I algebraic geometry

KAROL PALKA is a young researcher, who obtained his Ph.D. from the University of Warsaw in 2009. In his thesis he studied the class of Q-homology planes, i.e. complex surfaces having rational homology of a plane. The main result was a major generalization of a theorem of Koras-Russell on contractible surfaces, which was a crucial step in the proof of the Linearization Conjecture for C* actions on C^3. Results from the thesis and his further research led to classification results for arbitrarily singular Q-homology planes. Palka collaborates with researchers in affine geometry in Japan, France and Canada. His research is now concentrated on the following three topics:

1. 
   Analysis of singularities and fundamental groups of Q-homology planes of general type.
   
2. 
   Study of homologically trivial complex threefolds, in particular the class of contractible threefolds, which is crucial for the Zariski Cancellation Conjecture.
   
3. 
   Classification of closed C* embeddings into the plane and extension of the methods to analyze cuspidal curves in P^2.
   

Palka plans a 6-month visit in RIMS, Kyoto, Japan to collaborate with Prof. Masayoshi Miyanishi and Prof. Takahashi Kishimoto (Saitama University) on contractible threefolds and methods of the log Minimal Model Program. He plans a 4-month visit in Dijon, France to collaborate with prof. Adrien Dubouloz on contractible threefolds. He also plans a 3-month visit in Montreal, Canada to continue his collaboration with prof. Peter Russell on plane C* embeddings and on the Coolidge-Nagata conjecture.

A 1 year postdoctoral position will be opened for applicants to work on the subject of complex affine geometry.

II. PARTIAL DIFFERENTIAL EQUATIONS
Team leader: prof. Wojciech Zajaczkowski
Members:

• 
  prof. Teresa Reginska
  
• 
  dr Joanna Renclawowicz
  
• 
  dr Tomasz Cieslak,
  
• 
  phd student Jan Burczak
  

Outside members:

From University of Warsaw:

• 
  dr hab. Piotr Gwiazda
  
• 
  prof. Piotr Mucha
  
• 
  dr Agnieszka Swierczewska – Gwiazda
  
• 
  prof. Grzegorz Lukaszewicz
  
• 
  prof. Piotr Rybka
  
• 
  prof. Dariusz Wrzosek
  
• 
  dr Bernard Nowakowski
  
• 
  
  

From Systems Research Institute:

• 
  prof. Irena Pawlow
  

From Warsaw University of Technology:

• 
  dr hab. Ewa Zadrzynska
  
• 
  dr Adam Kubica