenz Schwachhöfer, Journal of Geometric Analysis, Vol. 19, No. 4 (2009), 929-943.

Cohomogeneity one disk bundles with normal homogeneous collars, with Lorenz Schwachhöfer, Proceedings of the London Mathematical Society, Vol. 99, no. 3 (2009), 609-632.

Flats in Riemannian Submersions from Lie groups, Asian Journal of Mathematics, Vol. 13, No. 4 (2009), 459-464.

Nonnegatively curved vector bundles with large normal holonomy groups, Proc. Amer. Math. Soc., Vol. 136, No. 1 (2008), 295-300.

Invariant Metrics with Nonnegative Curvature on SO(4) and other Lie groups, with Jack Huizenga, Michigan Math. Journal, Vol. 55, Issue 3 (2007), 609-630.

Invariant Metrics with Nonnegative Curvature on Compact Lie Groups, with Brown, Finck, Spencer, Wu., Canadian Mathematical Bulletin, Vol. 50, No. 1 (2007), 24-34.

Obstructions to Positive Curvature on Homogeneous Bundles, Geometriae Dedicata. 119, no. 1 (2006) 105-112.

Nonnegatively and positively curved invariant metrics on circle bundles, with Shankar and Tuschmann. Proc. Amer. Math. Soc. 133 (2005) 2449-2459.

Rigidity for nonnegatively curved metrics on S2xR3, Annals of Global Analysis and Geometry. 25 (2004) 43-58.

Quasi-positive curvature on homogeneous bundles, Journal of Differential Geometry. 65 (2003) 273-287.

Nonnegatively curved metrics on S2 x R2, with Detlef Gromoll Geometriae Dedicata 99 (2003), pp. 127-136.

Conditions for Nonnegative Curvature on Vector Bundles and Sphere Bundles, Duke Math. Journal. 116, no. 1 (2003), 77-101.

Finiteness Theorems for Submersions and Souls, Proc. Amer. Math. Soc., Vol. 130 (2002), no. 6, 1809--1817.

Bounded Riemannian Submersions, Indiana University Mathematics Journal, Vol. 49, No. 2 (Summer) 2000, 637—654.

Volume growth and holonomy in nonnegative curvature, Proc. Amer. Math. Soc. 127 (1999), no. 10, pp. 3035—3041.

The Geometry of Open Manifolds of Nonnegative Curvature, Ph.D. Thesis, University of Pennsylvania, 1999.