Dmitry Kleinbock 

Short Bio:

I completed my Ph.D. at Yale University in 1996 under the supervision of Grigory Margulis. After a postdoc at the Institute for Advanced Study in Princeton, NJ (supervised by Jean Bourgain), I joined the Mathematics Department of Rutgers University (New Brunswick, NJ) as a Hill Assistant Professor in 1997. I joined Brandeis University in 2000, becoming Full Professor of Mathematics in 2008 and Theodore and Evelyn G. Berenson Chair in Mathematics in 2024. 

Research interests:

• Lie groups, discrete subgroups and homogeneous spaces

• Ergodic theory and dynamical systems

• Metric Diophantine approximation

Most recent publications 

(see also my papers on arxiv.org and the link at the top of the page to access all my publications):

• 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)

               Recently graduated students: 

• Jiajie Zheng (2023)

• Mishel Skenderi (2021)

• Anurag Rao (2020)

• Shahriar Mirzadeh (2018)

Editorial boards: 

• Ergodic Theory and Dynamical Systems

• Journal of Modern Dynamics

• Selecta Mathematica

Support: 

• NSF Grant DMS-2155111

• Simons Foundation Research Fellowship (2014-2015 and 2022)

• BSF Grant 2016256

                A short fun video: Powers of two on the Numberphile Channel, with extra footage