My name is Ilya Kapovich,
and I am a Professor in the Department of Mathematics and Statistics at the Hunter College of CUNY, starting from with the Fall 2018 semester.

I am also a member of doctoral faculty at the CUNY Graduate Center. my photo

Contact info:

Department of Mathematics and Statistics, Hunter College
695 Park Avenue
New York, NY 10065

tel. 212-772-5303

e-mail: ik535 at

The above photo is licensed by under the Creative Commons Attribution-ShareAlike 4.0 license. The photo was taken by Ilya Kapovich in December 2012 at the University of Illinois in Urbana-Champaign.

Here is a link to my old webpage at the University of Illinois at Urbana-Champaign.

Here is a link to the webpage for the Spring 2017 Math 751 General Topology course I taught at Hunter.

My research papers in arXiv.

My March 15, 2017 talk at the Hunter College GRECS Seminar, ``Groups as geometric objects.

My office at Hunter is HE 917, tel. 212-772-5303

My second office, at the CUNY Graduate Center, is in 4214.07

Here is a reasonably up-to-date version of my CV (October 2022).

Contact information

e-mail [preferred way of contacting me]

office phone 212-772-5303

fax 212-772-4858

office location: Hunter East 917

Mailing address:

Department of Mathematics and Statistics
Room 919/944 East
Hunter College
695 Park Avenue
New York, NY 10065, U.S.A.

Geometric Group Theory mailing list.

I currently administer a geometric group theory mailing list for announcements about events and positions related to geometric group theory. To submit such an announcement, e-mail it directly to The list's homepage is located at this link. You can subscribe/unsubscribe to the list there (you can also do that by sending me an e-mail request at

New York Group Theory Seminar.

I am a co-organizer of the New York Group Theory Seminar at the CUNY Graduate Center. In the Fall 2022 semester the seminar meets in a hybrid format, with some in person talks and some online Zoom talks. The in-person talks are on Fridays at 4:15pm in room 6417 at the CUNY Graduate Center. The onine Zoom talks are on Fridays at 4:00pm U.S. eastern time. I also maintain the NYGT Seminar mailing list. If you would like to receive the weekly announcements, including Zoom links and passwords, for the seminar talks, please e-mail me (from an academic institution affiliated e-mail address) a request to Videos of prior NYGT Seminar talks are available at the NYGT Youtube channel.

Human rights work

*I served as the Chair of the AMS Committee on the Human Rights of Mathematicians (02/01/2020-01/31/2021)
If you have a matter requiring the committee's attention, please e-mail

*I am a member of the Steering Committee of the AAAS Science and Human Rights Coalition.

*AMS and ICM 2022, letter to the editor, Notices of the American Mathematical Society, volume 68, number 5 (May 2021), pp. 681-682

* The case of Azat Miftakhov

* Putin is distracting the world from his atrocities letter to the editor, Washington Post, February 21, 2022


