Research
My broad research interests include topics in geometric analysis, differential geometry, PDE, low dimensional topology, and graph theory. For specific information about details of and motivation for my work, please see the following research overview. Thank you for your interest!
A research colloquium talk I gave to a general mathematics audience at California State University-San Bernardino.
Manuscripts
Published and Accepted for Publication
Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues. Joint with Grant Lakeland and Holger Then arXiv:1908.00199 Accepted by Proc. Am. Math. Soc.
Volume growth, curvature, and Buser-type inequalities in graphs. Joint with Peter Ralli and Prasad Tetali. arXiv:1802.01952 To appear in Int Math Res Not
Mean Value Theorems for Riemannian Manifolds via the Obstacle Problem. Joint with Ivan Blank and Jeremy LeCrone. Journal of Geometric Analysis, Vol 29, Issue 3, 2752-2775, DOI:10.1007/s12220-018-0093-4, arXiv:1704.07518.
A note on a Newtonian Approximation in a Schwarzchild background. Joint with Marcelo M. Disconzi. The African Review of Physics, Vol 13, 2018, 12 pages.
Torsion and ground state maxima: close but not the same. Joint with Richard S. Laugesen, Michael L. Minion, and Bartlomiej A. Siudeja. Irish Mathematical Society Bulletin 78 (Winter 2016) 81-88, arXiv:1507.01565.
Sturm-Liouville Estimates for the Spectrum and Cheeger Constant. Int Math Res Not, Vol. 2015, No. 16, pp. 7510-7551. rnu175. arXiv:1308.5936 MR3428972 MSC 58J50
G-parking functions, acyclic orientations and spanning trees. Joint with Deeparnab Chakrabarty and Prasad Tetali. Discrete Math. 310 (2010), no. 8, 1340-1353. arXiv:0801.1114 MR2592488 MSC 05C57
Preprints and Works Submitted for Peer-Review
The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces. arXiv:1509.08993
Work in Progress
Cheeger Constants of Principal Congruence Arithmetic Surfaces. Joint with Jeffrey Meyer
The Spanning Tree Modulus and the Laplace Spectrum of a Graph. Joint with Nathan Albin and Pietro Poggi-Corradini
Miscellaneous
The Three Hat Problem. Joint with Yang Wang, arXiv:0710.2685. (A fun project that introduced me to the research process in mathematics!)