Papers sorted by topics

• Large genus asymptotic geometry of moduli spaces
• Meanders
  
• Square-tiled surfaces. Masur-Veech volumes
• Lyapunov exponents of the Hodge bundle along the Teichmuller flow 
• Moduli of Abelian and quadratic differentials: components, principal boundary, Siegel-Veech constants
• Leaves of closed 1-forms. Billiards. Interval exchanges. Deviation from ergodic averages
• Integral geometry
• Integration on supermanifolds. Cohomology of supermanifolds
• Surveys. Popularization papers
• Open problems
  
• Maryam Mirzakhani

Large genus asymptotic geometry of moduli spaces

• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves, 
  with V. Delecroix, E. Goujard, P. Zograf, submitted,
  arXiv:2007.04740.
  
• Uniform lower bound for intersection numbers of  psi-classes,
  with V. Delecroix, E. Goujard, P. Zograf,
  special issue in honor of Dmitry Fuchs,
  SIGMA, Symmetry Integrability Geom. Methods Appl. 16 (2020), Paper No. 086, 13 pp.
  arXiv: 2004.02749;   Math. Rev. 4139931. 
• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials,
  with A. Aggarwal, V. Delecroix, E. Goujard, P. Zograf,
  Arnold Mathematical Journal 6 (2020), no. 2, 149–161;
  arXiv:1912.1170;   Math. Rev. 4134482.
• Asymptotic values of Siegel–Veech constants,
  appendix to the paper of A. Aggarwal, Large genus asymptotics for volumes of strata of abelian differentials,
  Journal of the AMS, 33:4 (2020) 975–989;
  arXiv:1804.05431;   Math. Rev.  4155217. 

Meanders

• Enumeration of meanders and Masur–Veech volumes,
  with V. Delecroix, E. Goujard, P. Zograf,
  Forum of Mathematics Pi, 8:4 (2020) 80 pp;  
  arXiv:1705.05190;   Math. Rev. 4079755. 

Square-tiled surfaces. Masur-Veech volumes

• Counting lattice points in moduli spaces of quadratic differentials,
  with V. Delecroix, E. Goujard, P. Zograf,
  Proceedings of the ICM 2022, Vol. 3, pp. 2196–2211. EMS Press, Berlin, 2023.
• Masur–Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves,
  with V. Delecroix, E. Goujard, P. Zograf,
  Duke Math. Journal, 170:12 (2021), 2633–2718;
  arXiv:2011.05306;   Math. Rev. 4305379.
• Contribution of one-cylinder square-tiled surfaces to Masur–Veech volumes,
  with V. Delecroix, E. Goujard, P. Zograf and with appendix of Ph. Engel,
  in collection "Some aspects of dynamical systems: a tribute to Jean-Christophe Yoccoz"
  Astérisque 415:1 (2020), 223–274;
  arXiv:1903.10904;   Math. Rev. 4142454.
• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials,
  with A. Aggarwal, V. Delecroix, E. Goujard, P. Zograf,
  Arnold Mathematical Journal 6 (2020), no. 2, 149–161;
  arXiv:1912.1170;   Math. Rev. 4134482.
• Right-angled  billiards  and  volumes  of  moduli  spaces  of quadratic differentials on  CP¹ ,  
  with J. Athreya, A. Eskin and with appendix of J. Chaika,
  Ann. Scient. ENS, 4ème série, 49 (2016), 1307–1381;
  arXiv:1212.1660.   Math. Rev. 3592359. 
• Volumes of strata of Abelian differentials and Siegel–Veech constants in large genera,
  with A. Eskin,
  Arnold Mathematical Journal, 1:4 (2015), 481–488;
  arXiv:1507.05296.   Math. Rev. 3434506. 
Counting generalized Jenkins–Strebel differentials,
with J. Athreya and A. Eskin
Geometriae Dedicata, 170:1 (2014), 195–217;
arXiv:1212.1714;   Math. Rev. 3199485. 
• Lyapunov spectrum of equivariant subbundles of the Hodge bundle,
  with G. Forni and C. Matheus,
  Ergodic Th. and Dynam. Syst., 34:2 (2014), 353–408;
  arXiv:1112.0370;   Math. Rev. 3233697.
• Square-tiled cyclic covers,
  with G. Forni and C. Matheus,
  Journal of Modern Dynamics, 5 (2011), no. 2, 285–318;
  arXiv:1007.4275;   Math. Rev. 2820563 .
• Explicit Jenkins-Strebel representatives of all strata of abelian and quadratic differentials,
  Journal of Modern Dynamics, 2 (2008), no. 1, 139–185;
  arXiv:1011.0395;  Math. Rev. 2366233.
• Square tiled surfaces and Teichm?ller volumes of the moduli spaces of abelian differentials,
  Rigidity in dynamics and geometry (Cambridge, 2000), 459–471, Springer, Berlin, 2002;
  Math. Rev. 1919417.

