Piotr Mizerka

collaborators

4 papers

math.GR2025

Sampling elements of a finite group: efficiency of the product replacement algorithm with an accumulator

MichaÅ Marcinkowski, Piotr Mizerka

Let $G$ be a finite group generated by $k$ elements. The well-known product replacement algorithm provides an effective method for sampling generating sets of $G$ . We study a refin…

math.GR2025

Inducing spectral gaps for the cohomological Laplacians of $Sp_{2 n} (Z)$

Piotr Mizerka, Jakub SzymaÅski

We show that the spectral gap of the first cohomological Laplacian $I^_{1}$ for $Sp_{2 n} (Z)$ follows once a slightly stronger assumption holds for some $\oper…

math.GR2025

Inducing spectral gaps for the cohomological Laplacians of $SL_{n} (Z)$ and $SAut (F_{n})$

Piotr Mizerka

The technique of inducing spectral gaps for cohomological Laplacians in degree zero was used by Kaluba, Kielak and Nowak to prove property (T) for $SAut (F_{n})$ and $\…

math.GR2024

Non-vanishing unitary cohomology of low-rank integral special linear groups

Benjamin BrÃ¼ck, Sam Hughes, Dawid Kielak +1

We construct explicit finite-dimensional orthogonal representations $I ¨ _{N}$ of $SL_{N} (Z)$ for $N \in {3, 4}$ all of whose invariant vectors are trivial, an…

Sampling elements of a finite group: efficiency of the product replacement algorithm with an accumulator

Inducing spectral gaps for the cohomological Laplacians of Sp2n​(Z)

Inducing spectral gaps for the cohomological Laplacians of SLn​(Z) and SAut(Fn​)

Non-vanishing unitary cohomology of low-rank integral special linear groups

Inducing spectral gaps for the cohomological Laplacians of $Sp_{2 n} (Z)$

Inducing spectral gaps for the cohomological Laplacians of $SL_{n} (Z)$ and $SAut (F_{n})$