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

• Fall 2012: Math 203

Some preprints and publications

• Isolation, Equidistribution, and Orbit Closures for the SL(2,R) action on moduli space. (abstract, arxiv), (with M. Mirzakhani and A. Mohammadi).

• Invariant and stationary measures for the SL(2,R) action on moduli space. (abstract, arxiv)
  (with M. Mirzakhani).
  
  Lecture notes from a minicourse on this paper given at Luminy in April 2012 (revised June 4, 2013) are available here.
  
  
• Every flat surface is Birkhoff and Osceledets generic in almost every direction. (abstract, arxiv)
  (with J. Chaika).
  
  
• Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\mathbb{C}P^1$. (abstract, arxiv)
  (with J. Athreya and A. Zorich). Preprint
  
  
• Counting generalized Jenkins-Strebel differentials. (abstract, arxiv)
  (with J. Athreya and A. Zorich). Preprint
  
  
• Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle. (abstract, arxiv)
  (with A. Avila and M. Moeller). Preprint
  
  
• A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves. (abstract, arxiv)
  (with Carlos Matheus). Preprint
  
  
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. (abstract, arxiv)
  (with M. Kontsevich and A. Zorich). Preprint
  
  
• Lyapunov spectrum of square-tiled cyclic covers. (abstract, arxiv)
  (with M. Kontsevich and A. Zorich). J. Mod. Dyn. 5 (2011), no. 2, 319--353.
  
  
• Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups (abstract, arxiv)
  (with M. Bestvina and K.Wortman). Accepted to J. Eur. Math. Soc.
  
  
• Counting closed geodesics in strata. (abstract, arxiv)
  (with M. Mirzakhani and K. Rafi). Preprint.
  
  
• Counting closed geodesics in Moduli space. (abstract, arxiv)
  (with M. Mirzakhani). J. Mod. Dyn. 5 (2011), no. 1, 71--105.
  
  
• Lattice Point Asymptotics and Volume Growth on Teichmuller space. (abstract, arxiv)
  (with J. Athreya, A. Bufetov and M. Mirzakhani). Duke Math. J. 161 (2012), no. 6, 1055--1111.
  
  
• Unipotent flows and applications. (abstract, pdf)
  Homogeneous flows, moduli spaces and arithmetic, 71--129, Clay Math. Proc., 10, Amer. Math. Soc., Providence, RI, 2010.
  
  
• Slow Divergence and Unique Ergodicity. (abstract, arxiv)
  (with Y. Cheung). Preprint.
  
  
• Unique Ergodicity of Translation Flows. (abstract, arxiv)
  (with Y. Cheung). Proceedings of the Partially hyperbolic dynamics, laminations, and Teichmuller flow Workshop, Toronto, Jan. 5-9, 2006.
  
  
• Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lampligher groups. (abstract, arxiv)
  (with D. Fisher and K. Whyte). Ann. of Math 177 (2013), no. 3, 869-910
  
  
• Coarse differentiation of quasi-isometries I: spaces not quasi-isometric to Cayley graphs. (abstract, arxiv)
  (with D. Fisher and K. Whyte). Ann. of Math 176 (2012), no. 1, 221-260
  
  
• Quasi-isometric rigidity of solvable groups. (abstract, pdf)
  (with D. Fisher). Proceedings of the International Congress of Mathematicians, Vol. III 1185--1208, Hindustan Book Agency, New Delhi, 2010.
  
  
• Quasi-isometries and rigidity of solvable groups. (abstract, arxiv)
  (with D. Fisher and K. Whyte). Pure Appl. Math. Q. 3 (2007), no. 4, part 1, 927--947.
  
  
• Counting Problems in moduli space. (abstract, pdf)
  Handbook of dynamical systems. Vol. 1B, 581--595, Elsevier B. V., Amsterdam, 2006.
  
  
• Unipotent flows on the space of branched covers of Veech surfaces. (abstract, arxiv)
  (with J. Marklof and D. Witte Morris). Ergodic Theory Dynam. Systems 26 (2006), no. 1, 129--162.
  
  
• Pillowcases and quasimodular forms. (abstract, arxiv)
  (with A. Okounkov). Algebraic geometry and number theory, 1--25, Progr. Math., 253, Birkhäuser Boston, Boston, MA, 2006.
  
  
• The theta characteristic of a branched covering. (abstract, arxiv)
  (with A. Okounkov and R. Pandharipande). Adv. Math. 217 (2008), no. 3, 873--888.
  
  
• 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). Random walks and geometry, 431--444, Walter de Gruyter GmbH & Co. KG, Berlin, 2004.
  
  
• Representations of integers by an invariant polynomial and unipotent flows. (abstract, dvi or ps)
  (with H. Oh). Duke Math. J. 135 (2006), no. 3, 481--506.
  
  
• Ergodic theoretic proof of equidistribution of Hecke points. (abstract, dvi or ps)
  (with H. Oh). Ergodic Theory Dynam. Systems 26 (2006), no. 1, 163--167.
  
  
• On Uniform exponential growth for linear groups. (abstract, dvi or ps)
  (with S. Mozes and H. Oh). Invent. Math. 160 (2005), no. 1, 1--30.
  
  
• 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.
  
  
• 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 International Congress of Mathematicians, Vol. II (Berlin, 1998).
  
  
• Quadratic forms of signature (2,2) and eigenvalue spacings on flat 2-tori. (dvi or ps)
  (with G.A. Margulis and S. Mozes). Ann. of Math. (2) 161 (2005), no. 2, 679--725
  
  
• Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture. (abstract, dvi or ps)
  (with G.A. Margulis and S. Mozes). Ann. 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). Ann. 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). Lie groups and ergodic theory (Mumbai, 1996), 75--103, Tata Inst. Fund. Res. Stud. Math., 14, Tata Inst. Fund. Res., Bombay, 1998.
  
  
• 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)
  

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