Link to my papers posted at arxiv.og 

I am currently supported by the NSF grant DMS-1905641
  1. "Ascending chain condition in generic groups," preprint, 2023; arXiv:2306.06706
  2. "Primitivity rank for random elements in free groups," Journal of Group Theory 25 (2022), no. 5, 823-835
  3. "Primitivity index bounds in free groups, and the second Chebyshev function" (joint with Zachary Simon) International Journal of Algebra and Computation 33 (2023), no. 1, pp. 105-122
  4. "Complexity and Randomness in Group Theory. GAGTA BOOK 1." (By Frederique Bassino, Ilya Kapovich, Markus Lohrey, Alexei Miasnikov, Cyril Nicaud, Andrey Nikolaev, Igor Rivin, Vladimir Shpilrain, Alexander Ushakov, Pascal Weil), De Gruyter, 2020; ISBN 9783110667028
  5. "Random trees in the boundary of Outer space" , (joint with Joseph Maher, Catherine Pfaff, and Samuel Taylor); Geometry & Topology 26 (2022), no. 1, 127-162
  6. "Generic-case complexity of Whitehead's algorithm, revisited ", preprint arXiv:1903.07040
  7. "Random outer automorphisms of free groups: Attracting trees and their singularity structures", (joint with Joseph Maher, Catherine Pfaff, and Samuel Taylor); Transactions of the American Mathematical Society 375 (2022), no. 1, pp. 525-557
  8. "Counting conjugacy classes of fully irreducibles: double exponential growth", (joint with Catherine Pfaff); preprint arXiv:1801.07471
  9. "Counting conjugacy classes in Out(FN)", (joint with Michael Hull), Bulletin of the Australian Mathematical Society 97 (2018), no 3, 412-421
  10. "Stable Strata of Geodesics in Outer Space", (joint with Yael Algom-Kfir and Catherine Pfaff), Internat. Math. Res. Notices (IMRN) 2019 (2019), no. 14, pp. 4549-4578
  11. "Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell", Experimental Mathematics, 28 (2019), no. 1, pp. 24-38
  12. "Endomorphisms, train track maps, and fully irreducible monodromies ", (joint with Spencer Dowdall and Christopher Leininger), Groups, Geometry, and Dynamics 11 (2017), no. 4, pp. 1179-1200
  13. "The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With an appendix by Khalid Bou-Rabee." (joint with Neha Gupta), Mathematical Proceedings of the Cambridge Philosophical Society 166 (2019), no. 1, pp. 83-121 Published version at the publisher's website
  14. "McMullen polynomials and Lipschitz flows for free-by-cyclic groups" , (joint with Spencer Dowdall and Christopher J. Leininger); Journal of the European Mathematical Society (JEMS) 19 (2017), no. 11, pp. 3253-3353
  15. "An integral weight realization theorem for subset currents on free groups" , Topology Proceedings 50 (2017), pp. 213-236
  16. "Wolfgang Haken: A biographical sketch", Illinois Journal of Mathematics 60 (2016), no. 1, pp. 3-9; special issue in honor of Wolfgang Haken
  17. "Cannon-Thurston maps for hyperbolic free group extensions", (joint with Spencer Dowdall and Samuel Taylor), Israel J. Math. 216 (2016), no. 2, pp. 753-797
  18. "Musings on generic-case complexity", preprint
  19. "On purely loxodromic actions" , Monatshefte fur Mathematik 181 (2016), no. 1, pp. 89-101
  20. "Conical limit points and the Cannon-Thurston map" (joint with Woojin Jeon, Christopher Leininger and Ken'ichi Ohshika), Conformal Geometry and Dynamics, 20 (2016), pp. 58-80
  21. "Nielsen equivalence in a class of random groups" (joint with Richard Weidmann), Journal of Topology 9 (2016), no. 2, 502-534

