Research
A non-exhaustive list of my current research interests:
Geometry of infinite volume locally symmetric spaces, especially in higher rank.
Minimal surfaces in locally symmetric spaces and applications to homology growth or waist inequalities.
Flexible stability, higher property (T) and higher rigidity phenomena (whatever that may be)
Unimodular random graphs and unimodular random manifolds.
Patterson-Sullivan measures and BCG (Besson-Courtois-Gallot) maps in higher rank
Sarnak's density hypotheses.
Publications / accepted preprints
(with Minju Lee) Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank, preprint arXiv:2305.00610 (accepted in Geometry and Topology, arxiv)
(with Miklos Abert and Ben Hayes) Co-spectral radius, equivalence relations and the growth of unimodular random rooted trees, preprint arXiv:2205.06692 (accepted in Ergodic Theory and Dynamical Systems, arxiv)
(with Wouter van Limbeek) Heat kernels are not uniform expanders, preprint arXiv:1905.13584 accepted in Annales Henri Lebesgue (arxiv)
(with Sam Edwards, Minju Lee and Hee Oh) Infinite volume and atoms at the bottom of the spectrum, preprint arXiv:2304.14565 (to appear in Comptes Rendus Mathématique) (arxiv)
(with Wouter van Limbeek) Co-spectral radius of intersections, preprint (to appear in Ergodic Theory and Dynamical Systems) (arxiv)
(with Lam L. Pham) Bottom of the Length Spectrum of Arithmetic Orbifolds, Trans. Amer. Math. Soc. 376 (2023), 4745-4764 (journal, arxiv)
(with Gergely Harcos, Peter Maga, Djordje Milićević) The density hypothesis for horizontal families of lattices, preprint (accepted in American Journal of Math.) arXiv:2007.13961 ( arxiv)
(with Tsachik Gelander) Infinite Volume and Infinite Injectivity Radius, Ann. of Math. (2) 197(1): 389-421 (2023) (arxiv, journal)
(with Miklos Abert, Nicolas Bergeron, Mikołaj Frączyk, Damien Gaboriau) On homology torsion growth. J. Eur. Math. Soc. (2024) (arxiv, journal)
(with Itai Benjamini and Gabor Kun) Expander spanning subgraphs with large girth, Israel Journal of Math. 251, no. 1, 155–171 (2022) (journal, arxiv)
Growth of mod-2 homology in higher-rank locally symmetric spaces, Duke Math. J. 171(2): 247-271 (2022) (arxiv, journal)
Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds, Inventiones Mathematicae 224 (3), 917-985 (2021) (arxiv, journal)
(with Gergely Harcos and Peter Maga) Counting Bounded Elements of a Number Field, IMRN, Volume 2022, Issue 1, January 2022, Pages 373–390 (2020) (arxiv, journal)
Kesten’s theorem for uniformly recurrent subgroups. Ergodic Theory and Dynamical Systems, 40(10), 2778-2787 (2020) (arxiv, journal)
(with Jean Raimbault) Betti numbers of Shimura curves and arithmetic three-orbifolds, Algebra & Number Theory Vol. 13 (2019), No. 10, 2359–2382 (arxiv, journal)
(with Jakub Byszewski and Anna Szumowicz) Simultaneous p-orderings and minimizing volumes in number fields, Journal of Number Theory 173, 478-511, (2017) (arxiv, journal)
(with Taras Banakh) The covering number of the difference sets in partitions of G-spaces and groups. European Journal of Mathematics 1, 762–772 (2015) (arxiv, journal)
Preprints
(with Alex Gorodnik and Amos Nevo) Automorphic density estimates and optimal Diophantine exponents, preprint (arXiv)
(with Ben Hayes, Madhu Sudan and Yufei Zhao) Spectral non-concentration near the top for unimodular random graphs, preprint (arxiv)
(with Miklos Abert and Ben Hayes) Growth dichotomy for unimodular random rooted trees, preprint (submitted, arxiv)
(with Sam Mellick and Amanda Wilkens) Poisson-Voronoi tessellations and fixed price in higher rank, preprint arxiv:2307.01194 (submitted, arXiv)
(with Sebastian Hurtado and Jean Raimbault) Homotopy type and homology versus volume for arithmetic locally symmetric spaces, preprint arXiv:2202.13619 (submitted, arxiv)
(with Anna Szumowicz) On the optimal rate of equidistribution in number fields, preprint arXiv:1810.11110 (submitted, arxiv)