Research
Publications / preprints
Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups (joint with Pierre-Louis Blayac, Richard Canary, and Andrew Zimmer).
Preprint available at arXiv:2404.09718.Patterson-Sullivan theory for coarse cocycles (joint with Pierre-Louis Blayac, Richard Canary, and Andrew Zimmer).
Preprint available at arXiv:2404.09713.Topological restrictions on relatively Anosov representations (joint with Kostas Tsouvalas).
Submitted. Preprint available at arXiv:2401.03050.Cubulated hyperbolic groups admit Anosov representations
(joint with Sami Douba, Balthazar Fléchelles, and Theodore Weisman).
Submitted. Preprint available at arXiv:2309.03695.Relatively Anosov representations via flows I: theory (joint with Andrew Zimmer).
Submitted. Preprint available at arXiv:2207.14737.Relatively Anosov representations via flows II: examples (joint with Andrew Zimmer).
Accepted to J. Lond. Math. Soc. (2). Preprint available at arXiv:2207.14738.Ergodicity and equidistribution in Hilbert geometry (joint with Pierre-Louis Blayac).
J. Mod. Dyn. 19(2023), 879–945. DOI:10.3934/jmd.2023026
Pre-publication version available at arXiv:2106.08079.Relatively dominated representations from eigenvalue gaps and limit maps.
Geom. Dedicata 217, 39 (2023). DOI:10.1007/s10711-023-00775-1
Pre-publication version available at arXiv:2102.10611.Ergodicity and equidistribution in strictly convex Hilbert geometry.
Preprint, available at arXiv:2008.00328, or as an Expanded version.Relatively dominated representations.
Ann. Inst. Fourier (Grenoble) 71 (2021), no. 5, 2169–2235. DOI:10.5802/aif.3449
Pre-publication version available at arXiv:1912.13152.
My PhD thesis ("Relatively dominated representations"; mostly similar to the oldest paper above, very slightly chattier in parts) is available here
Slides from selected talks
Relatively Anosov representations
@ MSRI Random and Arithmetic Structures in Topology semester program, Postdoc seminar, 2020 Sep 24Ergodicity and equidistribution in Hilbert geometry
@ IU Bloomington geometry seminar, 2020 Nov 12Lightning talks!
A 5-minute lightning talk @ GGTea, 2020 Oct 30, which gives an overview of my research and where (relatively) Anosov representations fit into the broader landscape of geometric topology / geometric group theory
Pappus's theorem, Farey addition, and Schwartz representations @ GSTGC 2019. Pappus-Schwartz representations are (i) an example of relatively Anosov representations; (ii) kind of neat and surprising even if you don't care about those.
Miscellaneous / expository
"Coordinating Sensors with Topology": slide deck from a Michigan undergrad Math Club talk on applied topology