  22. "Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space", (joint with Martin Lustig), Pacific J. Math. 277 (2015), no. 2, pp. 371-398
  23. "Dynamics on free-by-cyclic groups" , (joint with Spencer Dowdall and Christopher J. Leininger); Geometry and Topology 19 (2015), 2801-2899
  24. "A train track directed random walk on $Out(F_r)$" (joint with Catherine Pfaff), International Journal of Algebra and Computation 25 (2015), no. 5, pp. 745-798
  25. "Cannon-Thurston fibers for iwip automorphisms of $F_N$", (joint with Martin Lustig), Jour. London Math. Soc. 91 (2015), no. 1, 203-224
  26. "Unbounded asymmetry of stretch factors", (joint with Spencer Dowdall and Christopher J. Leininger); Comptes Rendus Mathematique, 352 (2014), no. 11, 885-887
  27. "Algorithmic detectability of iwip automorphisms", Bull. London Math. Soc. 46 (2014), no. 2, pp. 279-290; online version at the BLMS site available here
  28. "On hyperbolicity of free splitting and free factor complexes", (joint with Kasra Rafi), Groups, Geometry and Dynamics, 8 (2014), no. 2, pp. 391-414
  29. "Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups", (joint with Anton Lukyanenko), Conformal Geometry and Dynamics, 16 (2012), 269-282
  30. "Spectral rigidity of automorphic orbits in free groups", (joint with Mathieu Carette, Stefano Francaviglia and Armando Martino), Algebraic and Geometric Topology 12 (2012), pp. 1457-1486
    "Corrigendum to ''Spectral rigidity of automorphic orbits in free groups''", (joint with Mathieu Carette, Stefano Francaviglia and Armando Martino);   Algebraic and Geometric Topology 14 (2014), no. 5, pp. 3081-3088
  31. "Subset currents on free groups", (joint with Tatiana Nagnibeda), Geometriae Dedicata, 166 (2013), 307-348
  32. "Invariant laminations for irreducible automorphisms of free groups", (joint with Martin Lustig), Quarterly J. Math. 65 (2014), no. 4, pp. 1241-1275  Q. J. Math. doi: 10.1093/qmath/hat056
  33. "Random length-spectrum rigidity for free groups", Proceedings of AMS 140 (2012), no. 5, pp. 1549-1560
  34. "Stabilizers of R-trees with free isometric actions of FN ", (with Martin Lustig), Journal of Group Theory, 14 (2011), no. 5, pp. 673-694
  35. "Domains of proper discontinuity on the boundary of Outer space",(with Martin Lustig), Illinois J. Math., 54 (2010), no. 1, pp. 89-108, special issue dedicated to Paul Schupp
  36. "On mathematical contributions of Paul E. Schupp", Illinois J. Math., 54 (2010), no. 1, pp. 1-9, special issue dedicated to Paul Schupp
  37. "Ping-pong and Outer space", (with Martin Lustig), Journal of Topology and Analysis 2 (2010), no. 2, pp. 173-201
  38. "Nielsen equivalence in small cancellation groups", (with Richard Weidmann), preprint
  39. "Geometric entropy of geodesic currents on free groups", (with Tatiana Nagnibeda), Dynamical Numbers: Interplay Between Dynamical Systems and Number Theory, Contemporary Mathematics series, American Mathematical Society, 2010, pp. 149-176
  40. "Intersection form, laminations and currents on free groups ", (with Martin Lustig), Geom. Funct. Anal. 19 (2010), no. 5, pp. 1426-1467
  41. "Geometric Intersection Number and analogues of the Curve Complex for free groups", (with Martin Lustig), Geometry and Topology 13 (2009), pp. 1805-1833
  42. "Some Quantitative Aspects of Fractional Computability", (with Paul Schupp), preprint
  43. "On group-theoretic models of randomness and genericity" (with Paul Schupp), Groups, Geometry and Dynamics 2 (2008), no. 3, pp. 383-404
  44. "The actions of $Out(F_k)$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility" (with Martin Lustig), Ergodic Theory and Dynamical Systems 27 (2007), no. 3, pp. 827-847
  45. "Random quotients of the modular group are rigid and essentially incompressible" (with Paul Schupp), Journal fur die reine und angewandte Mathematik (Crelle's Journal), 628 (2009),  pp. 91-119
  46. "On the absence of McShane-type identities for the outer space" (with Igor Rivin), Journal of Algebra 320 (2008), no. 10, pp. 3659-3670
  47. "Clusters, currents and Whitehead's algorithm", Experimental Mathematics 16 (2007), no. 1, pp. 67-76
  48. " Densities in free groups and $\mathbb{Z}^k$, Visible Points and Test Elements" (with Igor Rivin, Paul Schupp and Vladimir Shpilrain), Math. Research Letters 14 (2007), no. 2, pp. 263-284
  49. "The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms" (with Vadim Kaimanovich and Paul Schupp), Israel J. Math. 157 (2007), pp. 1-46
  50. "Translation equivalence in free groups", (with Gilbert Levitt, Paul Schupp and Vladimir Shpilrain),  Transact. Amer. Math. Soc. 359 (2007), no. 4, pp. 1527-1546
  51. "The Patterson-Sullivan embedding and minimal volume entropy for outer space", (joint with Tatiana Nagnibeda), Geom. Funct. Anal. (GAFA) 17 (2007), no 4, pp 1201-1236
  52. "Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups" (with Paul Schupp and Vladimir Shpilrain), Pacific J. Math. 223 (2006), no. 1, pp. 113-140
  53. "Currents on free groups",   Topological and Asymptotic Aspects of Group Theory (R. Grigorchuk, M. Mihalik, M. Sapir and Z. Sunik, Editors), AMS Contemporary Mathematics Series, vol. 394, 2006, pp. 149-176
