Sixth Framework Programme

Marie Curie Actions


EU Research Training Network CODY

Conformal Structures and Dynamics

Research Training Networks





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

Leader: Kari Astala (click here for the address of the Helsinki Mathematics deparment)

In Finland, the Helsinki Mathematics department is the leading center of mathematical research. Currently the department participates in several Centers of Excellence nominated by the Academy of Finland, with two of them coordinated from Helsinki. The department occupies a new modern building, offering all modern technological facilities.

Finland has particularly strong traditions in geometric analysis based on conformal and quasiconformal methods, and the Finnish team collects the leading experts in the country, from the universities of Helsinki (HU) and Jyväskylä (JU). In addition the team is joined by groups from geometric measure theory and mathematical physics, where in both the senior members are international leading experts in their fields. The teams have regularly organized conferences and different training activities, with the annual international Jyväskylä summer school offering a regular basis for further training in the topics of this proposal.

Principal researchers for this project:
Kari Astala (HU, Academy Professor; Team Coordinator): Salem Prize 1994, Expert in quasiconformal mappings and their applications. Used dynamical methods to prove the fundamental Gehring-Reich conjecture on qc-mappings. Organized several conferences and summerschools, President of the Finnish mathematical Society. (50%)
Antti Kupiainen. (Academy Professor) Expert in mathematical physics, has pioneered the renormalization group in rigorous quantum field theory, random systems, PDE’s and dynamics. Introduced anomalous scaling in turbulent systems; proved the ergodicity of the two-dimensional stochastic Navier-Stokes dynamics. (30%)
Pertti Mattila (Professor) Expert in geometric measure theory, rectifiablity and multifractal phenomena. Introduced new novel methods in removable singularities of bounded holomorphic functions. Leader of Finnish CoE in geometric analysis. (30%)
Ilkka Holopainen (lecturer) Expert in quasiconformal mappings and analysis in metric spaces (20%)
Pekka Koskela (JU, Professor) Expert in mappings of finite and bounded distortion, analysis in metric spaces. Established the quasiconformal theory of metric measure spaces and foundations of modern theory of mappings of finite distortion in space (30%)
Esa Järvenpää (JU, Professor). Expert in geometric measure theory and extended dynamical systems (20%)
Maarit Järvenpää (JU, Lecturer) Expert in geomteric measure theory (20%)
Kaj Rajala (JU, Academy researcher). Expert in quasiconformal and quasiregular mappings in space (50%)

Selected publications:
J. Bricmont, A. Kupiainen and A. Schenkel, Renormalization group and the Melnikov problem for PDE's. Comm. Math. Phys. 221 (2001), no. 1, 101—140.
D. Faraco, P. Koskela, Pekka, X. Zhong, Mappings of finite distortion: the degree of regularity. Adv. Math. 190 (2005), no. 2, 300--318.
Mattila, Pertti, Hausdorff dimension, projections, and the Fourier transform. Publ. Mat. 48 (2004), no. 1, 3--48.