Zakład Układów Dynamicznych
prof. IM PAN
22 5228 218
Research interests: Holomorphic Dynamics, Parabolic Renormalization, Resurgence Theory, Computability and Computational Complexity in Dynamics
Representations of infinite-dimensional groups, Groups acting on rooted trees, Self-similar groups, Spectral Theory, Ergodic Theory
- (joint with I. Gorbovickis and W. Tucker) Lower bounds on the Hausdorff dimension of some Julia sets, [ arXiv: math.DS/2204.07880 ]
- (joint with R. Grigorchuk) On spectral properties of the Schreier graphs of the Thompson group F, accepted for publication in the Transactions of the American Mathematical Society; [ arXiv: math.SP/2107.01109 ]
- On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization, Bulletin Polish Acad. Sci. Math. 68 (2020), 151-168.
- (joint with S. Sutherland) On the Lebesgue measure of the Feigenbaum Julia set, Invent. math. 221 (2020), 167-202; [ arXiv: math.DS/1712.08638 ]
- (joint with M. Yampolsky) On computational complexity of Cremer Julia sets, Fund. Math. 252 (2021), no. 3, 343-353 [ arxiv: math.DS/1907.11047 ]
- (joint with R. Grigorchuk) On the question "Can one hear the shape of a group?" and Hulanicki type theorem for graphs, Israel J. Math. 237 (2020), no. 1, 53-74; [ arXiv:math.GR/1809.04008 ]
- (joint with K. Medynets) On invariant random subgroups of block-diagonal limits of symmetric groups, Proc. of AMS, 147 (2019), no. 6, 2481-2494; [ arXiv: math.GR / 1711.01653 ]
- On irreducibility of Koopman representations corresponding to measure contracting actions, Groups, Geometry and Dynamics, 12 (2018), no. 4, 1417-1427; [ arxiv.math.RT/1512.02687 ]
- (joint with M. Yampolsky) Almost every real quadratic polynomial has a poly-time computable Julia set, Found. Comp. Math., 18 (2018), no. 5, 1233-1243; [ arXiv: math.DS / 1702.05768 ]
- (joint with R. Grigorchuk) On diagonal actions of branch groups and the corresponding characters, J. Funct. Anal. 274 (2018), no. 11, 3033-3055; [ arxiv:math.RT/1412.5476 ]
- (joint with R. Grigorchuk) On spectra of Koopman, groupoid and quasi-regular representations, Journal of Modern Dynamics, Volume 11 (2017), 99-123; [ arxiv:math.RT/1510.00897 ]
- (joint with R. Grigorchuk) On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups, Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov, AMS Cont. Math. Ser., Volume 692 (2017), 51-66; [ arxiv:math.RT/1508.05452 ].
- (joint with M. Yampolsky) Poly-time Computability of the Feigenbaum Julia set, Ergodic Theory and Dynam. Sys., to appear. [ arXiv: math.DS/1404.1236 ]
- (joint with D. Sauzin) On the resurgent approach to Ecalle-Voronin's invariants, Comptes Rendus Mathematique, Volume 353, 3 (2015), 265–271. [ arXiv: math.DS/1307.8095 ]
- (joint with D. Sauzin) The resurgent character of the Fatou coordinates of a simple parabolic germ, Comptes Rendus Mathematique, Volume 352, 3 (2014), 255-261. [ arXiv: math.DS/1307.8093 ]
- Computability of the Julia set. Nonrecurrent critical orbits, Discrete and Continuous Dynamical Systems, Volume 34, 7 (2014), 2751-2778. [ arXiv: math.DS/1109.2946 ]
- (joint with K. Medynets) Finite Factor Representations of Higman-Thompson groups, Groups, Geometry, and Dynamics 8 (2014). [ arXiv: math.RT/1212.1230 ]
- (joint with K. Medynets) On Characters of Inductive Limits of Symmetric Groups, Journal of Functional Analysis 264 (2013), no.7, 1565-1598. [ arXiv: math.RT/1105.6325 ]
- Characters on the Full Group of an Ergodic Hyperfinite Equivalence Relation, Journal of Functional Analysis 261 (2011), no. 6, 1401-1414. [ arXiv: math.RT/1005.4289 ]
- (joint with S. Favorov), A uniformly spread measure criterion, Anal. Math. Phys., Volume 1, 2-3 (2011), 115-119. [ arXiv: math.CA/0805.0959 ]
- (joint with T. Banakh and D. Repovs) Symmetric monochromatic subsets in colorings of the Lobachevsky plane, Discrete Math. Theor. Comput. Sci. 12 (2010), no. 1 12-20. [ arXiv: math.CO/0804.1335 ]
- A description of characters on generalized groups of motions associated with GL(\infty,F_q), (Russian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 2008, no. 10, 14-19.
