Ph.D., Mathematics, Purdue University, 2003

This material is based upon work supported by the National Science Foundation under grants DMS-0400636, DMS-0653439, DMS-0703617, DMS-1001144, DMS-1800180, DMS-2247364. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

ArXiv Publications

• with Alexandre Eremenko, Caratheodory convergence and the conformal type problem
  https://arxiv.org/abs/2412.05995
   
• with Misha Lyubich, Sabya Mukherjee, and Dimitrios Ntalampekos, David extension of circle homeomorphisms, welding, mating, and removability
  Mem. Amer. Math. Soc. 313 (2025), no. 1588, v+110 pp.
  https://arxiv.org/abs/2010.11256
   
• On a question of Kwakkel and Markovic on existence of wandering domains with bounded geometry
  Duke Math. J. 174 (2025), no. 9, 1849-1873.
  https://arxiv.org/abs/2405.02176
   
• No bounded geometry wandering domains for sufficiently regular automorphisms
  Trans. Amer. Math. Soc. 378 (2025), no. 03, 1503-1530.
  https://arxiv.org/abs/2105.08760
   
• with Maria Sabitova, On Z^d-odometers associated to integer matrices
  Groups Geom. Dyn. 19 (2025), 265-279.
  https://arxiv.org/abs/2209.09374
   
• with Russell Lodge, Misha Lyubich, and Sabya Mukherjee, On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections
  Conform. Geom. Dyn. 27 (2023), 1-54.
  https://arxiv.org/abs/1912.13438
   
• with Mario Bonk, Square Sierpinski carpets and Lattes maps
  Math. Z. 296 (2020), no. 1-2, 695-718.
  https://arxiv.org/abs/1801.09320
   
• No round wandering domains for C¹-diffeomorphisms of tori
  Ergodic Theory Dynam. Systems 39 (2019), no. 11, 3127-3135.
  https://arXiv.org/abs/1705.01512
   
• with Misha Lyubich, Quasisymmetries of the basilica and the Thompson group
  Geom. Funct. Anal. 28 (2018), no. 3, 727-754.
  http://arXiv.org/abs/1612.08492
   
• with Mario Bonk and Misha Lyubich, Quasisymmetries of Sierpinski carpet Julia sets
  Adv. Math. 301 (2016), 383-422.
  http://arXiv.org/abs/1403.0392
   
• with Maria Sabitova, From Apollonian packings to homogeneous sets
  Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 2, 711-727.
  http://arXiv.org/abs/1402.5632
   
• Local rigidity for hyperbolic groups with Sierpinski carpet boundaries
  Compos. Math. 150 (2014), no. 11, 1928-1938.
  http://arXiv.org/abs/1307.1792
   
• Local rigidity of Schottky maps
  Proc. Amer. Math. Soc. 142 (2014), no. 12, 4321-4332.
  http://arXiv.org/abs/1305.4683
   
• with Kevin Wildrick, Quasisymmetric Koebe uniformization
  Rev. Mat. Iberoam. 29 (2013), no. 3, 859-910.
  http://arXiv.org/abs/1109.3441
   
• with Mario Bonk, Quasisymmetric rigidity of square Sierpinski carpets
  Ann. of Math. (2) 177 (2013), no. 2, 591-643.
  http://arXiv.org/abs/1102.3224
   
• with Vadim Zharnitsky, Hausdorff dimension of three-period orbits in Birkhoff billiards
  Nonlinearity 25 (2012), no. 7, 1947-1954.
  http://arXiv.org/abs/1112.2745
   
• Planar relative Schottky sets and quasisymmetric maps
  Proc. Lond. Math. Soc. (3) 104 (2012), 455-485.
  http://arXiv.org/abs/1305.4158
   
• A Sierpinski carpet with the co-Hopfian property
  Invent. Math., Vol. 180, Issue 2 (2010), 361-388.
  http://arXiv.org/abs/1305.4161
   
• with Mario Bonk and Bruce Kleiner, Rigidity of Schottky sets
  Amer. J. Math. 131 (2009), no. 2, 409-443.
  http://arXiv.org/abs/1102.4381
   
• Rapidly growing entire functions with three singular values
  Illinois J. Math. 52 (2008), no. 2, 473-491.
  http://arXiv.org/abs/1305.4214
   
• with Lukas Geyer, A hyperbolic surface with a square grid net
  J. d'Analyse Math., Vol. 96 (2005), 357-367.
  http://arXiv.org/abs/math/0409560
   
• with Alexandre Eremenko, Nevanlinna functions with real zeros
  Illinois J. Math., 49 (2005), no. 4, 1093-1110.
  http://arXiv.org/abs/math/0310496
   
• with Itai Benjamini and Oded Schramm, A negative answer to Nevanlinna's type question and a parabolic surface with a lot of negative curvature
  Proc. Amer. Math. Soc., 132 (2004), no. 3, 641-647.
  http://arXiv.org/abs/math/0209334
   
• Determining biholomorphic type of a manifold using combinatorial and algebraic structures
  Thesis (Ph.D.)-Purdue University. 2003. 65 pp. ISBN: 978-0496-61336-6, ProQuest LLC, Thesis.
  http://arXiv.org/abs/1305.5230
   
• with Gregery Buzzard, Maps conjugating holomorphic maps in Cⁿ
  Indiana Univ. Math. J., 52 (2003), no. 5, 1135-1146.
  http://arXiv.org/abs/math/0301120
   
• Equivalence of domains with isomorphic semigroups of endomorphisms
  Proc. Amer. Math. Soc., 130 (2002), no. 6, 1743-1753.
  http://arXiv.org/abs/1305.4387
   
• On the Cauchy transform of weighted Bergman spaces
  Visnyk, Kharkiv State Univ., 475 (2000), 133-140.
  http://arXiv.org/abs/1305.4217
   
• On the Cauchy transform of the Bergman space
  Mat. Fiz. Anal. Geom., 7 (2000), no. 1, 119-127.
  http://arXiv.org/abs/1305.4386
   

Doctoral Faculty

Mathematics Program
CUNY Graduate Center
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