# CODY Streszczenie raportu

Project ID:
35651

Źródło dofinansowania:
FP6-MOBILITY

Kraj:
United Kingdom

## Final Activity Report Summary - CODY (Conformal Structures and Dynamics)

Throughout science and engineering, objects with fractal-like structures appear which cannot be modelled via basic Euclidean geometry. Sometimes these come about by intrinsic properties of the space, but more often because of the properties of underlying dynamical, percolation or diffusion processes. Here one can think of arteries or crystal formation. It turns out that frequently these fractal structures are "conformally self-similar", i.e. look locally everywhere the same when one zooms-in far enough with an angle preserving rescaling. The research aim of the CODY network (Conformal Structures and Dynamics) was to understand these conformal structures, by combining and using cross-pollination from different branches of mathematics: analysis, dynamical systems and mathematical physics. Members of the network were able to obtain spectacular progress in this area, and trained-up a new generation of researchers.

In total 46 young researchers (ESR and ER's) were employed for periods between 3 and 30 months. Because quite a few senior members of the network are female, it managed to appoint 13 female researchers. Even after their appointments, fellows were able to benefit from their network contacts and continued to be actively involved in many of the network events (in total almost 50 major international workshops and conferences were organised). The scientific success of the network was recognised by the community, as evidenced by the major prizes that were awarded to some of its senior members. The mathematical equivalent of the Nobel prize - the Field Medal - was awarded to Stanislav Smirnov (the team leader of the Swiss node). Artur Avila, a member of the French node of the network, was awarded the European Mathematical Prize. Members of the network also gave invited talks at the International Congress of Mathematicians.

It is likely that the CODY network will have a lasting impact on the scientific community. Cooperation of European researchers of within this field was enhanced significantly by this network. Many of these collaborations resulted in joint publications between members from different countries. It is pleasing that young researchers played such an active role in the network and that several of the researchers who were trained by the network are likely to become new leaders in the field.

In total 46 young researchers (ESR and ER's) were employed for periods between 3 and 30 months. Because quite a few senior members of the network are female, it managed to appoint 13 female researchers. Even after their appointments, fellows were able to benefit from their network contacts and continued to be actively involved in many of the network events (in total almost 50 major international workshops and conferences were organised). The scientific success of the network was recognised by the community, as evidenced by the major prizes that were awarded to some of its senior members. The mathematical equivalent of the Nobel prize - the Field Medal - was awarded to Stanislav Smirnov (the team leader of the Swiss node). Artur Avila, a member of the French node of the network, was awarded the European Mathematical Prize. Members of the network also gave invited talks at the International Congress of Mathematicians.

It is likely that the CODY network will have a lasting impact on the scientific community. Cooperation of European researchers of within this field was enhanced significantly by this network. Many of these collaborations resulted in joint publications between members from different countries. It is pleasing that young researchers played such an active role in the network and that several of the researchers who were trained by the network are likely to become new leaders in the field.