Publications and Preprints
- (with I. Pasquinelli) The geometry of Deligne--Mostow lattices in PU(3,1) with four-fold symmetry.. (In preparation)
- (with M. Cook, K. Pine, B. Robinson) Fisher-Rao distances on the covariance cone. Preprint. October 2020. (arχiv Preprint)
- Hyperbolic groups are finitely presented. Newsletter of the Ramanujan Math Society. 31.1 (June 2020), pp. 9--12. (Expository). (Preprint)
- Non-arithmetic hybrid lattices in PU(2,1). Geom. Dedicata 208 (2020) pp 1-11. (arχiv Preprint) (errata)
- (with J. Paupert) Hybrid lattices and thin subgroups of Picard modular groups. Topology and its Appl. 269 (2020). pp 106918, 15. (arχiv Preprint)
- Hybrid subgroups of complex hyperbolic isometries. PhD Thesis. May 2019. (PDF)
Click here for an Overleaf file containing open questions that I have.
Some Past Talks
If it involves complex hyperbolic geometry in any way, I'm probably interested in it. Specifically, my research is focused around discrete subgroups of complex hyperbolic isometries, and in particular lattices (both arithmetic and non-). I'm interested in finding techniques analogous to "hybridization" (a process produced by Gromov and Piatetski-Shapiro for real hyperbolic lattices) to allow for the construction of new commensurability classes of lattices in PU(n,1).
Lately, I've also taken an interest in the embedding of hyperbolic 3-manifolds into the boundary of complex hyperbolic 2-space. Such embeddings help to provide answers to the following question about geometric transitions: "Which hyperbolic 3-manifolds can be endowed with a (uniformized) spherical CR structure?"
This work is supported in part by Lost Dutchman Coffee Roasters and Mill Mountain Coffee and Tea.