Lyapunov exponents of the Hodge bundle along the Teichmüller flow

• Lower bounds for Lyapunov exponents of flat bundles on curves,
  with A. Eskin, M. Kontsevich, M. M?ller,
  Geometry and Topology 22:4 (2018), 2299–2338;
  arXiv:1609.01170;   Math. Rev. 3784522. 
• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow,
  with A. Eskin, M. Kontsevich,
  Publications de l'IHES, 120:1 (2014), 207–333;
  arXiv:1112.5872;   Math. Rev. 3270590. 
• Zero Lyapunov exponents of the Hodge bundle,
  with G. Forni and C. Matheus,
  Commentari Math. Helvetici, 89:2 (2014), 489–535;
  arXiv:1201.6075.   Math. Rev. 3225454. 
• Lyapunov spectrum of equivariant subbundles of the Hodge bundle,
  with G. Forni and C. Matheus,
  Ergodic Th. and Dynam. Syst., 34:2 (2014), 353–408;
  arXiv:1112.0370;   Math. Rev. 3233697.
• Lyapunov spectrum of square-tiled cyclic covers,
  with A. Eskin and M. Kontsevich,
  Journal of Modern Dynamics, 5 (2011), no. 2, 319–353;
  arXiv:1007.5330;   Math. Rev. 2820564.
• Lyapunov exponents and Hodge theory,
  with M. Kontsevich,
  extended version of the paper of M. Kontsevich with the same name,
  The mathematical beauty of physics (Saclay, 1996), 318–332,
  Adv. Ser. Math. Phys., 24, World Sci. Publ., River Edge, NJ, 1997;
  arXiv:hep-th/9701164;    Math. Rev. 1490861.
• Deviation for interval exchange transformations,
  Ergodic Theory Dynam. Systems, 17 (1997), no. 6, 1477–1499;
  Math. Rev. 1488330.
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents,
  Ann. Inst. Fourier, 46 (1996), no. 2, 325–370;
  Math. Rev. 1393518.

Moduli of Abelian and quadratic differentials: components, principal boundary, Siegel-Veech constants

• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials,
  with A. Aggarwal, V. Delecroix, E. Goujard, P. Zograf,
  Arnold Mathematical Journal 6 (2020), no. 2, 149–161;
  arXiv:1912.1170;   Math. Rev. 4134482.
• Multiple saddle connections on flat surfaces and the principal boundary of the moduli spaces of quadratic differentials,
  with H. Masur,
  Geom. Funct. Anal., 18 (2008), no. 3, 919–987;
  arXiv:math/0402197;  Math. Rev. 2439000.
• Explicit Jenkins-Strebel representatives of all strata of abelian and quadratic differentials,
  Journal of Modern Dynamics, 2 (2008), no. 1, 139–185;
  arXiv:1011.0395;  Math. Rev. 2366233.
• Moduli spaces of abelian differentials: the principal boundary, counting problems, and the Siegel-Veech constants,
  with A. Eskin and  H. Masur,
  Publications IHES, 97 (2003), 61–179;
  arXiv:math/0202134;  Math. Rev. 2010740.
• Connected components of the moduli spaces of Abelian differentials with prescribed singularities.
  with M. Kontsevich,
  Inventiones Math. 153 (2003), no. 3, 631–678;
  arXiv:math/0201292;  Math. Rev. 2000471.

