Alex Eskin

How to reach me

• Paper mail:
  Department of Mathematics
  University of Chicago
  5734 University Avenue
  Chicago, IL 60637-1514
  USA
  
  
• Office: Eckhart Hall 412A
  
• E-mail: eskin@math.uchicago.edu
  
• Phone: (773) 702-7380 (Office)
  
• Fax: (773) 702-9787
  

Teaching

• Winter 2012: Math 204

Some preprints and publications

• Invariant and stationary measures for the SL(2,R) action on moduli space. (abstract, pdf), (with M. Mirzakhani). Preprint, Preliminary version.
  
  Lecture notes from a minicourse on this paper given at Luminy in April 2012 are available here.
  
  
• Counting closed geodesics in Moduli space. (abstract, dvi, pdf, or ps)
  (with M. Mirzakhani). Preprint.
  
  
• Lattice Point Asymptotics and Volume Growth on Teichmuller space. (abstract, dvi, pdf, or ps)
  (with J. Athreya, A. Bufetov and M. Mirzakhani). Preprint.
  
  
• Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs. (abstract, dvi, pdf, or ps)
  (with D. Fisher and K. Whyte). Preprint.
  
  
• Quasi-isometries and rigidity of solvable groups. (abstract, dvi, pdf, or ps)
  (with D. Fisher and K. Whyte). Preprint.
  
  
• Unipotent flows on the space of branched covers of Veech surfaces. (abstract, dvi or ps)
  (with J. Marklof and D. Witte Morris). Preprint.
  
  
• Moduli Spaces of Abelian Differentials: The Principal Boundary, Counting Problems and the Siegel--Veech Constants. (abstract, dvi or ps)
  (with H. Masur and A. Zorich). Publ. Math. Inst. Hautes Etudes Sci. 97 (2003), 61--179.
  
  
• Recurrence Properties of Random Walks on Finite Volume Homogeneous Manifolds (abstract, dvi or ps)
  (with G. Margulis). Preprint
  
  
• Representations of integers by an invariant polynomial and unipotent flows. (abstract, dvi or ps)
  (with H. Oh). Preprint.
  
  
• Ergodic theoretic proof of equidistribution of Hecke points. (abstract, dvi or ps)
  (with H. Oh). Preprint.
  
  
• On Uniform exponential growth for linear groups. (abstract, dvi or ps)
  (with S. Mozes and H. Oh). To appear in Invent. Math.
  
  
• Uniform exponential growth for linear groups.(Announcement) (abstract, dvi or ps)
  (with S. Mozes and H. Oh). Int. Math. Res. Not. 31(2002), 1675--1683.
  
  
• Billiards in rectangles with barriers. (abstract, dvi or ps)
  (with H. Masur and M. Schmoll). Duke Math. J. 118(2003), pp. 427--463
  
  
• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials. (abstract, dvi or ps)
  (with A. Okounkov). Invent. Math. 145 (2001), no. 1, 59--103.
  
  
• Quadratic forms of signature (2,2) and eigenvalue spacings on rectangular 2-tori. (dvi or ps)
  (with G.A. Margulis and S. Mozes). To appear in Ann. Math.
  
  
• Pointwise asymptotic formulas on flat surfaces. (dvi or ps)
  (with H. Masur). Ergodic Theory Dynam. Systems 21 (2001), no. 2, 443--478.
  
  
• Counting problems and semisimple groups. (abstract, dvi or ps)
  Proceedings of the ICM. , Berlin 1998.
  
  
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture. (abstract, dvi or ps)
  (with G.A. Margulis and S. Mozes). Annals of Math. 147 (1998), no. 1, 93--141
  
  
• Unipotent flows and counting lattice points on homogeneous spaces. (abstract, dvi or ps)
  (with S. Mozes and N. Shah). Annals of Math. 143(1996) 253-299.
  
  
• Non-divergence of translates of certain algebraic measures. (abstract, dvi or ps)
  (with S. Mozes and N. Shah). GAFA. 7(1997), pp. 48-80
  
  
• Quasi-flats and rigidity in symmetric spaces. (abstract, dvi or ps)
  (with B. Farb). Journal of the AMS 10(1997), pp. 653-692
  
  
• Quasi-flats in H²xH². (abstract, dvi or ps)
  (with B. Farb). Preprint.
  
  
• Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces.
  (abstract, dvi or ps) Journal of the AMS. 11(1998)
  , no. 2, pp. 321-361
  
• Singular symmetric matrices. (abstract, dvi or ps)
  (with Y. Katznelson). Duke Math. J. 79(1995)
  
  
• Mixing, counting and equidistribution in Lie groups. (abstract, dvi or ps)
  (with C. McMullen). Duke Math. J. 71(1993)
  
  
• A proof of Siegel's weight formula. (abstract)
  (with Z. Rudnick and P. Sarnak). Duke Math. Jour. Int. Math. Research Announcements. 5(1991)
  

Curriculum Vitae

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