Publications.

Link to my papers posted at arxiv.og 

1. Ilya Kapovich, "On the Hausdorff dimension and attracting laminations for fully irreducible automorphisms of free groups," preprint, 2024; arXiv:2410.02058
2. Naomi Andrew, Edgar A. Bering IV, Ilya Kapovich, Stefano Vidussi; with an appendix by Peter Shalen, "On two-generator subgroups of mapping torus groups," preprint, 2024; arXiv:2405.08985
3. "Counting conjugacy classes of fully irreducibles: double exponential growth", (joint with Catherine Pfaff); Geometriae Dedicata 218 (2024), no. 2, Paper no. 39; DOI: 10.1007/s10711-024-00885-4
4. "Ascending chain condition in generic groups," preprint, 2023; arXiv:2306.06706
5. "Primitivity rank for random elements in free groups," Journal of Group Theory 25 (2022), no. 5, 823-835
6. "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
7. "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
8. "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
9. "Generic-case complexity of Whitehead's algorithm, revisited ", preprint arXiv:1903.07040
10. "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
11. "Counting conjugacy classes of fully irreducibles: double exponential growth", (joint with Catherine Pfaff); preprint arXiv:1801.07471
12. "Counting conjugacy classes in Out(F_N)", (joint with Michael Hull), Bulletin of the Australian Mathematical Society 97 (2018), no 3, 412-421
13. "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
14. "Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell", Experimental Mathematics, 28 (2019), no. 1, pp. 24-38
15. "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
16. "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
17. "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
18. "An integral weight realization theorem for subset currents on free groups" , Topology Proceedings 50 (2017), pp. 213-236
19. "Wolfgang Haken: A biographical sketch", Illinois Journal of Mathematics 60 (2016), no. 1, pp. 3-9; special issue in honor of Wolfgang Haken
20. "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
    
21. "Musings on generic-case complexity", preprint
    
22. "On purely loxodromic actions" , Monatshefte fur Mathematik 181 (2016), no. 1, pp. 89-101
23. "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
24. "Nielsen equivalence in a class of random groups" (joint with Richard Weidmann), Journal of Topology 9 (2016), no. 2, 502-534
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26. "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
    
27. "Dynamics on free-by-cyclic groups" , (joint with Spencer Dowdall and Christopher J. Leininger); Geometry and Topology 19 (2015), 2801-2899
28. "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
29. "Cannon-Thurston fibers for iwip automorphisms of $F_N$", (joint with Martin Lustig), Jour. London Math. Soc. 91 (2015), no. 1, 203-224
30. "Unbounded asymmetry of stretch factors", (joint with Spencer Dowdall and Christopher J. Leininger); Comptes Rendus Mathematique, 352 (2014), no. 11, 885-887
31. "Algorithmic detectability of iwip automorphisms", Bull. London Math. Soc. 46 (2014), no. 2, pp. 279-290; online version at the BLMS site available here
32. "On hyperbolicity of free splitting and free factor complexes", (joint with Kasra Rafi), Groups, Geometry and Dynamics, 8 (2014), no. 2, pp. 391-414
33. "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
    
34. "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
    
35. "Subset currents on free groups", (joint with Tatiana Nagnibeda), Geometriae Dedicata, 166 (2013), 307-348
36. "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. (2014) doi: 10.1093/qmath/hat056
37. "Random length-spectrum rigidity for free groups", Proceedings of AMS 140 (2012), no. 5, pp. 1549-1560
38. "Stabilizers of R-trees with free isometric actions of F_N ", (with Martin Lustig), Journal of Group Theory, 14 (2011), no. 5, pp. 673-694
39. "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
    
40. "On mathematical contributions of Paul E. Schupp", Illinois J. Math., 54 (2010), no. 1, pp. 1-9, special issue dedicated to Paul Schupp
    
41. "Ping-pong and Outer space", (with Martin Lustig), Journal of Topology and Analysis 2 (2010), no. 2, pp. 173-201
    
42. "Nielsen equivalence in small cancellation groups", (with Richard Weidmann), preprint
    
43. "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
    
44. "Intersection form, laminations and currents on free groups ", (with Martin Lustig), Geom. Funct. Anal. 19 (2010), no. 5, pp. 1426-1467
45. "Geometric Intersection Number and analogues of the Curve Complex for free groups", (with Martin Lustig), Geometry and Topology 13 (2009), pp. 1805-1833
    
46. "Some Quantitative Aspects of Fractional Computability", (with Paul Schupp), preprint
    
