Research

  • Infinite and finite dimensional integrable systems
  • Infinite dimensional geometry in Banach context
  • Banach Lie groupoids and algebroids: theory and examples, i.e. related to W*-algebras
  • Banach Lie-Poisson geometry, W*-algebras
  • Quantization and coherent states
  • Quantum logics, theory of measurement
  • Orthogonal polynomials in quantum optics
  • Factorization method

Grants

Our team takes part in a bilateral Polish-Austrian research project Banach Poisson-Lie groups and integrable systems together with Alice Barbara Tumpach (Mozart call). It is a 3 years project, which started Autumn 2020. During this time we organized several research group meetings and a school on infinite-dimensional geometry in Vienna.

In the past our team participated in the following Polish grants:

  • 1 P03A 001 29 Banach Lie-Poisson spaces, integrable systems, and quantization (KBN)
  • 2 P03A 012 19 Non-commutative Kahler structures (KBN)
  • DNK/SP/548722/2022 *XL Workshop on Geometric Methods in Physics ("Doskonała Nauka")

Ph.D. theses

In last years there were the following Ph.D. promotions in our group:

  • Alina Dobrogowska, 2004, Factorization method for second order q-difference equations, supervisor: A. Odzijewicz, University of Białystok
  • Agnieszka Tereszkiewicz, 2005, Integrability of Hamiltonians describing parametric conversion and Kerr-type effects in quantum optics, supervisor: A. Odzijewicz, University of Białystok
  • Grzegorz Jakimowicz, 2006, Quantum Minkowski space, supervisor: A. Odzijewicz, University of Białystok
  • Tomasz Goliński, 2010, Integrable systems on Banach Lie-Poisson spaces related to Sato Grassmannian, supervisor: A. Odzijewicz, Warsaw University of Technology
  • Aneta Sliżewska, 2011, Groupoids and semigroups related to von Neumann algebras, supervisor: A. Odzijewicz, Warsaw University of Technology
  • Marzena Szajewska, 2011, Special functions and orthogonal polynomials of compact simple Lie groups and some of their applications, supervisors: Z. Pasternak-Winiarski, J. Patera, Warsaw University of Technology

Habilitation

In last years there were the following habilitations in our group:

  • Alina Dobrogowska, 2016