Sixth Framework Programme

Marie Curie Actions

 

EU Research Training Network CODY

Conformal Structures and Dynamics

Research Training Networks
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Teams

Country UK Poland Finland France Spain Germany Denmark/Sweden Greece Switzerland
Node

Leader: Feliks Przytycki (click here for the address of IMPAN)

The Institute of Mathematics of Polish Academy of Sciences (IMPAN) and its conference/training branch: Stefan Banach International Mathematical Center (BC), employs about 40 researchers on full time permanent or long period positions and other about 40 on 1 year (mostly postdoc) or part time positions. It leads PhD studies with 22 PhD students now. It closely cooperates with Universities (Warsaw, Wroclaw, Poznan, Torun, Gdansk, Katowice, Krakow, Lodz, etc.); it has small branches in some of these cities. It is editing several international math. journals and serials: Acta Arithmetica, Annales Pol. Math., Applicationes Math., Banach Center Publ., Colloquium Math., Dissertationes Math., Fundamenta Mathematicae, Studia Mathematica. Its library is one of best math. libraries in the world. IMPAN-BC hosted a Center of Excellence and Marie Curie Training Site within FP5. Now it hosts two FP6 ToK's programmes; it is a node to ECRYPT NoE and the MC training network ‘phenomena in high dimensions’. The Banach Center, directed by an international scientific committee, organizes about yearly 30 international conferences and schools in Warsaw and new IMPAN conference/research centre in Bedlewo (near Poznan) having about 120 accomodation places. In Warsaw IMPAN building there are around 20 hotel rooms for visitors.

Warsaw has a long-standing tradition in Quasiconformal Mappings and Dynamical Systems. In particular the team will concentrate on holomorphic dynamics, and on analysis on metric spaces and connections between quasiconformal mappings and calculus of variations. Bojarski was among the pioneers of the analytic theory of quasiconformal mappings in two and more dimensions and the famous Measurable Riemann Mapping Theorem. Iwaniec, Hajlasz (both now in the USA) and Strzelecki, Kalamajska and Zatorska in the team, are his children and grandchildren. Dynamical systems started in 60s (influenced by Ja.Sinai), with Krzyzewski and Szlenk and later with Misiurewicz as pioneers. Around 1983 holomorphic iterations were started by Przytycki, Kotus, Urbanski and Zdunik which resulted in a theory comparing harmonic to Hausdorff and Gibbs equilibrium measures, influenced by L. Carleson (KTH), and iteration of meromorphic maps. Some other topics of activity of the group include conformal and invariant measures on Julia and radial Julia set for entire and meromorphic functions, iteration of holomorphic Collet-Eckmann maps, statistics of returns in dynamics, entropy, non-conformal IFS, relations with differential geometry and mechanics, etc. The team organized holomorphic iterations workshops in 1995 (within a larger programme) 1998, 1999, 2002 and 2005 in the Banach Center in Warsaw.

Principal researchers for this project:
Krzysztof Baranski, assistant professor. Iteration of transcendental functions, dimensions of graphs of lacunary Fourier series. Multifractals. (50%)
Bogdan Bojarski, full professor, member of the Polish Academy of Sciences. Pioneer in Quasiconformal Mappings Theory. (20%)
Agnieszka Kalamajska, assistant professor. PDE's and variational problems. (20%)
Boguslawa Karpinska, assistant professor. Iteration of entire and meromorphic maps. (30%)
Janina Kotus, professor. One of pioneers of iterations of meromorphic functions. (30%)
Feliks Przytycki (Team Coordinator), full professor. Applications of ergodic theory and thermodynamical formalism to holomorphic dynamics; boundary growth of analytic functions. (30%)
Michal Rams, assistant professor. IFS with overlaps, dimensions of solenoids, packings. (40%)
Pawel Strzelecki, associate professor. Expert in PDE and variational problems. (20%)
Maciej Wojtkowski, full professor. ICM 2002, Expert in hyperbolic dynamics, billiards, geodesic flows .(20%)
Anna Zatorska-Goldstein, PDE's and variational problems. (30%)
Anna Zdunik, associate professor. Expert in harmonic measure and equilibria in holomorphic dynamics, statistics of returns, meromorphic dynamics. (30%)

Associated researchers:
A. Lasota, R. Rudnicki, J.Jaroszewska, T. Szarek (Silesian University and IMPAN, Lab. of Biomathematics); H. Zoladek, J. Miekisz, G. Lukaszewicz (Warsaw); M. Lemanczyk, K. Fraczek (Torun); G. Swiatek (Penn State and Warsaw); T. Downarowicz (Wroclaw), T. Iwaniec (Syracuse, NY, and Warsaw); M. Urbanski (North Texas and Warsaw); G. Levin (Jerusalem), K. Simon (Budapest); J. Rivera-Letelier (Antofagasta); B. Skorulski (Antofagasta and Warsaw).

Selected publications:
F. Przytycki, J.Rivera-Letelier, S.Smirnov, Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps, Inventiones Math. 151, (2003), 29-63.
P. Strzelecki, A. Zatorska-Goldstein, A compactness theorem for weak solutions of higher-dimensional H-systems, Duke Mathematical Journal 121(2) (2004), 269-284.
M. Urbanski, A. Zdunik, Hausdorff dimension of harmonic measure for self-conformal sets, Advances in Math. 171 (2002), 1-58.