Leaves of closed 1-forms. Billiards. Interval exchanges. Deviation from ergodic averages

• Cries and whispers in wind-tree forests,
  with V. Delecroix,
  “The mathematical legacy of Bill Thurston”,
  Annals of Mathematics Studies,
  Number 205, 83–115. Princeton University Press 2020;
  arXiv:1502.06405;   Math. Rev. 4205637. 
• Right-angled  billiards  and  volumes  of  moduli  spaces  of quadratic differentials on  CP¹ ,  
  with J. Athreya, A. Eskin and with appendix of J. Chaika,
  Ann. Scient. ENS, 4ème série, 49 (2016), 1307–1381;
  arXiv:1212.1660.   Math. Rev. 3592359. 
• How do the leaves of a closed 1-form wind around a surface?
  Pseudoperiodic topology, AMS Transl. Ser. 2, 197, 135–178, Adv. Math. Sci., 46, AMS, Providence, RI, 1999.
  Math. Rev. 1733872.
• Deviation for interval exchange transformations,
  Ergodic Theory Dynam. Systems, 17 (1997), no. 6, 1477–1499;
  Math. Rev. 1488330.
• On hyperplane sections of periodic surfaces,
  Solitons, geometry, and topology: on the crossroad, AMS Transl. Ser. 2, 179, 173–189, Adv. Math. Sci., 33, AMS, Providence, RI, 1997;
  Math. Rev. 1437163.
• Finite Gauss measure on the space of interval exchange transformations. Lyapunov exponents,
  Ann. Inst. Fourier, 46 (1996), no. 2, 325–370;
  Math. Rev. 1393518.
• Asymptotic flag of an orientable measured foliation on a surface,
  Geometric study of foliations (Tokyo, 1993), 479–498,
  World Sci. Publ., River Edge, NJ, 1994;
  Math. Rev. 1363744.
• The quasiperiodic structure of level surfaces of a Morse 1-form
  that is close to a rational form — the problem of S. P. Novikov,
  Math. USSR — Izvestia, 31 (1988), no. 3, 635–655;
  Math. Rev. 0933967.
• S. P. Novikov's problem of the semiclassical motion of an electron in a homogeneous magnetic field that is close to rational,
  Uspekhi Mat. Nauk, 39 (1984), no. 5(239), 235–236;
  Math. Rev. 0764016.

Integral geometry

• Inversion of horospherical integral transform on real semisimple Lie groups,
  Infinite analysis, Part A, B (Kyoto, 1991), 1047–1071,
  Adv. Ser. Math. Phys., 16, World Sci. Publ., River Edge, NJ, 1992;
  Math. Rev. 1187588.
• Inversion of integral transformations connected with nilpotent subgroups of complex semisimple Lie groups,
  Leningrad Math. Jour. 2 (1991), no. 1, 65–96;
  Math. Rev. 1049906.
• Integration of pseudodifferential forms and inversion of integral transforms of Radon transform type,
  with Th. Voronov,
  Uspekhi Mat. Nauk, 42 (1987), no. 4(256), 185–186;
  Math. Rev. 0912066.

Integration on supermanifolds. Cohomology of supermanifolds

• Integration on vector bundles,
  with Th. Voronov,
  Funct. Anal. Appl., 22 (1988), no. 2, 94–103;
  Math. Rev. 0947602.
• Cohomology of supermanifolds, and integral geometry,
  with Th. Voronov,
  Soviet Math. Dokl. 37 (1988), no. 1, 96–101;
  Math. Rev. 0925953.
• Integration of pseudodifferential forms and inversion of integral transforms of Radon transform type,
  with Th. Voronov,
  Uspekhi Mat. Nauk, 42 (1987), no. 4(256), 185–186;
  Math. Rev. 0912066.
• Theory of bordisms and homotopy properties of supermanifolds,
  with Th. Voronov,
  Funct. Anal. Appl., 21 (1987), no. 3, 77–78.
  Math. Rev. 0911779.
• Integral transformations of pseudodifferential forms,
  with Th. Voronov,
  Uspekhi Mat. Nauk, 41 (1986), no. 6(252), 167–168;
  Math. Rev. 0890499.
• Complex of forms on a supermanifold,
  with Th. Voronov,
  Funct. Anal. Appl., 20 (1986), no. 2, 58–59;
  Math. Rev. 847142.

