University of California Santa Cruz
Department of Mathematics
1156 High Street
Santa Cruz, CA 95064
office: McHenry 4128
I am an Assistant Professor at the University of California Santa Cruz
. In Spring 2023, I will be a CRM-Simons Scholar at the thematic program Geometric Group Theory
at the Centre de Recherches Mathématiques in Montréal.
Previously I was an L.E. Dickson Instructor
at the University of Chicago
, and a Research Member at the MSRI program Random and Arithmetic Structures in Topology
I completed my PhD at McGill University
under the supervision of Piotr Przytycki
and Daniel Wise
My research is in geometric group theory. I am particularly interested in non-positive curvature, cube complexes, Artin groups, Coxeter groups, random groups, small cancellation theories, separability properties, algebraic fibering and coherence.
I am supported by NSF grant DMS-2203307
and and NSF CAREER grant DMS-2238198
Publications and Preprints:
- Finite stature in Artin groups Preprint, 2022.
- (Relative) hyperbolicity in non-metric cubical small cancellation theory (with M. Arenas and D.T. Wise) Preprint, 2022.
- The K(π,1)-conjecture implies the center conjecture for Artin groups (with K. Schreve) J. Algebra 615 (2023), 455-463. (arXiv)
- The boundary rigidity of lattices in product of trees (with A. Karrer, K. Ruane and B. Sathaye) Submitted, 2021. (arXiv)
- Cubulating small cancellation free products (with D.T. Wise) Indiana Univ. Math.
J. 71 (2022), 1397-1409. (arXiv)
- Splittings of triangle Artin groups Accepted to Groups Geom. Dyn., 2022. (arXiv)
- Right angled Artin subgroups of Artin groups (with K. Schreve) J. Lond. Math. Soc. 106 (2022), 818-854. (arXiv)
- Residual finiteness of certain 2-dimensional Artin groups Adv. Math. 405 (2022) Paper No. 108487. (arXiv)
- A curiously cubulated group (with D.T. Wise) Geom. Dedicata 212 (2021), 17-19. (arXiv)
- Groups acting on CAT(0) cube complexes with uniform exponential growth (with R. Gupta and T. Ng) Accepted to Alg. Geom. Top., 2021. (arXiv)
- Virtually fibering right-angled Coxeter groups (with S. Norin and D.T. Wise) J. Inst. Math. Jussieu. 20(3) (2021), 957-987. (arXiv)
- Lower bounds on cubical dimension of C'(1/6) groups Proc. Am. Math. Soc. 148 (2020), 3293-3306. (arXiv)
- The fundamental theorem of cubical small cancellation theory Trans. Amer. Math. Soc. 369 (2017), 4311-4346. (arXiv)
- Cocompactly cubulated 2-dimensional Artin groups (with J. Huang and P. Przytycki) Comment. Math. Helv. 91 (2016), 519–542. (arXiv)
- Incoherent Coxeter groups (with D. T. Wise) Proc. Amer. Math. Soc. 144 (2016), 1857-1866. (arXiv)
- A sharper threshold for random groups at density one-half (with M. Duchin, S. C. Kilmer, S. Lelievre, J. M. Mackay and A. Sanchez) Groups Geom. Dyn. 10 (2016) no. 3, 985-1005. (arXiv)
Thesis: Cubical dimension and obstructions to actions on CAT(0) cube complexes
, Thesis (Ph.D.) McGill University (Canada), 2018, 94 pp.
AWM at UCSC
Math Seminars at UCSC
Geometry/Topology Seminar at UChicago
GGT Seminar at McGill