I algebraic geometry

Current research:

1. 
   The Peter-Weyl-Galois theory of classical and quantum compact principal bundles (Baum, Hajac, Szymanski)
   
2. 
   The invention of the Toeplitz quantum projective spaces (Hajac, Kaygun and Zielinski)
   
3. 
   Noncommutative join construction by Dabrowski, Hadfield, and Hajac
   
4. 
   Constructions of new cyclic modules by Boehm and Hajac
   
5. 
   The investigation of certain probabilistic aspects of (locally) compact quantum groups (Skalski)
   
6. 
   The study of connections between quantum group theories and noncommutative topological entropy (Skalski)
   
7. 
   The analysis of various phenomena related to topological quantum group actions on classical and quantum spaces (Soltan, Skalski)
   
8. 
   The construction of an adjunction between noncommutative algebras and quantum sets (Maszczyk)
   
9. 
   Monoidal categorical duality between Galois theory and spectral theory (Maszczyk)