Dmitry Kleinbock
Degrees
Yale University, Ph.D.Moscow Gubkin Institute, M.S.
Expertise
Dynamical systems. Ergodic theory. Number theory.Profile
Please visit my new faculty profile page.
Ph.D. (1996, Yale University), at Brandeis since 2000. Webpage
Courses Taught
| MATH | 22b | Honors Linear Algebra and Multi-variable Calculus, Part II |
| MATH | 23b | Introduction to Proofs |
| 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.