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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 $n > 6$.
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Math. Ann. (2019) 375: 1169

We prove that $\operatorname{Aut}(\mathbb{F}_5)$ has Kazhdan's property (T).
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Recent Publications

We prove that $\operatorname{Aut}(F_n)$ has Kazhdan's property (T) for every $n \geqslant 6$. Together with the previous result of …
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We prove that $\operatorname{Aut}(\mathbb{F}_5)$ has Kazhdan's property (T).
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We establish a lower bound on the spectral gap of the Laplace operator on some special linear groups using conic optimisation.
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We try to integrate group actions to the topological complexity setting, by introducing «jumps» in the planner. This approach is based …
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We compute and compare the invariant and equivariant versions of TC for various spaces and ponder what is the right way to introduce …
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Experience

 
 
 
 
 

MATH+ postdoc

Technische Universität Berlin

Feb 2019 – Present Berlin, Germany
Approximate Convex Hulls With Bounded Complexity
 
 
 
 
 

Postdoc

Mathematical Institute of Polish Academy of Sciences

Oct 2015 – Nov 2017 Warsaw, Poland
Computational aspects of Kazhdan's property (T)
 
 
 
 
 

Assistant Professor

Faculty of Mathematics and Computer Science of AMU

Oct 2014 – Present Poznań, Poland

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Recent Posts

Splitting Conic Solver or scs is a well established solver for conic optimization problems. It has bindings to julia via SCS.jl. Part …
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Installation The following instructions were prepared using julia-1.1.1. Before exploring the notebook you need to clone the main …
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This post documents replication details for paper $\operatorname{Aut}(\mathbb{F}_5)$ has property (T) by M. Kaluba, P.W. Nowak and N. …
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This post documents replication details for paper Certifying numerical estimates of spectral gaps by M. Kaluba, P.W. Nowak. Installing …
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Contact

  • kalmar@amu.edu.pl
  • (0048 61 829) 5497
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