• Fall 2012: Math 111a (Real Analysis)


• Spring 2012: Math 20a (Multivariable Calculus), Math 200b (Second Year Seminar)


• Fall 2011: Math 47a (Introduction to Research)


• Spring 2011: Math 224b (Lie Groups)


• Fall 2010: Math 28a (Introduction to Groups), Math 204a (T.A. Practicum)


• Spring 2010: Math 200b (Second Year Seminar)


• Fall 2009: Math 22a (Linear Algebra), Math 211a (Dynamics and Number Theory)


• Spring 2009: Math 212b (Functional Analysis)


• 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)

• Lie groups, discrete subgroups and homogeneous spaces


• Ergodic theory and dynamical systems


• Metric Diophantine approximation

Most recent papers:

• PDF The set of badly approximable vectors is strongly C¹ incompressible
  (with R. Broderick, L. Fishman, A. Reich and B. Weiss, 18 pages, 2011)
  


• PDF Modified Schmidt games and a conjecture of Margulis
  (with B. Weiss, 33 pages, 2010)
  


• PDF Schmidt's game, fractals, and orbits of toral endomorphisms
  (with R. Broderick and L. Fishman, 14 pages, to appear in Ergodic Theory Dynam. Systems)
  


• PDF Modified Schmidt games and Diophantine approximation with weights
  (with B. Weiss, Advances in Math. 223 (2010), 1276-1298)
  


• PDF Schmidt's game, fractals, and numbers normal to no base
  (with R. Broderick, Y. Bugeaud, L. Fishman and B. Weiss, Math. Res. Letters 17 (2010), 307-321.)
  


• PDF Quantitative nondivergence and its Diophantine applications
  (Lecture Notes for Clay Institute Summer School (Pisa 2007), 26 pages, in: Homogeneous flows, moduli spaces and arithmetic, 131-153, Clay Math. Proc., 10, AMS, Providence, RI, 2010).
  


• PDF An `almost all versus no' dichotomy in homogeneous dynamics and Diophantine approximation
  (Geom. Dedicata 149 (2010), 205-218)


• PDF Metric Diophantine approximation for systems of linear forms via dynamics
  (with G. Margulis and J. Wang, Int. J. Number Theory 6 (2010), no. 5, 1139-1168)


• 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
  (Trans. Amer. Math. Soc. 360 (2008), 6497-6523)
  


• 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)