• Fall 2008: Math 36a (Probability), Math 111a (Real Analysis)


• Spring 2008: Math 23b (Introduction to Proofs), Math 211a (Hausdorff Dimension)


• Spring 2007: Math 203b (Topics in Number Theory)


• Fall 2006: Math 22a (Linear Algebra), Math 326a (Problem-Solving Workshop)


• Spring 2006: Math 21b (Intermediate Calculus), Math 311b (Dynamics and Number Theory)


• Fall 2005: Math 47a (Introduction to Research), Math 111a (Real Analysis)


• Spring 2005: Math 21b (Intermediate Calculus), Math 211b (Functional Analysis)


• Fall 2004: Math 36a (Probability), Math 211a (Dynamical Systems)

• Lie groups, discrete subgroups and homogeneous spaces


• Ergodic theory and dynamical systems


• Metric Diophantine approximation

Most recent papers:

• PDF Modified Schmidt games and Diophantine approximation with weights
  (with B. Weiss, 22 pages, 2008)
  


• PDF Ergodic Theory on Homogeneous Spaces and Metric Number Theory
  (a survey for Encyclopedia of Complexity and Systems Science, Springer Verlag, 19 pages, 2007)
  


• PDF On effective equidistribution of expanding translates of certain orbits in the space of lattices
  (with G. A. Margulis, 10 pages, 2007)
  


• PDF Dirichlet's theorem on diophantine approximation and homogeneous flows
  (with B. Weiss, J. Mod. Dyn. 4 (2008), 43-62)
  


• PDF Diophantine exponents of measures and homogeneous dynamics
  (Pure Appl. Math. Q. 4 (2008), 81-97)
  


• PDF An extension of quantitative nondivergence and applications to Diophantine exponents
  (26 pages, to appear in Trans. AMS)
  


• PDF Flows on S-arithmetic homogeneous spaces and applications to metric Diophantine approximation
  (with G. Tomanov, Comm. Math. Helv. 82 (2007), 519-581)
  


• PDF Measure rigidity and p-adic Littlewood-type problems
  (with M. Einsiedler, Compositio Math. 143 (2007), 689-702)
  


• PDF Friendly measures, homogeneous flows and singular vectors
  (with B. Weiss), in: Algebraic and Topological Dynamics, Contemp. Math. 385 (2005), AMS, Providence, RI, 2005, 281--292.
  


• PDF Badly approximable vectors on fractals
  (with B. Weiss, Israel J. Math. 149 (2005), 137-170)
  


• Abstract, PDF On fractal measures and Diophantine approximation
  (with E. Lindenstrauss and B. Weiss, Selecta Math. 10 (2004), 479-523)
  


• Abstract, PDF Bounded geodesics in moduli space
  (with B. Weiss, Internat. Math. Res. Notices 2004, no. 30, 1551-1560)
  


• PDF Baker-Sprindzhuk conjectures for complex analytic manifolds
  (in: Algebraic groups and Arithmetic, TIFR, India, 2004, 539-553)
• Abstract, PDF Extremal subspaces and their submanifolds
  (Geom. Funct. Anal. 13 (2003), no. 2, 437-466)
• Abstract, PDF Metric Diophantine approximation: the Khintchine-Groshev theorem for non-degenerate manifolds
  (with V. Beresnevich, V. Bernik and G.A. Margulis, Moscow Math. J. 2, no. 2 (2002), 203-225)
• Abstract, PDF Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions
  (with V. Bernik and G. A. Margulis, Internat. Math. Res. Notices 2001, no. 9, 453-486)
• PDF Some applications of homogeneous dynamics to number theory
  (a survey paper, in: Smooth ergodic theory and its applications, Proc. Sympos. Pure Math. 69,
  AMS, Providence, RI, 2001, 639-660)
• PDF Dynamics of subgroup actions on homogeneous spaces of Lie groups and applications to number theory
  (a BIG survey paper, with A. Starkov and N. Shah, in: Handbook on Dynamical Systems, Volume 1A,
  Elsevier Science, North Holland, 2002, 813-930)

Full list of publications

Support:

• NSF Grant DMS-0801064


• NSF CAREER Grant DMS-0239463


• BSF Grant 2000247, 2004149 and E.D. Bergmann Memorial Award


• Alfred P. Sloan Research Fellowship


• NSF Grants DMS-9704489, DMS-0072565