Research
 Lie groupoids and algebroids related to W*algebras
 Infinite and finite dimensional integrable systems
 Banach LiePoisson geometry, W*algebras
 Quantization and coherent states
 Quantum logics, theory of measurement
 Orthogonal polynomials in quantum optics
Grants
Our team have finished a KBN (Polish State Committee for Scientific Research) grant 2 P03A 012 19 Noncommutative Kahler structures
rated as "outstanding". Now we are beginning new project: 1 P03A 001 29 Banach LiePoisson spaces, integrable systems, and quantization
Project concerns the theory of Banach Poisson manifolds. The aim of projected research is to apply this theory to the description and quantization of finite and infinite dimensional Hamiltonian systems. In particular we will study the following problems
 Integrability of infinite Toda lattice by the construction of actionangle variables;
 Relation of integrability of multiboson systems with the theory of orthogonal polynomials;
 Infinite dimensional integrable systems on the restricted Grassmannian and their quantization by means of coherent state map;
 Coherent state map and logics related to W*algebras;
 Quantum complex Minkowski space and other quantum phase spaces.
Ph.D. theses
In last years there were the following Ph.D. promotions in our Division:
 Alina Dobrogowska, 2004, Factorization method for second order qdifference equations
 Agnieszka Tereszkiewicz, 2005, Integrability of Hamiltonians describing parametric conversion and Kerrtype effects in quantum optics
 Grzegorz Jakimowicz, 2006, Quantum Minkowski space
 Tomasz Goliński, 2010, Integrable systems on Banach LiePoisson spaces related to Sato Grassmannian
 Aneta Sliżewska, 2011, Groupoids and semigroups related to von Neumann algebras
Habilitation
In last years there were the following habilitations in our Division:
