I algebraic geometry

Future research plans:

Together with further development of the application of thermodynamics ideas, mathematical analysis and stochastic processes, there is dynamics to understand the small scale structures. We plan to involve in leading edge developments (using in particular Stochastic Loewner Evolution), in scaling limits, growth processes.

References

• 
  [Avila] A. Avila, Dynamics of renormalization operators, ICM 2010 Hyderabad, Plenary Lecture.
  
• 
  [PRS] F. Przytycki, J. Rivera-Letelier, S. Smirnov, Equivalence and topological invariance of conditions for non-uniform hyperbolicity in iteration of rational maps, Inventiones Mathematicae 151 (2003), 29-63.
  
• 
  [Smi] S. Smirnov, Discrete Complex Analysis and Probability, ICM 2010, Hyderabad, Plenary Lecture by Fields Medallist.
  

Tematyka zespołu Układów Dynamicznych, w której chcemy gości w celu ich wytrenowania:

1. 
   Multifractal spectra, fractal percolation. Scientist-in-charge: Michał Rams
   
2. 
   Holomorphic iteration techniques in entire and meromorphic functions. Scientist-in-charge: Feliks Przytycki, in cooperation with Janina Kotus (outside member of the team)
   
3. 
   Thermodynamical formalism in 1D-dynamics, real and complex. Scientist-in-charge: Feliks Przytycki
   
4. 
   Tame (zero entropy) dynamics, billiards and its complexity. Scientists-in-charge: Michał Rams and Eugene Gutkin.