Articles
  • Conditionally strictly negative definite kernels, ArXiv, Linear & Multilinear Algebra 63 (2015), 2406-2418.
  • Hopf Images in Locally Compact Quantum Groups (with P. Kasprzak & P. M. Sołtan), ArXiv, Journal of Mathematical Analysis and Applications 455 (2017), 141–166.
  • Remarks on Hopf images and quantum permutation groups , ArXiv, will appear in Canadian Mathematical Bulletin.
  • Quantum Bernstein's Theorem and the Hyperoctahedral Quantum Group (with K. Szpojankowski), ArXiv.
    Current activities and research interest

    Currently I'm interested in finding new interactions between quantum groups and free probability, and applications thereof in operator algebras in general:

  • operator-valued free probability treated as replacement for scalars in linear probabilistic problems ;
  • Connes' embedding property for via quantum increasing sequences and quantum Ryll-Nardzewski theorem;
  • lattice of quantum subgroups of particular quantum groups (e.g. of ), idempotent states and random walks.

    • I used to fight against harmonic analysis on discrete groups and graphs, approximation properties for discrete groups and presumably something else. I might still have some insight in those areas.

    Other

    I defended my PhD dissertation, written under supervision of dr hab. Piotr Sołtan and dr hab. Paweł Kasprzak from KMMF FUW, on 30th March, 2017. The Scientific Council of IMPAN granted me the PhD degree on 20th April, 2017. Here is my dissertation, most of my work from there is included in the articles Hopf Images in Locally Compact Quantum Groups and Remarks on Hopf images and quantum permutation groups .

    I defended my MSC thesis in University of Wrocław on 29th June, 2012. My supervisor was prof. Marek Bożejko. Here is my thesis (written in Polish), most of my work from here is included in the article Conditionally strictly negative definite kernels. The thesis were awarded Grand Prix in the contest of master theses in pure mathematics by Polish Mathematical Society in 2012, link.