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

• Autumn 2017: Math 203

Some preprints and publications

• Self-Joinings for 3-IET's. (abstract, arxiv),
  (with J. Chaika). Preprint.
  

• Billiards, quadrilaterals and moduli spaces. (abstract, pdf),
  (with C. McMullen, R. Mukamel and A. Wright). Preprint.
  

• Projective cocycles over SL(2,R) actions: measures invariant under the upper triangular group. (abstract, arxiv),
  (with C. Bonatti and A. Wilkinson). Preprint.
  

• Random walks on locally homogeneous spaces. (abstract, pdf),
  (with E. Lindenstrauss). Preprint.
  

• Zariski dense random walks on homogeneous spaces. (abstract, pdf),
  (with E. Lindenstrauss). Preprint.
  

• The algebraic hull of the Kontsevich-Zorich cocycle. (abstract, arxiv),
  (with S. Filip and A. Wright). Preprint.
  

• Lower bounds for Lyapunov exponents of flat bundles on curves. (abstract, arxiv),
  (with M. Kontsevich, M. Moeller and A. Zorich). Preprint.
  

• Mobius disjointness for interval exchange transformations on three intervals. (abstract, arxiv),
  (with J. Chaika). Preprint.
  

• Volumes of strata of Abelian differentials and Siegel-Veech constants in large genera. (abstract, arxiv),
  (with A. Zorich). Arnold Math. J. 1 (2015), no. 4, 481--488.

• Rigidity of Teichmuller space. (abstract, arxiv),
  (with H. Masur and K. Rafi). Preprint.
  

• Semisimplicity of the Lyapunov spectrum for irreducible cocycles. (abstract, arxiv),
  (with C. Matheus). Preprint.
  

• Large scale rank of Teichmuller space. (abstract, arxiv),
  (with H. Masur and K. Rafi). Duke Math J. 166 (2017), no. 8, 1517--1572.

• Isolation, Equidistribution, and Orbit Closures for the SL(2,R) action on moduli space. (abstract, arxiv),
  (with M. Mirzakhani and A. Mohammadi). Ann. of Math. (2) 182 (2015), no. 2, 673--721.

• Invariant and stationary measures for the SL(2,R) action on moduli space. (abstract, arxiv)
  (with M. Mirzakhani). Preprint.
  
  Lecture notes from a minicourse on this paper given at Luminy in April 2012 (revised Oct 29 2013, minor edits April 8, 2017) are available here.
  
  
• Every flat surface is Birkhoff and Osceledets generic in almost every direction. (abstract, arxiv)
  (with J. Chaika). J. Mod. Dyn. 9 (2015), 1--23.
  
  
• Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\mathbb{C}P^1$. (abstract, arxiv)
  (with J. Athreya and A. Zorich). Ann. Sci. Ec. Norm. Super. (4) 49 (2016), no. 6, 1311--1386.
  
  
• Counting generalized Jenkins-Strebel differentials. (abstract, arxiv)
  (with J. Athreya and A. Zorich). Geom. Dedicata 170 (2014), 195--217.
  
  
• Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle. (abstract, arxiv)
  (with A. Avila and M. Moeller). To appear in Crelle's Journal.
  
  
• A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves. (abstract, arxiv)
  (with Carlos Matheus). Geom. Dedicata 179 (2015), 45--67
  
  
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. (abstract, arxiv)
  (with M. Kontsevich and A. Zorich). Publ. Math. Inst. Hautes Etudes Sci. 120 (2014), 207--333.
  
  
• 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). J. Eur. Math. Soc. (JEMS) 15 (2013), no. 6, 2165--2195.
  
  
• 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)
  

Curriculum Vitae

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