# Research

- Lie groupoids and algebroids related to W*-algebras
- Infinite and finite dimensional integrable systems
- Banach Lie-Poisson 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

**Non-commutative Kahler structures**
rated as "outstanding". Now we are beginning new project: 1 P03A 001 29

**Banach Lie-Poisson 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 action-angle 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 q-difference equations**
- Agnieszka Tereszkiewicz, 2005,
**Integrability of Hamiltonians describing parametric conversion and Kerr-type effects in quantum optics **
- Grzegorz Jakimowicz, 2006,
**Quantum Minkowski space**
- Tomasz Goliński, 2010,
**Integrable systems on Banach Lie-Poisson 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: