All Stories

  1. COUNTING CONJUGACY CLASSES IN

    Article • Bulletin of the Australian Mathematical Society, March 2018, Cambridge University Press

    Professor Ilya Kapovich

  2. Stable Strata of Geodesics in Outer Space

    Article • International Mathematics Research Notices, January 2018, Oxford University Press (OUP)

    Professor Ilya Kapovich

  3. Endomorphisms, train track maps, and fully irreducible monodromies

    Article • Groups Geometry and Dynamics, December 2017, European Mathematical Publishing House

    Professor Ilya Kapovich

  4. The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With the appendix by Khalid Bou–Rabee

    Article • Mathematical Proceedings of the Cambridge Philosophical Society, October 2017, Cambridge University Press

    Professor Ilya Kapovich, Neha Gupta

  5. Detecting Fully Irreducible Automorphisms: A Polynomial Time Algorithm

    Article • Experimental Mathematics, May 2017, Taylor & Francis

    Professor Ilya Kapovich

  6. McMullen polynomials and Lipschitz flows for free-by-cyclic groups

    Article • January 2017, European Mathematical Publishing House

    Professor Ilya Kapovich

  7. Cannon–Thurston maps for hyperbolic free group extensions

    Article • Israel Journal of Mathematics, October 2016, Springer Science + Business Media

    Professor Ilya Kapovich

  8. Nielsen equivalence in a class of random groups

    Article • Journal of Topology, May 2016, Oxford University Press (OUP)

    Professor Ilya Kapovich

  9. Conical limit points and the Cannon-Thurston map

    Article • Conformal Geometry and Dynamics of the American Mathematical Society, March 2016, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  10. Dynamics on free-by-cyclic groups

    Article • Geometry & Topology, October 2015, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  11. Patterson–Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for outer space

    Article • Pacific Journal of Mathematics, September 2015, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  12. A train track directed random walk onOut(Fr)

    Article • International Journal of Algebra and Computation, August 2015, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  13. On purely loxodromic actions

    Article • Monatshefte für Mathematik, July 2015, Springer Science + Business Media

    Professor Ilya Kapovich

  14. Cannon-Thurston fibers for iwip automorphisms of FN

    Article • January 2015, Oxford University Press (OUP)

    Professor Ilya Kapovich

  15. Corrigendum: “Spectral rigidity of automorphic orbits in free groups”

    Article • Algebraic & Geometric Topology, November 2014, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  16. Unbounded asymmetry of stretch factors

    Article • Comptes Rendus Mathématique, November 2014, Elsevier

    Professor Ilya Kapovich

  17. Algorithmic detectability of iwip automorphisms

    Article • January 2014, Oxford University Press (OUP)

    Professor Ilya Kapovich

  18. On hyperbolicity of free splitting and free factor complexes

    Article • Groups Geometry and Dynamics, January 2014, European Mathematical Publishing House

    Professor Ilya Kapovich

  19. Subset currents on free groups

    Article • Geometriae Dedicata, November 2012, Springer Science + Business Media

    Professor Ilya Kapovich

  20. Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups

    Article • Conformal Geometry and Dynamics of the American Mathematical Society, October 2012, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  21. Preprint servers: no author fees

    Article • Nature, September 2012, Springer Science + Business Media

    Professor Ilya Kapovich

  22. Spectral rigidity of automorphic orbits in free groups

    Article • Algebraic & Geometric Topology, July 2012, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  23. Random length-spectrum rigidity for free groups

    Article • Proceedings of the American Mathematical Society, May 2012, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  24. Stabilizers of ℝ-trees with free isometric actions of FN

    Article • Journal of Group Theory, January 2011, De Gruyter

    Professor Ilya Kapovich

  25. PING-PONG AND OUTER SPACE

    Article • Journal of Topology and Analysis, June 2010, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  26. Geometric entropy of geodesic currents on free groups

    Article • January 2010, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  27. Intersection Form, Laminations and Currents on Free Groups

    Article • Geometric and Functional Analysis, December 2009, Springer Science + Business Media

    Professor Ilya Kapovich

  28. Geometric intersection number and analogues of the curve complex for free groups

    Article • Geometry & Topology, March 2009, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  29. Random quotients of the modular group are rigid and essentially incompressible

    Article • Journal für die reine und angewandte Mathematik (Crelles Journal), January 2009, De Gruyter

    Professor Ilya Kapovich

  30. On the absence of McShane-type identities for the outer space

    Article • November 2008, Elsevier

    Professor Ilya Kapovich

  31. On group-theoretic models of randomness and genericity

    Article • Groups Geometry and Dynamics, January 2008, European Mathematical Publishing House

    Professor Ilya Kapovich

  32. The actions of ${\mathit{Out}(F_k)}$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility

    Article • Ergodic Theory and Dynamical Systems, April 2007, Cambridge University Press

