I am an Assistant Professor at University of Tennessee at Knoxville. My research interests lie in low-dimensional topology and geometric group theory.
My current research focuses on asymptotic properties of various finitely generated groups as well as the big mapping class groups. Specifically, I am interested in generalization of the Gromov boundary, various notions of genericity in groups, Out(Fn) and generalizations of curve graphs in different settings.
Email: email@example.com, firstname.lastname@example.org
Ayres Hall, 1403 Circle Dr
Knoxville, TN 37916
An algorithm to decide if an outer automorphism is geometric with Edgar A. Bering IV. [pdf]
Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller space with Ilya Gekhtman and Kasra Rafi, submitted. [pdf]
Sublinear bilipschitz equivalence and sublinearly Morse boundary with Gabriel Pallier, submitted. [pdf]
Sublinearly Morse Boundary of CAT(0) admissible groups with Hoang Thanh Nguyen, submitted. [pdf]
Sublinearly Morse Boundary II: Proper geodesic spaces with Kasra Rafi and Giulio Tiozzo, to appear in Geometry & Topology. [pdf]
Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization with Devin Murray and Abdul Zalloum. Algebraic & Geometric Topology 22 (2022) 1337-1374. [arxiv]
Topological properties of sublinearly Morse boundaries of CAT(0) groups with Abdul Zalloum, submitted. [pdf]
Sub-linearly Morse boundary I: CAT(0) spaces with Kasra Rafi and Giulio Tiozzo, Advances in Mathematics 404, August 2022, 108442. [pdf]
Dilatations of right-angled Artin groups with Corey Bregman, submitted. [pdf]
Hyperbolic actions of big mapping class groups with Camille Horbez and Kasra Rafi, Journal of the Institute of Mathematics of Jussieu Volume 21 , Issue 6 , November 2022 , 2173-2204. [pdf]
Convexity of balls in Outer space with Kasra Rafi. Groups, Geometry, and Dynamics 15 (2021), no. 3, 893–934 [pdf]
Quasi-geodesics in Out(Fn) and their shadows in sub-factors with Kasra Rafi, Journal of the London Mathematical Society 104 (1), January 2021, 147-168. [pdf]
Excursions of generic geodesics in right-angled Artin groups and graph products with Giulio Tiozzo. International Mathematics Research Notices 2021 (22), 16910-16937
Uniform fellow traveling between surgery paths in the sphere graph
with Matt Clay and Kasra Rafi. Algebraic & Geometric Topology 17(2017) 3751-3778
Actions of right-angled Coxeter groups on the Croke-Kleiner spaces , Geometriae Dedicata 185(1), 1-14, 2016
Geometry of right-angled Coxeter groups on the Croke-Kleiner spaces, Geometriae Dedicata 183(1), 113-122, 2016
Currently I am a faculty mentor for honors students at University of Tennessee.
Previously I was in undergraduate mentoring for advanced math majors at Fudan University, as well as the Mentorship program at University of Toronto in 2017. I was an instructor at Math Circles at Harvard University and Founder for Math Circle at Tufts University. I was the teaching assistant for Professor Aaron Abrams at the RTG summer workshop at University of California Berkeley in 2012. I was the Research Mentor for two summers in the RSI Summer Program at MIT in 2007 and 2008.