Carolyn R. Abbott
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Email: abbott (at) math.columbia.edu
Office: Room 629, Mathematics Building

Department of Mathematics
Columbia University
2990 Broadway Ave.
New York, NY 10027

About Me: Starting in Fall 2021, I will be an Assistant Professor at Brandeis University. I am currently an NSF Postdoctoral Fellow at Columbia University.  In 2018-2019, I was a NSF Postdoctoral Fellow at UC Berkeley, and in 2017-2018 I was a Morrey Visiting Assistant Professor, also at UC Berkeley. I received my Ph.D. from the University of Wisconsin-Madison in 2017, where I studied geometric group theory under the supervision of Tullia Dymarz.  

Here is a copy of my CV (updated November 2019).

Research interests: I study geometric group theory and low-dimensional topology.  In particular, I am interested in group actions by isometries on hyperbolic spaces, especially acylindrical actions.  The kinds of groups I think about include hyperbolic and relatively hyperbolic groups, mapping class groups, Out(F_n), CAT(0) groups, three manifold groups, hierarchically hyperbolic groups, and many more.  
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Papers:
  1. Not all finitely generated groups have universal acylindrical actions. Proc. Amer. Math. Soc., 144(10):4151–4155, 2016, pdf.
  2. (with F. Dahmani) Acylindrically hyperbolic groups have property P_naive. arXiv:1610.04143.  Math. Z., 291(1-2):555-568, 2019.
  3. (with S. Balasubramanya and D. Osin) Hyperbolic structures on groups.  arXiv:1710.05197. Algebr. Geom. Topol., 19-4, 1747-1835, 2019.
  4. (with D. Hume and D. Osin) Extending group actions on metric spaces.   arXiv:1703.03010.  J. Topol. Anal., 12(3): 625--665, 2020, pdf.
  5. (with D. Hume) The geometry of generalized loxodromic elements.  arXiv:1802.03089. To appear in Ann. I. Fourier.
  6. (with J. Behrstock and M. Durham) Largest acylindrical actions and stability in hierarchically hyperbolic groups, with an appendix by Daniel Berlyne and Jacob Russell. arXiv:1705.06219. To appear in Trans. Amer. Math. Soc.
  7. (with D. Hume) Actions of small cancellation groups on hyperbolic spaces.  arXiv:1807.10524. To appear in ​Geom. Dedicata
  8. (with J. Behrstock) Conjugator lengths in hierarchically hyperbolic groups.  arXiv:1808.09604.
  9. (with A. Rasmussen) Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces.  arXiv:1906.04227​
  10. (with M. Hull) Random walks and quasi-convexity in acylindrically hyperbolic groups.  arXiv:1909.10876
  11. (with T. Ng and D. Spriano) Uniform exponential growth in hierarchically hyperbolic groups. arxiv.org/abs/1909.00439
  12. (with J. Manning) Boundaries of coned-off hyperbolic spaces, arXiv:1906.09319.
  13. (with A. Rasmussen) Largest hyperbolic actions and quasi-parabolic actions of groups.  arXiv:1910.14157.
  14. (with N. Miller and P. Patel) Big mapping class groups and quasi-morphisms.  In preparation.
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