Piotr Mizerka

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math.GR2025

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

Michał 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 Szymański

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

math.GR2024

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

Benjamin Brück, Sam Hughes, Dawid Kielak +1

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

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)

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

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