  54. "The frequency space of a free group", Internat. J. Alg. Comput. (special Gaeta Grigorchuk's 50's birthday issue), 15 (2005), no. 5-6, pp. 939-969
  55. "Delzant's T-invariant, Kolmogorov complexity and one-relator groups" (with Paul Schupp), Commentari Math. Helv. 80 (2005), no. 4, pp. 911-933
  56. "Kleinian groups and the rank problem", (with Richard Weidmann), Geometry and Topology 9 (2005), pp. 375-402
  57. "Foldings, graphs of groups and the membership problem" (with Richard Weidmann and Alexei Myasnikov), Internat. J. Alg. Comput. 15 (2005), no. 1, 95-128
  58. "Acylindrical accessibility for groups acting on R-trees" (with Richard Weidmann), Math. Zeitschrift 249 (2005), no. 4, pp. 773-782
  59. "Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups" (with Paul Schupp),  Mathematische Annalen 331(2005), no. 1, pp. 1-19
  60. "Average-case complexity and decision problems in group theory" (with Alexei Myasnikov, Paul Schupp and Vladimir Shpilrain), Advances in Mathematics 190 (2005), no. 2, pp. 343-359
  61. "Relative hyperbolicity and Artin groups"(with Paul Schupp),  Geom. Dedicata 107 (2004), no. 1, pp. 153-167
  62. "Freely indecomposable groups acting on hyperbolic spaces"(with Richard Weidmann),  Internat. J. Algebra and Comput. 14 (2004), no. 2, pp. 115-171
  63. "Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion" (with Paul Schupp), Proceedings of the London Mathematical Society 88 (2004), no. 1, pp. 89-113
  64. "Generic-case complexity, decision problems in group theory and random walks" (with Alexei Myasnikov, Paul Schupp and Vladimir Shpilrain),  J. Algebra 264 (2003), no. 2, pp. 665-694
  65. "Nielsen methods and groups acting on hyperbolic spaces" (with Richard Weidmann), Geometriae Dedicata 98 (2003), no. 1, pp. 95-121
  66. "The Frattini subgroup for subgroups of hyperbolic groups",  J. Group Theory 6 (2003), no. 1, pp. 115-126
  67. "The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups", Ensign. Math. 48 (2002), no. 3-4, pp. 359-375
  68. "The geometry of relative Cayley graphs for subgroups of hyperbolic  groups", preprint
  69. "A remark on mapping tori of free group endomorphisms",  preprint
  70. "Boundaries of hyperbolic groups" (with Nadia Benakli), Combinatorial and Geometric Group Theory (R.Gilman, et al, editors), Contemporary Mathematics, vol. 296, 2002, pp. 39-94
  71. "A note on the Poenaru condition",   J. Group Theory 5 (2002), no. 1,  pp. 119-127
  72. "Stallings foldings and the subgroup structure of free groups" (with Alexey Myasnikov), J. Algebra 248 (2002), no 2,   pp. 608-668, and an Addendum
  73. "The Combination Theorem and Quasiconvexity",  Intern. J. Algebra Comput. 11 (2001), no. 2,  pp. 185-216
  74. "The subgroup properties of fully residually free groups" , Transact. Amer. Math. Soc. 354 (2002), no. 1,  pp. 335-362; and an ERRATUM Transact. Amer. Math. Soc.  355 (2003), no. 3,  pp. 1295--1296
  75. "On the failure of the Co-Hopf property for subgroups of word-hyperbolic groups" (with Dani Wise),   Israel. J. Math. 122 (2001),  pp. 125-147
  76.  "Mapping tori of endomorphisms of free groups",  Comm. in Algebra 28 (2000), no. 6,  pp. 2895-2917
  77. "Equivalence of some residual properties for word-hyperbolic groups"(with Dani Wise),   J. Algebra 223 (2000), no. 2, pp. 562-583
  78. " Two-generated groups acting on Trees"(with Richard Weidmann), Archiv der Mathematik (Basel) 73 (1999), no. 3, pp. 172-181
  79. "On the structure of two-generated word-hyperbolic groups" (with Richard Weidmann),   Math. Z. 231 (1999), no. 4, pp. 783-801
  80. "One-relator groups and the Howson property", Comm. in Algebra 27 (1999), no. 3,  pp. 1057-1072
  81. "A non-quasiconvexity embedding theorem for hyperbolic groups",   Math Proc. Cambridge Phil. Soc. 127 (1999), no. 3,  pp. 461-486
  82. "Quasiconvexity and amalgams", Intern. J. Alg. Computation 7 (1997), no. 6,  pp. 771-811
  83. "Amalgamated products and the Howson Property" , Canadian Math. Bulletin, 40 (1997), no. 3,  pp. 330-340
  84. "Small cancellation groups and translation numbers", Trans. Amer. Math. Soc., 349 (1997), no. 5,  pp. 1851-1875
  85. "Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups" (with Hamish Short), Canadian J. Math., 48 (1996), no. 6, pp. 1224-1244
  86.  "An example of a non-quasiconvex subgroup of a word hyperbolic group with an exotic limit set"New York J. Math., 1 (1995),  pp. 184-195
  87. "Detecting quasiconvexity: algorithmic aspects",  AMS DIMACS series, 25,  Geometric and Computational Perspectives on Infinite Groups, 1995, pp. 91-100

My graduate students
  1. Lucas Sabalka (PhD 2006, UIUC); an applied mathematician at Nebraska Global
  2. Gregory Kelsey (PhD 2011, UIUC); Assistant Professor at Bellarmine University
  3. Brent Solie (PhD 2011, UIUC); Assistant Professor at Embry-Riddle Aeronautical University
  4. Patrick Reynolds (PhD 2011, UIUC); Machine learning engineer, Apple
  5. Brian Ray (PhD 2014, UIUC); senior analyst at Daniel H. Wagner Associates)
  6. Neha Gupta (PhD 2016, UIUC); Director of Math Scheduling, Georgia Tech
  7. Caglar Uyanik (PhD 2017, UIUC); Gibbs Assistant Professor, Yale
  8. Elizabeth Field (PhD 2020, UIUC); postdoctoral researcher, University of Utah
  9. Heejoung Kim (UIUC, current PhD student)
  10. Zachary Simon (M.Sc. 2020, City College of CUNY)