Mikolaj Frkaczyk

collaborators

3 papers

math.PR2026

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

Mikołaj Frączyk, 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

Mikołaj Frączyk, 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.DG2018

Betti numbers of Shimura curves and arithmetic three--orbifolds

Mikołaj Frączyk, Jean Raimbault

We show that asymptotically the first Betti number, or the arithmetic genus, of a Shimura curve satisfies the Gauss--Bonnet equality. We also show that the first Betti number of a…

ASLn​(Z) invariant random subsets of Zn

Benjamini--Schramm convergence of arithmetic locally symmetric spaces

Betti numbers of Shimura curves and arithmetic three--orbifolds

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