Mikolaj Frkaczyk

collaborators

3 papers

math.PR2026

$ASL_{n} (Z)$ invariant random subsets of $Z^{n}$

MikoÅaj FrÄ czyk, Simon Machado

We classify measures on ${0, 1}^{Z^{d}}$ , $d \geq 3$ , the space of subsets of $Z^{d}$ , which are invariant under all affine special linear transformations. In other…

math.NT2026

Benjamini--Schramm convergence of arithmetic locally symmetric spaces

MikoÅaj FrÄ czyk, Sebastian Hurtado, Jean Raimbault

We prove that the thin parts of arithmetically defined locally symmetric space take up a negligible part of their volume and deduce asymptotic results on their Betti numbers.

math.NT2026

Topological complexity of arithmetic locally symmetric spaces

MikoÅaj FrÄ czyk, Sebastian Hurtado, Jean Raimbault

We prove that any arithmetic locally symmetric space is homotopy equivalent to a simplicial complex where the number of simplices is bounded linearly in the volume of the space. Th…

ASLn​(Z) invariant random subsets of Zn

Benjamini--Schramm convergence of arithmetic locally symmetric spaces

Topological complexity of arithmetic locally symmetric spaces

$ASL_{n} (Z)$ invariant random subsets of $Z^{n}$