Office: PG (45 St. George Street) 303A
E-mail: artem DOT dudko AT utoronto.ca
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
Spring 2017: MAT378H5S (Introduction to Real Analysis)
Fall 2015: MAT334H5F (Complex Variables)
- (joint with S. Sutherland) The measure of the Feigenbaum Julia set,
- (joint with M. Yampolsky) Almost every real quadratic polynomial has a poly-time computable Julia set.
- 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 quasi-regular representations,
Journal of Modern Dynamics, Volume 11 (2017), 99-123;
[ 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 quasi-regular 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) 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.
Recent invited talks
- 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.