Mikołaj Frączyk

activity

20142026

most citedStrong Limit Multiplicity for arithmetic hyperbolic surfaces and

3

-manifolds

9 citations · 18 across the 21 of their papers we have counts for

collaborators

24 papers

math.DG2026

Minimal Submanifolds and Waists of Locally Symmetric Spaces

Mikolaj Fraczyk, Ben Lowe

We show that compact locally symmetric manifolds $M$ with universal cover the symmetric space $X$ for $S L (n, R)$ form a topological higher $d$ -expander family for $d\leq n/…

math.DS2026

On some aspects of discrete groups acting ergodically on the boundary

Subhadip Dey, Mikołaj Frączyk, Sebastian Hurtado

We show that if $G$ is a real semisimple Lie group and $Γ < G$ is a discrete subgroup with slow growth, in the sense that its growth indicator function is smaller than $ρ$ , then $Γ$ …

math.DS2025

Infinitesimal containment and sparse factors of iid

Mikołaj Frączyk

We introduce infinitesimal weak containment for measure-preserving actions of a countable group $Γ$ : an action $(X, μ)$ is infinitesimally contained in $(Y, ν)$ if the statistics of…

math.DG2024

Minimal Submanifolds and Waists of Locally Symmetric Spaces

Mikolaj Fraczyk, Ben Lowe

We study the higher expansion properties of locally symmetric spaces, with a particular focus on octonionic hyperbolic manifolds. We show that codimension two minimal submanifolds…

math.GR2024

Zariski dense non-tempered subgroups in higher rank of nearly optimal growth

Mikolaj Fraczyk, Hee Oh

We construct the first example of a Zariski-dense, discrete, non-lattice subgroup $Γ_{0}$ of a higher rank simple Lie group $G$ , which is non-tempered in the sense that the quasi-reg…

math.NT2024

Automorphic density estimates and optimal Diophantine exponents

Mikolaj Fraczyk, Alexander Gorodnik, Amos Nevo

The present paper is devoted to establishing an optimal approximation exponent for the action of an irreducible uniform lattice subgroup of a product group on its proper factors. P…

math.PR2024

Spectral non-concentration near the top for unimodular random graphs

Mikolaj Fraczyk, Ben Hayes, Madhu Sudan +1

In recent work on equiangular lines, Jiang, Tidor, Yuan, Zhang, and Zhao showed that a connected bounded degree graph has sublinear second eigenvalue multiplicity. More generally t…

math.GT2023

Poisson-Voronoi tessellations and fixed price in higher rank

Mikolaj Fraczyk, Sam Mellick, Amanda Wilkens

Let $G$ be a higher rank semisimple real Lie group or the product of at least two automorphism groups of regular trees. We prove all probability measure preserving actions of latti…

math.DS2023

Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank

Mikolaj Fraczyk, Minju Lee

Let $G$ be a connected semisimple real algebraic group and $Γ < G$ be its Zariski dense discrete subgroup. We prove that if $Γ\ G$ admits any finite Bowen-Margulis-Sullivan…

math.SP2023

Infinite volume and atoms at the bottom of the spectrum

Sam Edwards, Mikolaj Fraczyk, Minju Lee +1

Let $G$ be a higher rank simple real algebraic group, or more generally, any semisimple real algebraic group with no rank one factors and $X$ the associated Riemannian symmetric sp…

math.GT2022

Bottom of the Length Spectrum of Arithmetic Orbifolds

Mikolaj Fraczyk, Lam L. Pham

We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from $1$ . We also prove an anal…

math.GR2022

Co-spectral radius of intersections

Mikolaj Fraczyk, Wouter van Limbeek

We study the behavior of the co-spectral radius of a subgroup $H$ of a discrete group $Γ$ under taking intersections. Our main result is that the co-spectral radius of an invariant…

math.PR2022

Co-spectral radius for countable equivalence relations

Miklós Abert, Mikolaj Fraczyk, Ben Hayes

We define the co-spectral radius of inclusions $S \leq R$ of discrete, probability measure-preserving equivalence relations, as the sampling exponent of a genera…

math.GT2021★ 1 cited

On homology torsion growth

Miklos Abert, Nicolas Bergeron, Mikolaj Fraczyk +1

We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic lattices, Artin groups and mapping class groups. The growth is understood along Fa…

