# Dmitry Kleinbock

Degrees

Yale University, Ph.D.Moscow Gubkin Institute, M.S.

Expertise

Dynamical systems. Ergodic theory. Number theory.Profile

Ph.D. (1996, Yale University), at Brandeis since 2000. WebpageCourses Taught

MATH | 22a | Honors Linear Algebra and Multi-variable Calculus, Part I |

MATH | 22b | Honors Linear Algebra and Multi-variable Calculus, Part II |

MATH | 110a | Introduction to Real Analysis, Part I |

MATH | 141a | Real Analysis |

MATH | 200a | Second-Year Seminar |

MATH | 211a | Topics in Differential Geometry and Analysis I |

Awards and Honors

Dean's Mentor Award (2019)

Dynamics on Parameter Spaces BSF grant 2016256 (with Hooper, Smillie and Weiss) (2017 - 2021)

Fellow of the American Mathematical Society (2016)

Simons Research Fellowship in Mathematics (2014 - 2015)

Dynamics on Parameter Spaces Grant from US-Israel Binational Science Foundation (2011 - 2014)

Dynamics on Parameter Spaces Grant from US-Israel Binational Science Foundation (2005 - 2009)

NSF CAREER Grant DMS-0239463 (2003 - 2008)

Alfred P. Sloan Foundation Fellowship Award (2001 - 2003)

E.D. Bergmann Memorial Award (2001 - 2004)

Alfred P.Sloan Graduate Dissertation Fellowship (1995 - 1996)

J. F. Edwards Research Grant (Yale) (1995 - 1996)

Scholarship

Kleinbock, Dmitry, Rao, Anurag, and Sathiamurthy, Srinivasan. "Critical loci of convex domains in the plane." __Indagationes Mathematicae__ (2021). (forthcoming)

Kleinbock, Dmitry, and Skenderi, Mishel. "Khintchine-type theorems for values of subhomogeneous functions at integer points." __Monatshefte fur Mathematik__ 194. 3 (2021): 523-554.

Kleinbock, Dmitry and Mirzadeh, Shahriar. "Dimension estimates for the set of points with non-dense orbit in homogeneous spaces." __Mathematische Zeitschrift__ 295. (2020): 1355-1383.

Kleinbock, Dmitry, and Yu, Shucheng. "A dynamical Borel-Cantelli lemma via improvements to Dirichlet's theorem." __Moscow J. Comb. Number Theory__ 9. 2 (2020): 101-122.

Kleinbock, Dmitry, and de Saxce, Nicolas. "Rational approximation on quadrics: a simplex lemma and its consequences." __Enseign. Math.__ 64. 3/4 (2019): 459-476.

Kleinbock, Dmitry, and Mirzadeh, Shahriar. "Dimension estimates for the set of points with non-dense orbit in homogeneous spaces." __Math. Zeitschrift__ (2019).

Kleinbock, Dmitry, and Moshchevitin, Nikolay. "Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials." __Acta Arithmetica__ 190. (2019): 87-100.

Kleinbock, Dmitry, and Wadleigh, Nicholas. "An inhomogeneous Dirichlet theorem via shrinking targets." __Compositio Math.__ 155. 7 (2019): 1402-1423.

Fishman, Lior, Kleinbock, Dmitry, Merril, Keith, and Simmons, David. "Intrinsic Diophantine approximation on manifolds: General theory." __Trans. Amer. Math. Soc.__ 370. 1 (2018): 577–599.

Hussain, Mumtaz, Kleinbock, Dmitry, Wang, Bao-Wei, and Wadleigh, Nicholas. "Hausdorff measure of sets of Dirichlet non-improvable numbers." __Mathematika__ 64. 2 (2018): 502--518.

Kleinbock, Dmitry, and Margulis, Gregory. "Erratum to: Logarithm laws for flows on homogeneous spaces." __Inv. Math.__ 211. 2 (2018): 855–862.

Kleinbock, Dmitry, and Wadleigh, Nicholas. "A zero-one law for improvements to Dirichlet's heorem." __Proc. Amer. Math. Soc.__ 146. (2018): 1833–1844.

Kadyrov, Shirali, Kleinbock, Dmitry, Lindenstrauss, Elon, and Margulis, Gregory. "Singular systems of linear forms and non-escape of mass in the space of lattices." __J. d'Anal. Math.__ 33. 1 (2017): 253–277.

Kleinbock, Dmitry, Shi, Ronggang, and Weiss, Barak. "Pointwise equidistribution with an error rate and with respect to unbounded functions." __Math. Annalen__ 367. 1-2 (2017): 857-879.

Kleinbock, Dmitry; Shi, Ronggang, and Tomanov, Georges. "S-adic version of Minkowski's geometry of numbers and Mahler's compactness criterion." __J. Number Theory__ 174. (2017): 150–163.

