My research interests can be broadly defined as the investigation of topological, geometric, and combinatorial objects (especially polytopes). The main topic I study is Geometric Group Theory especially through the lens of embedded combinatorial structures. My current research has close connections to the combinatorics of Non-Crossing Partitions and the topological properties for classifying spaces of the Braid Group.
A few of my papers are being prepared currently, a (non-exhaustive) list includes :
- Garside Structures and Real Polynomials (joint with J. McCammond)
- Fubini Rankings Polytopes (joint with J. Elder, P.E. Harris, J. Kretschmann, C. Martinez Mori)
- Unit-Interval Parking Functions and the Permutohedron (joint with L. Chaves Meyles; P. E. Harris; G. Kirby Rojas; R. Jordaan; E. Spingarn)--- Arxiv link; To appear in Journal of Combinatorics
- Parking functions of Fixed Displacement (joint with L. Chaves Meyles; R. Jordaan; E. Spingarn)
- Symmetric and Palindromic Non-Crossing Partitions
My Master's Thesis from San Francisco State University:
Geometric Extensions and the 1/3--2/3 Conjecture
Geometric Extensions and the 1/3--2/3 Conjecture
