Featured Publications

ArXiv preprint

We prove that $\operatorname{Aut}(F_n)$ has Kazhdan’s property (T) for every $n \geqslant 6$. Together with the previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \geqslant 5$. We also provide new, explicit lower bounds for the Kazhdan constants of $\operatorname{SAut}(F_n)$ (with $n \geqslant 6$) and of $\operatorname{SL}_n(\mathbb{Z})$ (with $n \geqslant 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n > 6$.
Dataset Slides ArXiv ipynb
ArXiv preprint

We prove that $\operatorname{Aut}(\mathbb{F}_5)$ has Kazhdan’s property (T).
Code Dataset Slides ArXiv Nextjournal

Recent Publications

Quickly discover relevant content by filtering publications.

We prove that $\operatorname{Aut}(F_n)$ has Kazhdan’s property (T) for every $n \geqslant 6$. Together with the previous result …
Dataset Slides ArXiv ipynb

We prove that $\operatorname{Aut}(\mathbb{F}_5)$ has Kazhdan’s property (T).
Code Dataset Slides ArXiv Nextjournal

We establish a lower bound on the spectral gap of the Laplace operator on some special linear groups using conic optimisation.
PDF Code Slides DOI ArXiv

We try to integrate group actions to the topological complexity setting, by introducing «jumps» in the planner. This approach is based …
PDF DOI ArXiv

We survey the results on group actions on Euclidean spaces, disks and spheres and summarise my results on perfect group actions on …
PDF
See all publications

Experience

 
 
 
 
 

MATH+ Post-Doc

Technische Universität Berlin

Feb 2019 – Present Berlin, Germany
Main research topic: machine learning meets polytope theory
 
 
 
 
 

Post-Doc

Mathematical Institute of Polish Academy of Sciences

Oct 2015 – Nov 2017 Warsaw, Poland
Main research topic: computational aspects of Kazhdan’s property (T)
 
 
 
 
 

Assistant Professor

Faculty of Mathematics and Computer Science of AMU

Oct 2014 – Present Poznań, Poland

Upcoming Talks

  • Rigidity, 24-28.06.2019, IMPAN, Warsaw, Poland (invited talk)
  • ICCOPT, 03-08.08.2019, TU Berlin, Berlin, Germany
  • 100 lat PTM, 03-07.09.2019, Jagiellonian University, Cracow, Poland
  • Outer Space in Bielefeld, 24-26.09.2019, University of Bielefeld, Bielefeld, Germany (invited talk)

Past talks

Recent Posts

Below are replication details for computations with special linear groups as described in Section 5.1 of paper On property (T) for …
13 min read

This post documents replication details for paper $\operatorname{Aut}(\mathbb{F}_5)$ has property (T) by M. Kaluba, P.W. Nowak and N. …
4 min read

This post documents replication details for paper Certifying numerical estimates of spectral gaps by M. Kaluba, P.W. Nowak. This guide …
3 min read

Contact

  • kalmar@amu.edu.pl
  • (0048 61 829) 5497
  • Room B1-30, Faculty of Mathematics and Computer Science, ul. Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
  • Tuesday 11:00 to 12:30,
    or appointment by e-mail