About & bio

I am interested in analytic and geometric group theory and non-commutative geometry, including large scale geometry. My advisor is dr hab. Piotr W. Nowak from the Warsaw GGT research group.

A considerable part of my PhD work has been devoted to the warped cone construction, providing a bridge between dynamical systems of finitely generated groups and metric geometry. Keywords: spectral gap; Baum–Connes conjecture; amenability and dimension for dynamical systems, metric spaces, etc.; metric embeddings; super-expander graphs; Kazhdan and Haagerup properties.

Previous education

I obtained my Master's degree at the Faculty of Mathematics, Informatics and Mechanics of the University of Warsaw in 2014. Before, I attended a Double Degree Program in Computer Science and Mathematics completing my Bachelor's degrees in 2014 and 2012 respectively.

My Master's thesis concerned equivariant asymptotic dimension. It was awarded the Marcinkiewicz prize by the Polish Mathematical Society. My mathematical Bachelor's thesis was devoted to another variant of asymptotic dimension called asymptotic Assouad–Nagata dimension (or "linearly controlled asymptotic dimension"). I wrote two articles based on the theses (see below).


Publications and preprints

  1. Warped cones violating the coarse Baum–Connes conjecture

  2. Warped cones, (non-)rigidity, and piecewise properties
    with a joint appendix with Dawid Kielak (arxiv | pdf)

  3. Straightening warped cones
    with Jianchao Wu (arxiv)

  4. Super-expanders and warped cones

  5. Warped cones and spectral gaps
    with Piotr W. Nowak
    Proceedings of the American Mathematical Society 145 (2017), 817–823 (journal | arxiv)

  6. Warped cones over profinite completions
    Journal of Topology and Analysis (journal | arxiv)

  7. On equivariant asymptotic dimension
    Groups, Geometry, and Dynamics 11 (2017), no. 3, 977–1002 (journal | arxiv)

  8. Remarks on coarse triviality of asymptotic Assouad–Nagata dimension
    Topology and its Applications 167 (2014), 69–75 (journal | arxiv)


  1. Equivariant asymptotic dimension
    Master's thesis, MIMUW, 2014.

  2. Funkcje liniowe w geometrii wielkiej skali: quasi-izometrie i wymiar asymptotyczny Assouada-Nagaty
    English title: Linear functions in large scale geometry: quasi-isometries and asymptotic Assouad-Nagata dimension
    Bachelor's thesis (in Polish), MIMUW, 2012.


Counterexamples to the coarse Baum–Connes conjecture from spectral-gap actions (abstract)
Operator algebra seminar, University of Copenhagen, February 2018

Large scale geometry of actions on compact spaces (abstract | lecture notes by Professor Pierre Pansu)
Workshop: Asymptotic decomposition methods in geometry, dynamics and operator algebras, University of Southampton, Isaac Newton Institute Satellite event, March 2017

Large scale geometry of group actions (abstract)
Dynamical Systems Seminar, IMPAN, February 2017

View on geometric group theory from the perspective of a warped cone (abstract)
Young Researchers' Colloquium, IMPAN, March 2016

Warped cones, profinite completions, coarse embeddings and property A (abstract | slides)
Séminaire Groupes et Analyse, Université de Neuchâtel, October 2015

Amenability and coarse embeddings of warped cones (abstract | slides)
Summer School: Probability on graphs and groups, CIB, EPFL, August 2015

Zgrupowane stożki i zgrubne zanurzenia (abstract)
Seminarium Geometrów (Geometry Seminar), University of Wrocław, May 2015

Attended events (posters, slides...)


research visit and a seminar talk at the University of Copenhagen
New Methods for Zimmer's Conjecture, IPAM, University of California, Los Angeles


Algebraic K- and L-Theory and Geometric Group Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany
Operator Algebras, Geometry, and Actions, Banach Centre, Warsaw
Geometric and Asymptotic Group Theory with Applications, University of the Basque Country, Bilbao, Spain
Approximation, deformation, quasification, Isaac Newton Institute, Cambridge, UK
Asymptotic decomposition methods in geometry, dynamics and operator algebras
University of Southampton, Isaac Newton Institute Satellite Workshop
(for information on my talk, see the Talks section)


Noncommutative geometry the next generation (Simons Semester), Banach Center, Warsaw
Workshop: Large Scale Dimensions, Regensburg, Germany
Poster: Equivariant asymptotic dimension (JPEG file, 0.5 MB)
Poster: Linear control of asymptotic dimension is coarsely void (JPEG file, 0.5 MB)
Groups, Dynamics, and Operator Algebras, Queen Mary University of London
Masterclass: Expanders and rigidity of group actions, Copenhagen
Combinatorics and Groups, Banach Center, Będlewo
Contributed talk: Large scale geometry of actions on compact spaces (abstract | slides)
Topological and Homological Methods in Group Theory, Bielefeld, Germany
Young Geometric Group Theory V, Karlsruhe, Germany
Poster: Warped cones and coarse embeddings (JPEG file, 0.5 MB)


"Groups, Graphs, Action!" Neuchâtel, Switzerland
GFT meets GGT, Banach Center, Warsaw
Topology Retreat, Banach Center, Będlewo
Contributed talk: On coarse (non)-amenability and (non)-embeddability of warped cones
Manifolds and Groups, Ventotene, Italy
Summer School: Probability on graphs and groups, Centre Interfacultaire Bernoulli, École polytechnique fédérale de Lausanne
Summer School: Cohomology and Large Scale Geometry, University of Regensburg
Geometric Group Theory (Januszkiewicz Conference), University of Wrocław
Poster: Warped cones over profinite completions (JPEG file, 0.5 MB)
Warsaw Summer School in Probability, University of Warsaw
research visit and a seminar talk at the University of Wrocław
Second Brazilian–Polish Topology Workshop, Banach Center, Warsaw
Young Geometric Group Theory IV, Spa, Belgium


Linear Algebra, Faculty of Economic Sciences, University of Warsaw
Mathematical Analysis II, Faculty of Economic Sciences, University of Warsaw
Mathematics (calculus), Faculty of Geology, University of Warsaw
Topology I*, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw (grading), materials