Istvan+Prause's+papers

Research topics

Conformal and geometric analysis, quasiconformal methods, complex analysis
Holomorphic motions and their applications to analysis and dynamics; holomorphic interpolation
Multifractal analysis and boundary behaviour of conformal maps
Limit shape phenomena in statistical mechanics: dimer model, five- and six-vertex model, random Young tableaux etc.

Publications and preprints

• On mappings of finite distortion that are quasiconformal in the unit disk (with Olli Hirviniemi, Lauri Hitruhin and Eero Saksman), to appear in J. Anal. Math., arXiv:2104.10961, 2021
• The genus-zero five-vertex model (with Rick Kenyon), arXiv:2101.04195, 2021
• Gradient variational problems in R² (with Rick Kenyon), to appear in Duke Math. J., arXiv:2006.01219, 2020
• Dimer models and conformal structures (with Kari Astala, Erik Duse and Xiao Zhong), arXiv:2004.02599, 2020
• Stretching and rotation of planar quasiconformal mappings on a line (with Olli Hirviniemi and Eero Saksman), to appear in Potential Anal., arXiv:2007.07735, 2020
• Localized regularity of planar maps of finite distortion (with Olli Hirviniemi and Eero Saksman), Rev. Mat. Iberoam. (online first), arXiv:2001.04173, 2020
• Quasidisks and twisting of the Riemann map, Int. Math. Res. Not. IMRN (7), 2019, 1936--1954, arXiv:1611.06734
• Quasiconformal extensions, Loewner chains, and the lambda-Lemma (with Pavel Gumenyuk), Anal. Math. Phys. (8), 2018, 621--635, A. Vasiliev Memorial Volume,  arXiv:1712.08632
• Asymptotic variance of the Beurling transform (with Kari Astala, Oleg Ivrii and Antti Perälä), GAFA 25 (6), 2015, 1647--1687, arXiv:1502.00459
• A hunt for sharp L^p-estimates and rank-one convex variational integrals (with Kari Astala, Tadeusz Iwaniec and Eero Saksman), Filomat 29 (2), 2015, 245--261, arXiv:1403.1095
• On a Hölder constant in the theory of quasiconformal mappings, Comput. Methods. Funct. Theory 14, 2014, 483--486, F.W. Gehring Memorial Volume, arXiv:1309.6748
• Bilipschitz and quasiconformal rotation, stretching and multifractal spectra (with Kari Astala, Tadeusz Iwaniec and Eero Saksman), Publ. Math. Inst. Hautes Études Sci. 121 (1), 2015, 113--154, arXiv:1303.2325
• Burkholder integrals, Morrey's problem and quasiconformal mappings (with Kari Astala, Tadeusz Iwaniec and Eero Saksman),
  J. Amer. Math. Soc. 25 (2), 2012, 507--531, arXiv:1012.0504
• Hausdorff measure of quasicircles (with Xavier Tolsa and Ignacio Uriarte-Tuero), Adv. Math. 229 (2), 2012, 1313--1328, arXiv:0912.3365
• Quasisymmetric distortion spectrum (with Stas Smirnov), Bull. London Math. Soc. 43 (2), 2011, 267--277, arXiv:0910.4723
• Flatness properties of quasispheres, Comput. Methods Funct. Theory 7, 2007, 527–541.
• On distortion of Hausdorff measures under quasiconformal mappings, Conform. Geom. Dyn. 11, 2007, 219--223.
• A remark on quasiconformal dimension distortion on the line, Ann. Acad. Sci. Fenn. Math. 32, 2007 no. 2, 341--352.

Slides from selected talks

• Integrability of limit shapes, Solvable lattice models seminar, November 2021 (video)
  
  
• Probabilistic limit shapes and harmonic functions, CAvid seminar, October 2021 (video)
  
  
• Random tilings, arctic curves and a Beltrami equation, Finnish Mathematical Days, Oulu, January 2020
  
  
• Schwarz lemma and quasiconformal mappings, Analysis aspects of dynamics, Imperial College, London, UK, May 2018
  
  
• Arctic curves beyond the arctic circle, 6th Workshop on Fourier Analysis and Related Fields, Pécs, Hungary, August 2017
  
  
• Quasidisks and twisting of the Riemann map, Analysis and Dynamics, BIRS-CMO Workshop, Oaxaca, Mexico, September 2016 (video)
  
  
• Holomorphic interpolation: from dynamics to analysis, Topics in Analysis and Holomorphic Dynamics, Simons Semester in Banach Center, Warsaw, Poland, September 2015
  
  
• Asymptotic variance of the Beurling transform, Workshop on Conformal Methods in Analysis, Random Structures and Dynamics,
  Chales, France, April 2015
  
  
• Area distortion, quasicircles and harmonic measure, Quasiconformal Geometry and Elliptic PDEs, 
  IPAM, Los Angeles, USA, May 2013 (video)
  
  
• Bilipschitz rotation versus quasiconformal stretching, Harmonic and Complex Analysis and its Applications (HCAA),
  Puerto de la Cruz, Tenerife, Spain, March 2012
   
• Burkholder integrals, Morrey's problem and quasiconformal mappings,
  Ahlfors-Bers Colloquium, Houston, USA, March 2011
   
• Quasisymmetric distortion spectrum, Conformal Methods in Analysis and Dynamics (CODY), Seillac, France, May 2010