7 papers
Infinitesimal containment and sparse factors of iid
MikoÅaj FrÄ czyk
We introduce infinitesimal weak containment for measure-preserving actions of a countable group : an action is infinitesimally contained in if the statistics…
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 of a higher rank simple Lie group , which is non-tempered in the sense that the quasi-re…
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…
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…
Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank
Mikolaj Fraczyk, Minju Lee
Let be a connected semisimple real algebraic group and be its Zariski dense discrete subgroup. We prove that if admits any finite Bowen-Margulis-Sulliva…
Co-spectral radius for countable equivalence relations
Miklós Abert, Mikolaj Fraczyk, Ben Hayes
We define the co-spectral radius of inclusions of discrete, probability measure-preserving equivalence relations, as the sampling exponent of a genera…