47. "On group-theoretic models of randomness and genericity" (with Paul Schupp), Groups, Geometry and Dynamics 2 (2008), no. 3, pp. 383-404
48. "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
49. "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
50. "On the absence of McShane-type identities for the outer space" (with Igor Rivin), Journal of Algebra 320 (2008), no. 10, pp. 3659-3670
51. "Clusters, currents and Whitehead's algorithm", Experimental Mathematics 16 (2007), no. 1, pp. 67-76
    
52. " 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
    
53. "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
    
54. "Translation equivalence in free groups", (with Gilbert Levitt, Paul Schupp and Vladimir Shpilrain),  Transact. Amer. Math. Soc. 359 (2007), no. 4, pp. 1527-1546
55. "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
    
56. "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
57. "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
    
58. "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
    
59. "Delzant's T-invariant, Kolmogorov complexity and one-relator groups" (with Paul Schupp), Commentari Math. Helv. 80 (2005), no. 4, pp. 911-933
    
60. "Kleinian groups and the rank problem", (with Richard Weidmann), Geometry and Topology 9 (2005), pp. 375-402
    
61. "Foldings, graphs of groups and the membership problem" (with Richard Weidmann and Alexei Myasnikov), Internat. J. Alg. Comput. 15 (2005), no. 1, 95-128
62. "Acylindrical accessibility for groups acting on R-trees" (with Richard Weidmann), Math. Zeitschrift 249 (2005), no. 4, pp. 773-782
63. "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
64. "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
65. "Relative hyperbolicity and Artin groups"(with Paul Schupp),  Geom. Dedicata 107 (2004), no. 1, pp. 153-167
66. "Freely indecomposable groups acting on hyperbolic spaces"(with Richard Weidmann),  Internat. J. Algebra and Comput. 14 (2004), no. 2, pp. 115-171
67. "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
68. "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
69. "Nielsen methods and groups acting on hyperbolic spaces" (with Richard Weidmann), Geometriae Dedicata 98 (2003), no. 1, pp. 95-121
70. "The Frattini subgroup for subgroups of hyperbolic groups",  J. Group Theory 6 (2003), no. 1, pp. 115-126
71. "The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups", Ensign. Math. 48 (2002), no. 3-4, pp. 359-375
72. "The geometry of relative Cayley graphs for subgroups of hyperbolic  groups", preprint
73. "A remark on mapping tori of free group endomorphisms",  preprint
74. "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
75. "A note on the Poenaru condition",   J. Group Theory 5 (2002), no. 1,  pp. 119-127
76. "Stallings foldings and the subgroup structure of free groups" (with Alexey Myasnikov), J. Algebra 248 (2002), no 2,   pp. 608-668, and an Addendum
77. "The Combination Theorem and Quasiconvexity",  Intern. J. Algebra Comput. 11 (2001), no. 2,  pp. 185-216
78. "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
79. "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
80.  "Mapping tori of endomorphisms of free groups",  Comm. in Algebra 28 (2000), no. 6,  pp. 2895-2917
81. "Equivalence of some residual properties for word-hyperbolic groups"(with Dani Wise),   J. Algebra 223 (2000), no. 2, pp. 562-583
82. " Two-generated groups acting on Trees"(with Richard Weidmann), Archiv der Mathematik (Basel) 73 (1999), no. 3, pp. 172-181
83. "On the structure of two-generated word-hyperbolic groups" (with Richard Weidmann),   Math. Z. 231 (1999), no. 4, pp. 783-801
84. "One-relator groups and the Howson property", Comm. in Algebra 27 (1999), no. 3,  pp. 1057-1072
85. "A non-quasiconvexity embedding theorem for hyperbolic groups",   Math Proc. Cambridge Phil. Soc. 127 (1999), no. 3,  pp. 461-486
86. "Quasiconvexity and amalgams", Intern. J. Alg. Computation 7 (1997), no. 6,  pp. 771-811
87. "Amalgamated products and the Howson Property" , Canadian Math. Bulletin, 40 (1997), no. 3,  pp. 330-340
88. "Small cancellation groups and translation numbers", Trans. Amer. Math. Soc., 349 (1997), no. 5,  pp. 1851-1875
89. "Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups" (with Hamish Short), Canadian J. Math., 48 (1996), no. 6, pp. 1224-1244
90.  "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
91. "Detecting quasiconvexity: algorithmic aspects",  AMS DIMACS series, 25,  Geometric and Computational Perspectives on Infinite Groups, 1995, pp. 91-100