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

my photo

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

Here is a reasonably up-to-date version of my CV (April 14, 2019).

In the Spring 2019 Semester I am teaching the course Math 311, Abstract Algebra I, Monday, Thursday 11:10am-12:15pm in HE 920. See Blackboard for more details. My office hours for Spring '19 are Tuesdays 9:30am-11:30am. My office is in HE 917.

In the Fall 2018 semester I was teaching the course Math 155, Calc II, Monday, Thursday 9:10am-11am in Hunter West 615. My office hours were M, Th 11am-12:30pm in the Mary Dolciani Center (7th Floor of the Library). A handout with main course information is available here. Please check Blackboard for more details. The WebAssign Class Key for this section was hunter 1358 2374.


Contact information

e-mail ik535@hunter.cuny.edu [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.



Papers.


Link to my papers posted at arxiv.og 


I am currently supported by the NSF grant DMS-1905641
  1. "Generic-case complexity of Whitehead's algorithm, revisited ", preprint arXiv:1903.07040
  2. "Random outer automorphisms of free groups: Attracting trees and their singularity structures", (joint with Joseph Maher, Catherine Pfaff, and Samuel Taylor); preprint arXiv:1805.12382
  3. "Counting conjugacy classes of fully irreducibles: double exponential growth", (joint with Catherine Pfaff); preprint arXiv:1801.07471
  4. "Counting conjugacy classes in Out(FN)", (joint with Michael Hull), Bulletin of the Australian Mathematical Society 97 (2018), no 3, 412-421
  5. "Stable Strata of Geodesics in Outer Space", (joint with Yael Algom-Kfir and Catherine Pfaff), Internat. Math. Res. Notices (IMRN); to appear
  6. "Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell", Experimental Mathematics, 28 (2019), no. 1, pp. 24-38
  7. "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
  8. "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
  9. "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
  10. "An integral weight realization theorem for subset currents on free groups" , Topology Proceedings 50 (2017), pp. 213-236
  11. "Wolfgang Haken: A biographical sketch", Illinois Journal of Mathematics 60 (2016), no. 1, pp. 3-9; special issue in honor of Wolfgang Haken
  12. "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
  13. "Musings on generic-case complexity", preprint
  14. "On purely loxodromic actions" , Monatshefte fur Mathematik 181 (2016), no. 1, pp. 89-101
  15. "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
  16. "Nielsen equivalence in a class of random groups" (joint with Richard Weidmann), Journal of Topology 9 (2016), no. 2, 502-534