- (joint with N. Nessonov) Invariant states on the wreath product. [ arXiv: math/RT/0903.4987 ]
- (joint with N. Nessonov), Characters of projective representations of the infinite generalized symmetric group, (Russian) Mat. Sb. 199 (2008), no. 10, 3-32; translation in Sb. Math. 199 (2008), no. 9-10 , 1421-1450.
- (joint with N. Nessonov), Projective characters of the infinite generalized symmetric group, (Russian) Funktsional. Anal. i Prilozhen. 42 (2008), no. 1, 82-85; translation in Funct. Anal. Appl. 42 (2008), no. 1, 69-71.
- (joint with N. Nessonov), A description of characters on the infinite wreath product, Methods Funct. Anal. Topology 13 (2007), no. 4, 301-317. [ arXiv: math.RT/0510597 ]
- Tame representations of the group GL(\infty,F_q) (Russian) Algebra i Analiz 18 (2006), no. 2, 57-79; translation in St. Petersburg Math. J. 18 (2007), no. 2, 223-239.
- May 31, 2022, New estimates from below on the Hausdorff dimension of some Julia sets, Workshop in Dynamics, Uppsala University, Sweden
- June 16, 2021, On Hausdorff dimension of Julia sets of real Feigenbaum maps, Conference "The 9th Visegrad Conference, Dynamical Systems", Prague, Czech Republic (on-line)
- May 13, 2019, On computational complexity of Julia sets, Mathematics Colloquium at Jacobs University, Bremen, Germany.
- January 28, 2019, Can one hear the shape of a group?, Alfred Renyi Institute of Mathematics, Budapest, Hungary.
- January 17, 2019, On computational complexity of Cremer Julia sets, Ergodic Theory and Dynamical Systems Seminar, University of Warwick, Coventy, UK.
- January 15, 2019, On Hausdorff dimension of the Feigenbaum Julia set, Dynamical Systems Seminar, Imperial College London, UK.
- July 23, 2018, On Hausdorff dimension of the Feigenbaum Julia set, Dynamical Systems Seminar, University of Barcelona, Spain.
- July 5, 2018, On computability and computational complexity of Julia sets, Workshop "New Developments in Complex Analysis and Function Theory", University of Crete, Heraklion, Greece.
- March 27, 2018, On the Lebesgue measure of the Feigenbaum Julia set, Workshop "Algorithmic Questions in Dynamical Systems", Institut de Mathématiques de Toulouse, France.
- August 14, 2017, On the Julia set of the Feigenbaum quadratic polynomial, Conference "Just a little calculation in dynamics", Bedlewo, Poland.
- April 5, 2016, On computational aspects of the Feigenbaum fixed point of period-doubling renormalization, Workshop "Computation in Dynamics", ICERM, Brown University, USA.
- March 20, 2016, On measure of the Feigenbaum fixed point Julia set, AMS special session "Holomorphic Dynamics", Spring Eastern Sectional Meeting, Stony Brook University, USA.
- February 26, 2016, On spectra of Koopman, groupoid and quasi-regular representations, New York Applied Algebra Collogquium, CUNY Graduate Center, USA.
- November 12, 2015, On Koopman, groupoid and quasi-regular representations and weakly branch groups, Conference "Geometric and Probabilistic Methods in Group Theory and Dynamical Systems", Texas A&M University, USA.
- September 12, 2014, On diagonal actions of branch groups and the corresponding characters, Linear Analysis Seminar, Texas A&M University, USA.
- September 10, 2014, Representations associated with group actions and spectra of Hecke type operators, Groups and Dynamics Seminar, Texas A&M University, USA.
- February 25, 2014, On characters of approximately finite groups and Higman-Thompson groups, Conference "Groups acting on rooted trees and around", Paris, France.
- December 8, 2013, The Julia set of the Feigenbaum map is poly-time computable, Section "Holomorphic dynamics and related topics", CMS Winter meeting, Ottawa, Canada.
- October 17, 2013, On the resurgent approach to local dynamics of simple parabolic germs, Workshop "Topological and Combinatorial Problems in One-dimensional Complex Dynamics", Pisa, Italy.
- January 21, 2013, Dynamics of parabolic germs via Resurgence Theory, Dynamical Systems Seminar, University of Toronto, Canada.
- February 16, 2012, Computability of Julia sets: a survey, Ergodic Theory and Probability Seminar, The Ohio State University, USA.
- September 9, 2011, On characters of inductive limits of symmetric groups, Workshop on Symmetric Functions and its Applications, City University of New York, USA.
- May 4, 2011, Ecalle-Voronin invariants and resurgent functions, Dynamical Systems Seminar, Centro di Ricerca Matematica Ennio de Giorgi, Pisa, Italy.