math.GR2021

Infinite Volume and Infinite Injectivity Radius

Mikolaj Fraczyk, Tsachik Gelander

We prove the following conjecture of Margulis. Let $G$ be a higher rank simple Lie group and let $Λ \leq G$ be a discrete subgroup of infinite covolume. Then, the locally symmetric s…

math.CO2020

Expander spanning subgraphs with large girth

Itai Benjamini, Mikolaj Fraczyk, Gabor Kun

We conjecture that finite graphs with positive Cheeger constant admit a spanning subgraph with positive Cheeger constant and girth proportional to the diameter. We prove this conje…

math.CO2020

A note on the structure of expanders

Itai Benjamini, Mikolaj Fraczyk

A conjecture regarding the structure of expander graphs is discussed.

math.NT2020★ 4 cited

The density hypothesis for horizontal families of lattices

Mikołaj Frączyk, Gergely Harcos, Péter Maga +1

We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving b…

math.CO2019★ 4 cited

Heat kernels are not uniform expanders

Mikolaj Fraczyk, Wouter van Limbeek

We study infinite analogues of expander graphs, namely graphs where subgraphs weighted by heat kernels form an expander family. Our main result is that there does not exist any inf…

math.NT2018

On the optimal rate of equidistribution in number fields

Mikolaj Fraczyk, Anna Szumowicz

Let $k$ be a number field. We study how well can finite sets of $O_{k}$ equidistribute modulo powers of prime ideals, for all prime ideals at the same time. Our main result…

math.AT2018

Growth of mod $- 2$ homology in higher rank locally symmetric spaces

Mikolaj Fraczyk

Let $X$ be a higher rank symmetric space or a Bruhat-Tits building of dimension at least $2$ such that the isometry group of $X$ has property $(T)$ . We prove that for every torsion…

math.GR2018

Kesten's theorem for uniformly recurrent subgroups

Mikolaj Fraczyk

We prove an inequality on the difference between the spectral radius of the Cayley graph of a group $G$ and the spectral radius of the Schreier graph $H \ G$ for any subgro…

math.NT2016★ 9 cited

Strong Limit Multiplicity for arithmetic hyperbolic surfaces and $3$ -manifolds

Mikolaj Fraczyk

We show that every sequence of torsion-free arithmetic congruence lattices in $PGL (2, R)$ or $PGL (2, C)$ satisfies a strong quantitative version of…

math.CO2014

The covering number of the difference sets in partitions of $G$ -spaces and groups

Taras Banakh, Mikolaj Fraczyk

We prove that for every finite partition $G = A_{1} \cup \dots \cup A_{n}$ of a group $G$ either $co v (A_{i} A_{i}^{- 1}) \leq n$ for all cells $A_{i}$ or else $co v (A_{i} A_{i}^{- 1} A_{i}) < n$ for some cell $A…

Minimal Submanifolds and Waists of Locally Symmetric Spaces

On some aspects of discrete groups acting ergodically on the boundary

Infinitesimal containment and sparse factors of iid

Minimal Submanifolds and Waists of Locally Symmetric Spaces

Zariski dense non-tempered subgroups in higher rank of nearly optimal growth

Automorphic density estimates and optimal Diophantine exponents

Spectral non-concentration near the top for unimodular random graphs

Poisson-Voronoi tessellations and fixed price in higher rank

Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank

Infinite volume and atoms at the bottom of the spectrum

Bottom of the Length Spectrum of Arithmetic Orbifolds

Co-spectral radius of intersections

Co-spectral radius for countable equivalence relations

On homology torsion growth

Infinite Volume and Infinite Injectivity Radius

Expander spanning subgraphs with large girth

A note on the structure of expanders

The density hypothesis for horizontal families of lattices

Heat kernels are not uniform expanders

On the optimal rate of equidistribution in number fields

Growth of mod−2 homology in higher rank locally symmetric spaces

Kesten's theorem for uniformly recurrent subgroups

Strong Limit Multiplicity for arithmetic hyperbolic surfaces and 3-manifolds

The covering number of the difference sets in partitions of G-spaces and groups

Growth of mod $- 2$ homology in higher rank locally symmetric spaces

Strong Limit Multiplicity for arithmetic hyperbolic surfaces and $3$ -manifolds

The covering number of the difference sets in partitions of $G$ -spaces and groups