Papers and Preprints

  1. A Combinatorial Characterization of Sol 3-Manifolds. (with D. Cooper and L. Mavrakis) 
  2. Combinatorial Characterizations and Branched Manifolds. (with D. Cooper and L. Mavrakis)
  3. Shift maps are not type-preserving. Geom Dedicata. 219, 82 (2025) (with C. Abbott and N. Miller)
  4. Constructing endperiodic loxodromics of infinite-type arc graphs. Math. Z. 310, 82 (2025) (with S. Taylor)
  5. ​Thurston's Theorem: Entropy in Dimension One. Math. Res. Lett. 31 (2024) no.1 127-174. (with R. Dickmann, G. Domat, T. Hill, S. Kwak, C. Ospina, and R. Rechkin)
  6. Infinite-type loxodromic isometries of the relative arc graph. Algebr. Geom. Topol. 25-1 (2025) 563-644. (with C. Abbott and N. Miller)
  7. A new construction of subgroups of big mapping class groups. New York J. Math. 32 (2026) 118-154. (with C. Abbott, H. Hoganson, M. Loving, and R. Skipper)
  8. Stable Commutator Length on Big Mapping Class Groups. Bull. London Math. Soc. 54, 2492-2512 (2022).  (with E. Field and A. Rasmussen)
  9. Free products from spinning and rotating families. Enseign. Math. 69 (2023) no. 3/4 235-260.  (with M. Bestvina, R. Dickmann, G. Domat, S. Kwak, and E. Stark)
  10. Isometry groups of infinite-genus hyperbolic surfaces. Math. Ann. 381(1) 459-498 (2021). (with T. Aougab and N. Vlamis)
  11. Covers of surfaces, Kleinian groups, and the curve complex. ​J. Topol. 2022;15:1833-1863. (with T. Aougab and S. Taylor)
  12. Effective virtual and residual properties of some arithmetic hyperbolic 3-manfiolds. Trans. Amer. Math. Soc. 373 (2020), no. 11, 8219-8257. (with J. Deblois and N. Miller)
  13. The first integral cohomology of pure mapping class groups. ​Int. Math. Res. Notices. 2020-22 (2020), 8973-8996.​ (with J. Aramayona and N. Vlamis)
  14. Algebraic and topological properties of big mapping class groups. Algebr. Geom. Topol. 18-7 (2018), 4109-4142. (with N. Vlamis)
  15. 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)
  16. Zariski closures and Subgroup Separability. Selecta Math. 23 (2017) Issue 3, pp 2019-2027. (with L. Louder and D.B. McReynolds)
  17. Quantifying separability in virtually special groups. Pacific J. Math. 284-1 (2016), pp 103-120. (with M.F. Hagen)
  18. On the Residual Finiteness Growths of Particular Hyperbolic Manifold Groups. Geom Dedicata. 185 (2016) Issue 1, pp 87-103.
  19. 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)
  20. On a Theorem of Peter Scott. Proc. Amer. Math. Soc. 142 (2014) pp 2891-2906.

I am an associate editor for the "K3--A new problem list in low-dimensional topology". A preliminary copy of the list is available here.
​
Here is an open problem list on infinite-type surfaces (last updated on 10/22/21).
 ​
Here is a feature my college did on me. 
Here and here are features my department did on me. ​
Here is an interview I did for Meet a Mathematician. 

Math Education Papers and Preprints

  1. Diverse Storylines of Entering the Mathematics Professoriate. Educ. Stud. Math. (with Kathleen Melhuish, Lino Guajardo, Kristen Lew, Paul Dawkins, Alexander Diaz-Lopez, Rebecca Garcia, Pamela E. Harris, Edna Jones, Kyeong Hah Roh, Shanise Walker, Dwight Anderson Williams II, and Aris Winger)
  2. Reading and Appreciating Mathematical Proofs. (Open Access Book)
    (with Kathleen Melhuish, Kristen Lew, Paul Dawkins, Alexander Diaz-Lopez, Rebecca Garcia, Pamela E. Harris, Edna Jones, Kyeong Hah Roh, Shanise Walker, Dwight Anderson Williams II, and Aris Winger)

Features in the press: