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
Super-expanders and warped cones
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.
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