Chair of Mathematical Physics
Faculty of Mathematics
University of Białystok
My research interests are related to various aspects of mathematical physics with emphasis on topics close to problems of functional analysis and operator algebras:
- infinite dimensional geometry with emphasis on Poisson geometry on Banach manifolds, Banach Lie groupoids and algebroids
- integrable systems both in quantum and classical setting, also in relation to quantum optics
- factorization method in discrete version
- in particular: geometry and integrable systems on the restricted Grassmannian
Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure, arXiv:2112.14690 (with F. Pelletier)
Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian, J. Funct. Anal. 258 (2010), no. 10, 3266 - 3294. DOI: 10.1016/j.jfa.2010.01.019 (with A. Odzijewicz)
Queer Poisson brackets, J. Geom. Phys. 132 (2018), 358-362. DOI: 10.1016/j.geomphys.2018.06.013 (with D. Beltita, A.-B. Tumpach)
Banach-Lie groupoids and generalized inversion, J. Funct. Anal. 276 (2019), no. 5, 1528-1574. DOI: 10.1016/j.jfa.2018.12.002 (with D. Beltita, G. Jakimowicz, F. Pelletier)
Factorization method for second order functional equations, J. Comput. Appl. Math. 176 (2005), no. 2, 331-355. DOI: 10.1016/j.cam.2004.07.023 (with A. Odzijewicz)
Workshop on Geometric Methods in Physics
For the better part of this century I've been a secretary of Workshop on Geometric Methods in Physics — annual international conference in the field of mathematical physics and mathematics organized in Białowieża. Head to the webpage to learn more or to register. You can also visit the Facebook page: facebook.com/wgmp.bialowieza. The event is accompaigned by School on Geometry and Physics intended for young researchers and graduate students. It takes place in the week preceding the Workshop and consists of several 3h courses by leading experts in mathematical physics.
I am starting 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 starting Autumn 2020. During this time we will organize several research group meetings and a school on infinite-dimensional geometry in Vienna.
You can find some of my code written as a hobby on Gitlab (there are also repositories on Github but they are not kept up to date due to the change in ownership of that website). It hosts among others my personal fork of Music on Console featuring new features and a C++ rewrite of SGallery - a generator of static photo gallery.
There is also a generator for stats for Opencaching to be found at tomaszg.pl/geo (with source also hosted on Gitlab).
My photography webpage is tomaszg.pl. There are major subsections devoted to music photography (mostly folk and sea shanties genre).