About Me
I received my Ph.D. from Rutgers University in 2013 under the supervision of Feng Luo. From 2013-2016, I was a postdoc at Purdue University working with Ben McReynolds, and I am now a postdoc at the University of California, Santa Barbara.
My research interests lie broadly in the fields of low-dimensional topology, hyperbolic geometry, and geometric group theory, with a focus on understanding finite covering spaces of hyperbolic manifolds. More specically, I study the connection between effective separability properties of the fundamental groups of hyperbolic manifolds and promoting immersed sets in such manifolds to embeddings in finite covers. Though my research program is centered around studying quantitive aspects of this connection, my projects have expanded into related fields of mathematics, including right-angled Artin groups and cube complexes, Teichmüller theory and mapping class groups of surfaces, as well as the representation theory of surfaces and 3–manifolds. More recently, I have also become interested in the mapping class groups of infinite type surfaces, referred to as "big mapping class groups".
Click here for my CV (last updated 8/19/17).
My research interests lie broadly in the fields of low-dimensional topology, hyperbolic geometry, and geometric group theory, with a focus on understanding finite covering spaces of hyperbolic manifolds. More specically, I study the connection between effective separability properties of the fundamental groups of hyperbolic manifolds and promoting immersed sets in such manifolds to embeddings in finite covers. Though my research program is centered around studying quantitive aspects of this connection, my projects have expanded into related fields of mathematics, including right-angled Artin groups and cube complexes, Teichmüller theory and mapping class groups of surfaces, as well as the representation theory of surfaces and 3–manifolds. More recently, I have also become interested in the mapping class groups of infinite type surfaces, referred to as "big mapping class groups".
Click here for my CV (last updated 8/19/17).
Papers and Preprints
0. PhD thesis: Quantifying Algebraic Properties of Surface Groups and 3-manifold Groups.
1. On a Theorem of Peter Scott. Proc. Amer. Math. Soc. 142 (2014) pp 2891-2906.
2. Residual Finiteness Growths of Virtually Special Groups. Math. Z. 279 (2015), no. 1-2, pp 297-310. (with K. Bou-Rabee and M.F. Hagen)
3. On the Residual Finiteness Growths of Particular Hyperbolic Manifold Groups. Geom Dedicata. 185 (2016) Issue 1, pp 87-103.
4. Quantifying separability in virtually special groups. Pacific J. Math. 284-1 (2016), pp 103-120. (with M.F. Hagen)
5. Zariski closures and Subgroup Separability. Selecta Math. 23 (2017) Issue 3, pp 2019-2027. (with L. Louder and D.B. McReynolds)
6. Building hyperbolic metrics suited to closed curves and applications to lifting simply. Math. Res. Lett. 24 (2017), no. 3, pp 593-617.
(with T. Aougab, J. Gaster, and J. Sapir) Preprint available at arXiv:1603.06303.
7. Algebraic and topological properties of big mapping class groups. (with N. Vlamis) Submitted. Preprint available at arXiv:1703.02665.
8. Topological automorphisms of big mapping class groups are geometric. (with J. Aramayona and N. Vlamis) In preparation.
9. Residual finiteness growths of closed hyperbolic manifolds in non-compact right-angled reflection orbifolds. (with J. Deblois, D.B. McReynolds, and J. Meyer) In preparation.
10. 3-Manifolds and the curve complex. (with T. Aougab and S. Taylor) In preparation.
Here is a link to a video of my talk at the Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups Workshop. (May 2016)
Here is a link to a video of my talk at the GGD/GEAR Seminar at UIUC (October 2014).
1. On a Theorem of Peter Scott. Proc. Amer. Math. Soc. 142 (2014) pp 2891-2906.
2. Residual Finiteness Growths of Virtually Special Groups. Math. Z. 279 (2015), no. 1-2, pp 297-310. (with K. Bou-Rabee and M.F. Hagen)
3. On the Residual Finiteness Growths of Particular Hyperbolic Manifold Groups. Geom Dedicata. 185 (2016) Issue 1, pp 87-103.
4. Quantifying separability in virtually special groups. Pacific J. Math. 284-1 (2016), pp 103-120. (with M.F. Hagen)
5. Zariski closures and Subgroup Separability. Selecta Math. 23 (2017) Issue 3, pp 2019-2027. (with L. Louder and D.B. McReynolds)
6. Building hyperbolic metrics suited to closed curves and applications to lifting simply. Math. Res. Lett. 24 (2017), no. 3, pp 593-617.
(with T. Aougab, J. Gaster, and J. Sapir) Preprint available at arXiv:1603.06303.
7. Algebraic and topological properties of big mapping class groups. (with N. Vlamis) Submitted. Preprint available at arXiv:1703.02665.
8. Topological automorphisms of big mapping class groups are geometric. (with J. Aramayona and N. Vlamis) In preparation.
9. Residual finiteness growths of closed hyperbolic manifolds in non-compact right-angled reflection orbifolds. (with J. Deblois, D.B. McReynolds, and J. Meyer) In preparation.
10. 3-Manifolds and the curve complex. (with T. Aougab and S. Taylor) In preparation.
Here is a link to a video of my talk at the Effective and Algorithmic Methods in Hyperbolic Geometry and Free Groups Workshop. (May 2016)
Here is a link to a video of my talk at the GGD/GEAR Seminar at UIUC (October 2014).
Upcoming Talks:
Temple University Geometry-Topology Seminar, October 2017
Joint Mathematics Meeting, Special Session on Boundaries for Groups and Spaces, January 2018
Geometry of Teichmüller space and mapping class groups, The University of Warwick, April 2018
Joint Mathematics Meeting, Special Session on Boundaries for Groups and Spaces, January 2018
Geometry of Teichmüller space and mapping class groups, The University of Warwick, April 2018
Collaborators:
|
Tarik Auogab
Khalid Bou-Rabee Jonah Gaster |
Mark Hagen
Lars Louder Ben McReynolds |
Jenya Sapir
Samuel Taylor Nicholas Vlamis |
Miscellaneous
Here is a link to my Math Genealogy.
