Mario Bonk
Professor
University of California, Los Angeles, Department of Mathematics
Box 95155, Los Angeles, CA, 90095-1555, USA
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Office
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MS 6137
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Office Hours
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We, 1-2pm, Th, 2-3pm, and by appointment
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E-Mail
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mbonk at math.ucla.edu
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FAX
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(310) 206-6673
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Research Seminar
Sylvester Eriksson-Bique, Misha Hlushchanka, Annina Iseli, and I are running an international Zoom research seminar "Quasiworld". The topics include quasiconformal geometry, complex dynamics, and analysis on metric spaces. For more information see: Quasiworld.
Teaching
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2024/25: Math 245A: Real Analysis.
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2023/24: Math 245A+B: Real Analysis. Math 246C: Complex Analysis.
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2017/18: Math 245A-C: Real Analysis. Math 174E: Mathematics of Finance.
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2016/17: Math 252A: Topics in Complex Analysis. Math 174E: Mathematics of Finance.
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2015/16: Math 245A+B: Real Analysis.
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2015: Bootcamp in Linear Algebra.
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2014/15: Math 275A-C: Probability Theory. Stochastic Processes.
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2013/14: Math 246A+C: Complex Analysis.
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2012/13: Math 252A+B: Topics in Complex Analysis. Math 33AH+33A: Linear Algebra and Applications.
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2011/12: Math 246A-C: Complex Analysis.
Research interests
- My research interests lie at the interface of geometry and analysis, including classical complex analysis, the geometry of negatively curved spaces, geometric group theory, dynamics of rational maps, and analysis on metric spaces. My current work often relies on an extension of classical results in geometry and analysis to a non-smooth or fractal setting.
Research Monograph
- M. Bonk and D. Meyer, Expanding Thurston maps, Mathematical Surveys and Monographs, Vol. 225, Amer. Math. Soc., Providence, RI, 2017, 478 pp. Available here: link.
Research papers after 2010
- M. Bonk, M. Hlushchanka,
and R. Lodge, Thurston's pullback map, invariant covers, and the global dynamics on curves, Preprint, November 2024, (arXiv link).
- M. Bonk, J. Junnila,
S.Rohde, and Y. Wang, Piecewise geodesic Jordan curves II: Loewner energy,
projective structures, and accessory parameters, Preprint, October 2024,
(arXiv link).
- M. Bonk, The quasi-periods of the Weierstrass zeta-function, Preprint, Update: February 2024, to appear in: L’Enseignement Mathématique, (arXiv link).
- M. Bonk, L. Capogna, and X. Zhou, Green functions in metric measure spaces, Preprint, November 2022, (arXiv link).
- M. Bonk, M. Hlushchanka, and A. Iseli, Eliminating Thurston obstructions and controlling dynamics on curves, Ergod. Th. & Dynam. Sys. 44 (2024), 2454--2532, (arXiv link).
- M. Bonk and D. Meyer, Uniformly branching trees, Trans. Amer. Math. Soc. 375 (2022), 3841-3897, (arXiv link).
- M. Bonk and A. Eremenko, Canonical embeddings of pairs of arcs, Comput. Methods Funct. Theory 21 (2021), 825-830, (arXiv link).
- M. Bonk and H. Tran, The continuum self-similar tree, in: Fractal Geometry and Stochastics VI (Eds. U. Freiberg et al.), Birkhäuser, Cham, 2021, pp. 143--189, (arXiv link).
- M. Bonk and D. Meyer, Quotients of torus endomorphisms and Lattès-type maps, Arnold Math. J. 6 (2020), 495-521, (arXiv link).
- M. Bonk and S. Merenkov, Square Sierpinski carpets and Lattès maps, Math. Z. 296 (2020), 695-718, (arXiv link).
- M. Bonk and D. Meyer, Quasiconformal and geodesic trees, Fundamenta Math. 250 (2020), 253-299, (arXiv link).
- M. Bonk, L. Capogna, P. Hajlasz, N. Shanmugalingam, and J. Tyson, Analysis on metric spaces, Notices Amer. Math. Soc. 67 (2020), 253-256, (arXiv link).
- M. Bonk and P. Poggi-Corradini, The Rickman-Picard Theorem, Annales Acad. Sci. Fennicae 44 (2019), 615-633, (arXiv link).
- M. Bonk, E. Saksman, and T. Soto, Triebel-Lizorkin spaces on metric spaces via hyperbolic fillings, Indiana Univ. Math. J. 67 (2018), 1625-1663, (arXiv link).
- M. Bonk and E. Saksman, Sobolev spaces and hyperbolic fillings, J. Reine Angew. Math. 737 (2018), 161-187, (arXiv link).
- M. Bonk, Uniformization by square domains, J. Analysis 24 (2016), 103-110, (arXiv link).
- M. Bonk, M. Lyubich, and S. Merenkov, Quasisymmetries of Sierpinski carpet Julia sets, Adv. Math. 301 (2016), 383-422, (arXiv link).
- M. Bonk and S. Merenkov, Quasisymmetric rigidity of square Sierpinski carpets, Ann. of Math. 177 (2013), 591-643, (arXiv link).
- M. Bonk, Uniformization of Sierpinski carpets in the plane, Invent. Math. 186 (2011), 559-665, (arXiv link).