  17. "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
  18. "Dynamics on free-by-cyclic groups" , (joint with Spencer Dowdall and Christopher J. Leininger); Geometry and Topology 19 (2015), 2801-2899
  19. "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
  20. "Cannon-Thurston fibers for iwip automorphisms of $F_N$", (joint with Martin Lustig), Jour. London Math. Soc. 91 (2015), no. 1, 203-224
  21. "Unbounded asymmetry of stretch factors", (joint with Spencer Dowdall and Christopher J. Leininger); Comptes Rendus Mathematique, 352 (2014), no. 11, 885-887
  22. "Algorithmic detectability of iwip automorphisms", Bull. London Math. Soc. 46 (2014), no. 2, pp. 279-290; online version at the BLMS site available here
  23. "On hyperbolicity of free splitting and free factor complexes", (joint with Kasra Rafi), Groups, Geometry and Dynamics, 8 (2014), no. 2, pp. 391-414
  24. "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
  25. "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
  26. "Subset currents on free groups", (joint with Tatiana Nagnibeda), Geometriae Dedicata, 166 (2013), 307-348
  27. "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
  28. "Random length-spectrum rigidity for free groups", Proceedings of AMS 140 (2012), no. 5, pp. 1549-1560
  29. "Stabilizers of R-trees with free isometric actions of FN ", (with Martin Lustig), Journal of Group Theory, 14 (2011), no. 5, pp. 673-694
  30. "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
  31. "On mathematical contributions of Paul E. Schupp", Illinois J. Math., 54 (2010), no. 1, pp. 1-9, special issue dedicated to Paul Schupp
  32. "Ping-pong and Outer space", (with Martin Lustig), Journal of Topology and Analysis 2 (2010), no. 2, pp. 173-201
  33. "Nielsen equivalence in small cancellation groups", (with Richard Weidmann), preprint
  34. "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
  35. "Intersection form, laminations and currents on free groups ", (with Martin Lustig), Geom. Funct. Anal. 19 (2010), no. 5, pp. 1426-1467
  36. "Geometric Intersection Number and analogues of the Curve Complex for free groups", (with Martin Lustig), Geometry and Topology 13 (2009), pp. 1805-1833
  37. "Some Quantitative Aspects of Fractional Computability", (with Paul Schupp), preprint
  38. "On group-theoretic models of randomness and genericity" (with Paul Schupp), Groups, Geometry and Dynamics 2 (2008), no. 3, pp. 383-404
  39. "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
  40. "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
  41. "On the absence of McShane-type identities for the outer space" (with Igor Rivin), Journal of Algebra 320 (2008), no. 10, pp. 3659-3670
  42. "Clusters, currents and Whitehead's algorithm", Experimental Mathematics 16 (2007), no. 1, pp. 67-76
  43. " 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
  44. "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
  45. "Translation equivalence in free groups", (with Gilbert Levitt, Paul Schupp and Vladimir Shpilrain),  Transact. Amer. Math. Soc. 359 (2007), no. 4, pp. 1527-1546
  46. "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
  47. "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
  48. "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
  49. "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
  50. "Delzant's T-invariant, Kolmogorov complexity and one-relator groups" (with Paul Schupp), Commentari Math. Helv. 80 (2005), no. 4, pp. 911-933
  51. "Kleinian groups and the rank problem", (with Richard Weidmann), Geometry and Topology 9 (2005), pp. 375-402
  52. "Foldings, graphs of groups and the membership problem" (with Richard Weidmann and Alexei Myasnikov), Internat. J. Alg. Comput. 15 (2005), no. 1, 95-128
  53. "Acylindrical accessibility for groups acting on R-trees" (with Richard Weidmann), Math. Zeitschrift 249 (2005), no. 4, pp. 773-782
  54. "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
  55. "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
  56. "Relative hyperbolicity and Artin groups"(with Paul Schupp),  Geom. Dedicata 107 (2004), no. 1, pp. 153-167
  57. "Freely indecomposable groups acting on hyperbolic spaces"(with Richard Weidmann),  Internat. J. Algebra and Comput. 14 (2004), no. 2, pp. 115-171
  58. "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
  59. "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
  60. "Nielsen methods and groups acting on hyperbolic spaces" (with Richard Weidmann), Geometriae Dedicata 98 (2003), no. 1, pp. 95-121
  61. "The Frattini subgroup for subgroups of hyperbolic groups",  J. Group Theory 6 (2003), no. 1, pp. 115-126
  62. "The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups", Ensign. Math. 48 (2002), no. 3-4, pp. 359-375
  63. "The geometry of relative Cayley graphs for subgroups of hyperbolic  groups", preprint
  64. "A remark on mapping tori of free group endomorphisms",  preprint
  65. "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
  66. "A note on the Poenaru condition",   J. Group Theory 5 (2002), no. 1,  pp. 119-127
  67. "Stallings foldings and the subgroup structure of free groups" (with Alexey Myasnikov), J. Algebra 248 (2002), no 2,   pp. 608-668, and an Addendum
  68. "The Combination Theorem and Quasiconvexity",  Intern. J. Algebra Comput. 11 (2001), no. 2,  pp. 185-216
  69. "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
  70. "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
  71.  "Mapping tori of endomorphisms of free groups",  Comm. in Algebra 28 (2000), no. 6,  pp. 2895-2917
  72. "Equivalence of some residual properties for word-hyperbolic groups"(with Dani Wise),   J. Algebra 223 (2000), no. 2, pp. 562-583
  73. " Two-generated groups acting on Trees"(with Richard Weidmann), Archiv der Mathematik (Basel) 73 (1999), no. 3, pp. 172-181
  74. "On the structure of two-generated word-hyperbolic groups" (with Richard Weidmann),   Math. Z. 231 (1999), no. 4, pp. 783-801
  75. "One-relator groups and the Howson property", Comm. in Algebra 27 (1999), no. 3,  pp. 1057-1072
  76. "A non-quasiconvexity embedding theorem for hyperbolic groups",   Math Proc. Cambridge Phil. Soc. 127 (1999), no. 3,  pp. 461-486
  77. "Quasiconvexity and amalgams", Intern. J. Alg. Computation 7 (1997), no. 6,  pp. 771-811
  78. "Amalgamated products and the Howson Property" , Canadian Math. Bulletin, 40 (1997), no. 3,  pp. 330-340
  79. "Small cancellation groups and translation numbers", Trans. Amer. Math. Soc., 349 (1997), no. 5,  pp. 1851-1875
  80. "Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups" (with Hamish Short), Canadian J. Math., 48 (1996), no. 6, pp. 1224-1244
  81.  "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
  82. "Detecting quasiconvexity: algorithmic aspects",  AMS DIMACS series, 25,  Geometric and Computational Perspectives on Infinite Groups, 1995, pp. 91-100