Contact information

Office: PG (45 St. George Street) 303A
Telephone: 4169786811
Email: artem DOT dudko AT utoronto.ca

Research interests

Holomorphic Dynamics, Parabolic Renormalization, Resurgence Theory, Computability and Computational Complexity in Dynamics
Representations of infinitedimensional groups, Groups acting on rooted trees, Selfsimilar groups, Spectral Theory, Ergodic Theory
CV

Teaching

Spring 2017: MAT378H5S (Introduction to Real Analysis)
Fall 2015: MAT334H5F (Complex Variables)

Publications

 (joint with S. Sutherland) The measure of the Feigenbaum Julia set,
in preparation
 (joint with M. Yampolsky) Almost every real quadratic polynomial has a polytime computable Julia set.
[ arXiv:math.DS/1702.05768]
 On irreducibility of Koopman representations corresponding to measure contracting actions, accepted for publication in Groups, Geometry and Dynamics;
[ arxiv.math.RT/1512.02687 ]
 (joint with R. Grigorchuk) On spectra of Koopman, groupoid and quasiregular representations,
Journal of Modern Dynamics, Volume 11 (2017), 99123;
[ arxiv:math.RT/1510.00897 ]
 (joint with R. Grigorchuk) On diagonal actions of branch groups and the corresponding characters.
[ arxiv:math.RT/1412.5476 ]
 (joint with R. Grigorchuk) On irreducibility and disjointness of Koopman and quasiregular representations
of weakly branch groups, Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov,
AMS Cont. Math. Ser. (2016), to appear;
[ arxiv:math.RT/1508.05452 ].
 (joint with M. Yampolsky) Polytime 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 EcalleVoronin'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), 255261.
[ arXiv: math.DS/1307.8093 ]
 Computability of the Julia set. Nonrecurrent critical orbits, Discrete and Continuous Dynamical Systems, Volume 34, 7 (2014), 27512778.
[ arXiv: math.DS/1109.2946 ]
 (joint with K. Medynets) Finite Factor Representations of HigmanThompson 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, 15651598. [ arXiv: math.RT/1105.6325 ]
 Characters on the Full Group of an Ergodic Hyperfinite Equivalence Relation, Journal of Functional Analysis 261 (2011), no. 6, 14011414. [ arXiv: math.RT/1005.4289 ]
 (joint with S. Favorov), A uniformly spread measure criterion, Anal. Math. Phys., Volume 1, 23 (2011), 115119. [ 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 1220. [ 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, 1419.
 (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, 332; translation in Sb. Math. 199 (2008), no. 910 , 14211450.
 (joint with N. Nessonov), Projective characters of the infinite generalized symmetric group, (Russian) Funktsional. Anal. i Prilozhen. 42 (2008), no. 1, 8285; translation in Funct. Anal. Appl. 42 (2008), no. 1, 6971.
 (joint with N. Nessonov), A description of characters on the infinite wreath product, Methods Funct. Anal. Topology 13 (2007), no. 4, 301317. [ arXiv: math.RT/0510597 ]
 Tame representations of the group GL(\infty,F_q) (Russian) Algebra i Analiz 18 (2006), no. 2, 5779; translation in St. Petersburg Math. J. 18 (2007), no. 2, 223239.

Recent invited talks

 April 5, 2016, On computational aspects of the Feigenbaum fixed point of perioddoubling 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 quasiregular representations,
New York Applied Algebra Collogquium, CUNY Graduate Center, USA
 November 12, 2015, On Koopman, groupoid and quasiregular 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 HigmanThompson groups, Conference "Groups acting on rooted trees and around", Paris, France.
 December 8, 2013, The Julia set of the Feigenbaum map is polytime 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 Onedimensional 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, EcalleVoronin invariants and resurgent functions, Dynamical Systems Seminar, Centro di Ricerca Matematica Ennio de Giorgi, Pisa, Italy.
