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I am a Professor of Mathematics and head of the Dynamics and Number Theory group at Brandeis University
Research directions:
Lie groups, discrete subgroups and homogeneous spaces
Ergodic theory and dynamical systems
Metric Diophantine approximation
Research group: Taehyeong Kim (postdoctoral instructor), Keith Merrill (professor), Vasiliy Neckrasov (graduate student)
Email: kleinboc [at] brandeis.edu
Office: Goldsmith 207
Mailing address: Brandeis University, Department of Mathematics, MS 050, 415 South Street, Waltham, MA 02453, USA
Short Bio:
1996: Ph.D. at Yale University, advised by Grigory Margulis
1996-97: a postdoc at the Institute for Advanced Study in Princeton, NJ, supervised by Jean Bourgain
1997-2000: Hill Assistant Professor at Rutgers University, New Brunswick, NJ
since 2000: Professor at the Math Department of Brandeis University (Full Professor since 2008, Theodore and Evelyn G. Berenson Chair since 2024)
Most recent publications
(see also my papers on arxiv.org and the link at the top of the page to access all my publications):
Density of the multidimensional Lagrange spectrum, Preprint (2026), arXiv:2608.30735.
Bounded trajectories of quasi-rays on homogeneous spaces and Diophantine approximation with weight functions (with V. Neckrasov), Preprint (2026), arXiv:2603.25988.
Uniform Diophantine approximation with restrictions via total density of collections of subspaces (with L. Hong and V. Neckrasov), Preprint (2026), arXiv:2603.25988.
Constructing bounded orbits of special types on homogeneous spaces (with M. Einsiedler and A. Rao), Preprint (2025), arXiv:2511.16095.
Simultaneously bounded and dense orbits for commuting Cartan actions (with C. Wu), Preprint (2025), arXiv:2509.05272.
Submanifold-genericity of R^d-actions and uniform multiplicative Diophantine approximation (with P. Bandi and R. Fregoli), Preprint (2025), arXiv:2504.02258.
On multiplicatively badly approximable vectors (with R. Fregoli), J. Number Theory 278 (2026), 570–621.
Singularity, weighted uniform approximation, intersections and rates (with N. Moshchevitin, J. Warren and B. Weiss), Compositio Math. 161 (2025), no. 11, 2990–3016.
Dimension drop for escape on average in homogeneous spaces (with S. Mirzadeh), Discrete Contin. Dyn. Syst. 45 (2025), no. 5, 1653–1671.
Dimension drop for diagonalizable flows on homogeneous spaces (with S. Mirzadeh), J. Mod. Dyn. 20 (2024), 441–478.
Selected video presentations:
Well approximable Dirichlet spectrum and full Hausdorff dimension of the Folklore Set (Banach Center, Warsaw, May 2026)
Dimension Drop Conjecture in Homogeneous Dynamics (ICTS, Bangalore, December 2022)
Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem (Number Theory Web Seminar, March 2022)
Khintchine-type theorems for values of homogeneous polynomials at integer points: lectures 1, 2, 3 (ICTS, Bangalore, September 2019)
Shrinking targets on homogeneous spaces and improving Dirichlet's Theorem (CIRM, Luminy, February 2017)
Hyperbolic dynamics and intrinsic Diophantine approximation (HSE, Moscow, May 2016)
Hausdorff dimension estimates for bounded orbits on homogeneous spaces of Lie groups (Isaac Newton Institute, Cambridge, July 2014)
Recent graduate students:
Vasiliy Neckrasov (expected to graduate in 2026)
Jiajie Zheng (2023)
Mishel Skenderi (2021)
Anurag Rao (2020)
Shahriar Mirzadeh (2018)
Editorial boards:
Support:
Simons Foundation Travel Support for Mathematicians SFI-MPS-TSM-00025199 (2026-2031)
NSF Grant DMS-2155111 (2021-2026)
Simons Foundation Research Fellowship (2014-2015 and 2022)
BSF Grant 2016256 (2020-2023)
A short fun video: Powers of two on the Numberphile Channel, with extra footage
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