Kleinbock, Dmitry and Ly, Tue. "Badly approximable S-numbers and absolute Schmidt games." __J. Number Theory__ 164.. (2016): 13–42.

__Powers of two (extra footage)__. Narrator Kleinbock, Dmitry. youtube.com, 2015.

__Powers of two__. Narrator Kleinbock, Dmitry. youtube.com, 2015.

An, Jinpeng, Guan, Lifan, and Kleinbock, Dmitry. "Bounded orbits of diagonalizable flows on SL_3(R)/SL_3(Z)." __Internat.\ Math.\ Res.\ Notices__ 2015. 24 (2015): 13623–13652.

Badziahin, Dzhmitry, Bugeaud, Yann, Einsiedler, Manfred, and Kleinbock, Dmitry. "On the complexity of a putative counterexample to the p-adic Littlewood conjecture." __Compositio Math.__ 151. (2015): 1647–1662.

Beresnevich, Victor, Kleinbock, Dmitry, and Margulis, Gregory. "Non-planarity and metric Diophantine approximation for systems of linear forms." __Journal de Théorie des Nombres de Bordeaux__ 27. 1 (2015): 1–31.

Broderick, Ryan, and Kleinbock, Dmitry. "Dimension estimates for sets of uniformly badly approximable systems of linear forms." __Int. J. Number Theory__ 11. 7 (2015): 2037–2054.

Kleinbock, Dmitry and Weiss, Barak. "Values of binary quadratic forms at integer points and Schmidt games." __Recent Trends in Ergodic Theory and Dynamical Systems__. vol. 631 Providence, RI: American Mathematical Society, 2015. 77--92.

Kleinbock, Dmitry, And Merrill, Keith. "Rational Approximation on Spheres." __Israel J. Math.__ 209. 1 (2015): 293–322.

Kleinbock, Dmitry and Weiss, Barak. "Modified Schmidt games and a conjecture of Margulis." __Journal of Modern Dynamics__ 7. 3 (2013): 429-460.

Kleinbock, Dmitry, Robert A. Meyers. "Ergodic theory on homogeneous spaces and metric number theory." __Encyclopedia of Complexity and Systems Science__. 2013.

Kleinbock, Dmitry; Margulis, Gregory. "On effective equidistribution of expanding translates of certain orbits in the space of lattices." __Number theory, Analysis and Geometry, in memory of Serge Lang__. 1 ed. vol. 1 Ed. Dorian Goldfeld et al. New York: Springer, 2012. 385-396.

Ryan Broderick, Dmitry Kleinbock, Lior Fishman, Asaf Reich and Barak Weiss. "The set of badly approximable vectors is strongly C^1 incompressible." __Math. Proc. Camb. Phil. Soc.__ 153. 2 (2012): 319-339.

R. Broderick, L. Fishman and D. Kleinbock. "Schmidt's game, fractals, and orbits of toral endomorphisms." __Ergodic Theory Dynam. Systems__ 31. 4 (2011): 1095–1107.

Broderick, Ryan; Bugeaud, Yann; Fishman, Lior; Kleinbock, Dmitry; Weiss, Barak. "Schmidt's game, fractals, and numbers normal to no base." __Math. Res. Letters__ 17. (2010): 307-321.

Kleinbock, Dmitry. "An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation." __Geom. Dedicata__ 149. (2010): 205-218.

Kleinbock, Dmitry. "Quantitative nondivergence and its Diophantine applications." __Proceedings of the CMI Summer School on "Homogeneous Flows, Moduli Spaces and Arithmetic''__. vol. 10 Providence, RI: AMS, 2010. 131-153.

Kleinbock, Dmitry; Weiss, Barak. "Modified Schmidt games and Diophantine approximation with weights." __Advances in Math.__ 223. (2010): 1276-1298.

Kleinbock, Dmitry; Margulis, Gregory; Wang, Junbo. "Metric Diophantine approximation for systems of linear forms via dynamics." __Int. J. Number Theory__ 6. 5 (2010): 1139-1168.

Kleinbock, Dmitry and Weiss, Barak. "Friendly measures, homogeneous flows and Dirichlet's Theorem." __J. Mod. Dyn__ 2. 1 (2008): 43-62.

Kleinbock, Dmitry. "An extension of quantitative nondivergence and applications to Diophantine exponents." __Trans. Amer. Math.Soc.__ 360. (2008): 6497--6523.

Kleinbock, Dmitry. "Diophantine properties of measures and homogeneous dynamics." __Pure and Applied Math Quarterly__ 4. 1 (2008): 81-97.

Kleinbock, Dmitry and Einsiedler, Manfred. "Measure rigidity and p-adic Littlewood-type problems." __Compositio Math.__ 143. (2007): 689-702.

Kleinbock, Dmitry and Tomanov, George. "Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation." __Comm. Math. Helv.__ 82. (2007): 519-581.