    Professor Ilya Kapovich

  33. Clusters, Currents, and Whitehead's Algorithm

    Article • Experimental Mathematics, January 2007, Taylor & Francis

    Professor Ilya Kapovich

  34. The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

    Article • January 2007, Springer Science + Business Media

    Professor Ilya Kapovich

  35. Densities in free groups and $\mathbb{Z}^k$, Visible Points and Test Elements

    Article • Mathematical Research Letters, January 2007, International Press of Boston

    Professor Ilya Kapovich

  36. Translation equivalence in free groups

    Article • October 2006, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  37. Generic properties of Whitehead’s algorithm and isomorphism rigidity of random one-relator groups

    Article • Pacific Journal of Mathematics, January 2006, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  38. Currents on free groups

    Article • January 2006, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  39. THE FREQUENCY SPACE OF A FREE GROUP

    Article • International Journal of Algebra and Computation, October 2005, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  40. Kleinian groups and the rank problem

    Article • Geometry & Topology, March 2005, Mathematical Sciences Publishers

    Professor Ilya Kapovich

  41. FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM

    Article • International Journal of Algebra and Computation, February 2005, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  42. Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups

    Article • January 2005, European Mathematical Publishing House

    Professor Ilya Kapovich

  43. Average-case complexity and decision problems in group theory

    Article • January 2005, Elsevier

    Professor Ilya Kapovich

  44. Acylindrical accessibility for groups acting on ?-trees

    Article • Mathematische Zeitschrift, October 2004, Springer Science + Business Media

    Professor Ilya Kapovich

  45. Genericity, the Arzhantseva-Ol?shanskii method and the isomorphism problem for one-relator groups

    Article • Mathematische Annalen, August 2004, Springer Science + Business Media

    Professor Ilya Kapovich

  46. Relative Hyperbolicity and Artin Groups

    Article • Geometriae Dedicata, August 2004, Springer Science + Business Media

    Professor Ilya Kapovich

  47. FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES

    Article • International Journal of Algebra and Computation, April 2004, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  48. Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion

    Article • Test´s Publication, January 2004, Oxford University Press (OUP)

    Professor Ilya Kapovich

  49. Generic-case complexity, decision problems in group theory, and random walks

    Article • June 2003, Elsevier

    Professor Ilya Kapovich

  50. The Frattini subgroups of subgroups of hyperbolic groups

    Article • Journal of Group Theory, January 2003, De Gruyter

    Professor Ilya Kapovich

  51. Article • January 2003, Springer Science + Business Media

    Professor Ilya Kapovich

  52. Stallings Foldings and Subgroups of Free Groups

    Article • February 2002, Elsevier

    Professor Ilya Kapovich

  53. Boundaries of hyperbolic groups

    Article • January 2002, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  54. On the failure of the co-hopf property for subgroups of word-hyperbolic groups

    Article • Israel Journal of Mathematics, December 2001, Springer Science + Business Media

    Professor Ilya Kapovich

  55. THE COMBINATION THEOREM AND QUASICONVEXITY

    Article • International Journal of Algebra and Computation, April 2001, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  56. A note on the Poénaru condition

    Article • Journal of Group Theory, January 2001, De Gruyter

    Professor Ilya Kapovich

  57. Mapping tori of endomorphisms of free groups

    Article • Communications in Algebra, January 2000, Taylor & Francis

    Professor Ilya Kapovich

  58. The Equivalence of some Residual Properties of Word-Hyperbolic Groups

    Article • January 2000, Elsevier

    Professor Ilya Kapovich

  59. A non-quasiconvexity embedding theorem for hyperbolic groups

    Article • November 1999, Cambridge University Press

    Professor Ilya Kapovich

  60. Two-generated groups acting on trees

    Article • September 1999, Springer Science + Business Media

    Professor Ilya Kapovich

  61. On the structure of two-generated hyperbolic groups

    Article • August 1999, Springer Science + Business Media

    Professor Ilya Kapovich

  62. Howson property and one-relator groups1

    Article • Communications in Algebra, January 1999, Taylor & Francis

    Professor Ilya Kapovich

  63. Quasiconvexity and Amalgams

    Article • International Journal of Algebra and Computation, December 1997, World Scientific Pub Co Pte Lt

    Professor Ilya Kapovich

  64. Amalgamated products and the Howson property

    Article • Canadian Mathematical Bulletin, September 1997, Canadian Mathematical Society

    Professor Ilya Kapovich

  65. Article • May 1997, American Mathematical Society (AMS)

    Professor Ilya Kapovich

  66. Greenberg's theorem for quasiconvex subgroups of word hyperbolic groups

    Article • Canadian Journal of Mathematics, December 1996, Canadian Mathematical Society

    Professor Ilya Kapovich

  67. Detecting quasiconvexity: Algorithmic aspects

    Article • November 1995, American Mathematical Society (AMS)

    Professor Ilya Kapovich