Seminars
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Analysis on Metric Spaces Seminar - Stony Brook University - Spring 2023 -
Analysis Seminar - Stony Brook University
Upcoming Events
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Quasiworld Workshop , University of Helsinki, Finland, August 14-18, 2023 -
Special Session on Quasiconformal analysis and geometry on metric spaces , AMS Spring Eastern Sectional Meeting, Virtual meeting, April 1-2, 2023
Preprints
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Conformal uniformization of planar packings by disk packings
Submitted. [arXiv] -
Polyhedral approximation and uniformization for non-length surfaces (joint with Matthew Romney)
Submitted. [arXiv] -
Definitions of quasiconformality and exceptional sets
Submitted. [arXiv] -
David extension of circle homeomorphisms, welding, mating, and removability (joint with Misha Lyubich, Sergei Merenkov, and Sabyasachi Mukherjee)
Submitted. [arXiv]
Monographs
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Potential Theory on Sierpiński Carpets With Applications To Uniformization
Lecture Notes in Mathematics, vol. 2268, Springer, Cham, 2020. [published version] [arXiv] [poster]
Publications
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Rigidity and continuous extension for conformal maps of circle domains
Trans. Amer. Math. Soc. (2023), to appear. [arXiv] -
Polyhedral approximation of metric surfaces and applications to uniformization (joint with Matthew Romney)
Duke Math. J. (2022), to appear. [arXiv] -
Extension of boundary homeomorphisms to mappings of finite distortion (joint with Christina Karafyllia)
Proc. Lond. Math. Soc. 125 (2022), no. 3, 488-510. [journal] [journal (free access)] [arXiv] -
On the Hausdorff dimension of the residual set of a packing by smooth curves (joint with Steven Maio)
J. Lond. Math. Soc. 105 (2022), no. 3, 1752-1786. [journal] [journal (free access)] [arXiv] -
Monotone Sobolev Functions in Planar Domains: Level Sets and Smooth Approximation
Arch. Ration. Mech. Anal. 238 (2020), no. 3, 1199-1230. [journal] [journal (free access)] [arXiv] -
Falconer's \((K,d)\) distance set conjecture can fail for strictly convex sets \(K\) in \(\mathbb R^d\) (joint with Christopher Bishop and Hindy Drillick)
Rev. Mat. Iberoam. 37 (2021), no. 5, 1953-1968. [journal] [preprint] -
Rigidity theorems for circle domains (joint with Malik Younsi)
Invent. Math. 220 (2020), no. 1, 129-183. [journal] [journal (free access)] [arXiv] [slides] -
On the inverse absolute continuity of quasiconformal mappings on hypersurfaces (joint with Matthew Romney)
Amer. J. Math. 143 (2021), no. 5, 1633-1659. [journal] [arXiv] -
Non-removability of Sierpiński spaces (joint with Jang-Mei Wu)
Proc. Amer. Math. Soc. 148 (2020), 203-212. [journal] [arXiv] -
Non-removability of Sierpiński carpets
Indiana Univ. Math. J. 70 (2021), no. 3, 847-854. [journal] [arXiv] -
Non-removability of the Sierpiński gasket
Invent. Math. 216 (2019), no. 2, 519-595. [journal] [journal (free access)] [arXiv] [slides] -
A removability theorem for Sobolev functions and detour sets
Math. Z. 296 (2020), 41-72. [journal] [journal (free access)] [arXiv] -
Semi-hyperbolic rational maps and size of Fatou components
Ann. Acad. Sci. Fenn. Math. 43 (2018), 425-446. [journal] [arXiv]
Thesis
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Potential theory on Sierpiński carpets with applications to uniformization
[ProQuest] [eScholarship]
Past Events
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CAFT 2018 - New Developments in Complex Analysis and Function Theory , University of Crete, Heraklion, Greece, July 2-6, 2018