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.

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).

Warped cones violating the coarse Baum–Connes conjecture

(pdf)Warped cones, (non-)rigidity, and piecewise properties

with a joint appendix with Dawid Kielak

Proceedings of the London Mathematical Society 118 (2019), no. 4, 753-786 (journal | arxiv)Straightening warped cones

with Jianchao Wu (arxiv)Super-expanders and warped cones

Annales de l'Institut Fourier, to appear (arxiv)Warped cones and spectral gaps

with Piotr W. Nowak

Proceedings of the American Mathematical Society 145 (2017), no. 2, 817–823 (journal | arxiv)Warped cones over profinite completions

Journal of Topology and Analysis 10 (2018), no. 3, 563–584 (journal | arxiv)On equivariant asymptotic dimension

Groups, Geometry, and Dynamics 11 (2017), no. 3, 977–1002 (journal | arxiv)Remarks on coarse triviality of asymptotic Assouad–Nagata dimension

Topology and its Applications 167 (2014), 69–75 (journal | arxiv)

Equivariant asymptotic dimension

Master's thesis, MIMUW, 2014.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.

Metric spaces defined by group actions (abstract)

Geometry and Topology Seminar, Adam Mickiewicz University, May 2018

Warped cones violating the coarse Baum–Connes conjecture (abstract)

Mini-Workshop: Superexpanders and their coarse geometry, Oberwolfach, April 2018

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

research visit and a seminar talk at the Adam Mickiewicz University

*(see also the Talks section)*

Mini-Workshop: Superexpanders and Their Coarse Geometry

Mathematisches Forschungsinstitut Oberwolfach, Germany

*(for information on my talk, see the Talks section)*

Mathematisches Forschungsinstitut Oberwolfach, Germany

New Methods for Zimmer's Conjecture,
IPAM, University of California, Los Angeles

Algebraic K- and L-Theory and Geometric Group Theory (Oberwolfach Seminar)

Mathematisches Forschungsinstitut Oberwolfach, Germany

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)*

University of Southampton, Isaac Newton Institute Satellite Workshop

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)

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

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)

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

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)

Poster: Warped cones over profinite completions (JPEG file, 0.5 MB)

Warsaw Summer School in Probability, University of Warsaw

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