Surveys. Proceedings. Popularization papers

• Counting lattice points in moduli spaces of quadratic differentials,
  with V. Delecroix, E. Goujard, P. Zograf,
  Proceedings of the ICM 2022, to appear.
• Flat surfaces and algebraic curves ,
  Abstracts from the workshop held September 16–22, 2018;
  with S. Grushevsky and M. Möller ,
  Oberwolfach Rep. 15, no. 3, 2583–2650 (2018);
  Math. Rev. 3998904.
• The work of the 2014 Fields medalists,
  with W. de Melo, B. Poonen, J. Quastel,
  Notices AMS 62 (2015), no. 11, 1334–1349.
  Math. Rev. 3937286.
• The magic wand theorem of A. Eskin and M. Mirzakhani,
  Gazette des mathématiciens,142 (2014), 39–54;
  arXiv1502.05654; Math. Rev. 3278429.
• Flat surfaces and dynamics on moduli space ,
  Abstracts from the workshop held March 23–29, 2014;
  with H. Masur and M. Möller ,
  Oberwolfach Rep. 11, no. 1 (2014) , 869–941.
  Math. Rev. 3379310.
• Billiards, flat surfaces, and dynamics on moduli space ,
  Abstracts from the workshop held May 8–14, 2011;
  with H. Masur and M. Möller ,
  Oberwolfach Rep. 8, no. 2 (2011) , 1361–1427.
  Math. Rev. 2978642.
• Geodesics on flat surfaces,
  International Congress of Mathematicians. Vol. III, 121–146, Eur. Math. Soc., 2006.;
  arXiv:math/0609399;   Math. Rev. 2275673.
• Flat surfaces,
  Frontiers in number theory, physics, and geometry. I, 437–583, Springer, Berlin, 2006;
  arXiv:math/0609392;  Math. Rev. 2261104.
• Deviation for interval exchange transformations,
  Ergodic Theory Dynam. Systems, 17 (1997), no. 6, 1477–1499;
  Math. Rev. 1488330.

Open problems

• Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials,
  with A. Aggarwal, V. Delecroix, E. Goujard, P. Zograf,
  Arnold Mathematical Journal 6 (2020), no. 2, 149–161;
  arXiv:1912.1170;   Math. Rev. 4134482.
• Volumes of strata of Abelian differentials and Siegel–Veech constants in large genera,
  with A. Eskin,
  Arnold Mathematical Journal, 1:4 (2015), 481–488;
  arXiv:1507.05296.   Math. Rev. 3434506.  (Solved in a series of papers of A. Aggarwal and D. Chen, A. Sauvaget,  M. Möller, D. Zagier.)
• Problems on billiards, flat surfaces and translation surfaces,
  with P. Hubert, H. Masur, T. Schmidt,
  Problems on mapping class groups and related topics, 233–243,
  Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI, 2006;
  Math. Rev. 2264543. (Problem 10 is solved by A. Eskin, M. Mirzakhani. There are advances in some other problems, some of them are considerable.)

Maryam Mirzakhani

• Maryam Mirzakhani(1977–2017) ,
  EMS Newsletter, 107:1 (2018), 28 – 33 .
  Math. Rev. 3791696.
• Maryam Mirzakhani: 1977-2017,
  with H. Barcelo, R. Beheshti I. Coskun, L. DeMarco, D. Dumas, D. Eisenbud, A. Eskin, U. Hamenstadt, S. Kennedy, E. Lindenstrauss, E. Sapir, P. Sarnak, A. Wright, S. Wolpert,
  Notices of the AMS, 65:10 (2018), 1221–1247.
  Math. Rev. 3837071. 
• Maryam Mirzakhani 1977-2017,
  Gazette des mathématiciens, 154 (2017), 77–80.
  Math. Rev. 3729186. 
• The work of the 2014 Fields medalists,
  with W. de Melo, B. Poonen, J. Quastel,
  Notices AMS 62 (2015), no. 11, 1334–1349.
  Math. Rev. 3937286.
• The magic wand theorem of A. Eskin and M. Mirzakhani,
  Gazette des mathématiciens,142 (2014), 39–54;
  arXiv1502.05654; Math. Rev. 3278429.