Ilya Kapovich
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Most Influential Person Now
Russian-American mathematician
Ilya Kapovich's AcademicInfluence.com Rankings
Ilya Kapovichmathematics Degrees
Mathematics
#6804
World Rank
#9355
Historical Rank
Group Theory
#188
World Rank
#221
Historical Rank
Measure Theory
#3865
World Rank
#4555
Historical Rank
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Mathematics
Ilya Kapovich's Degrees
- PhD Mathematics Tel Aviv University
Why Is Ilya Kapovich Influential?
(Suggest an Edit or Addition)According to Wikipedia, Ilya Kapovich is a Russian-American mathematician and a Professor of Mathematics at the Hunter College of the City University of New York. He is known for his contributions to geometric group theory, geometric topology, and complexity theory.
Ilya Kapovich's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Boundaries of hyperbolic groups (2002) (234)
- Stallings Foldings and Subgroups of Free Groups (2002) (229)
- Generic-case complexity, decision problems in group theory and random walks (2002) (188)
- Geometric Intersection Number and analogues of the Curve Complex for free groups (2007) (101)
- Generic properties of Whitehead’s algorithm and isomorphism rigidity of random one-relator groups (2003) (82)
- Currents on free groups (2004) (80)
- Foldings, Graphs of Groups and the Membership Problem (2003) (79)
- Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups (1996) (72)
- On hyperbolicity of free splitting and free factor complexes (2012) (71)
- Intersection Form, Laminations and Currents on Free Groups (2007) (69)
- Average-case complexity and decision problems in group theory (2002) (63)
- Genericity, the Arzhantseva-Ol’shanskii method and the isomorphism problem for one-relator groups (2002) (59)
- The Frequency Space of a Free Group (2003) (58)
- The Patterson–Sullivan Embedding and Minimal Volume Entropy for Outer Space (2005) (50)
- The equivalence of some residual properties of word-hyperbolic groups (2000) (49)
- The actions of ${\mathit{Out}(F_k)}$ on the boundary of Outer space and on the space of currents: minimal sets and equivariant incompatibility (2006) (45)
- PING-PONG AND OUTER SPACE (2009) (38)
- A non-quasiconvexity embedding theorem for hyperbolic groups (1997) (37)
- The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms (2005) (37)
- Mapping tori of endomorphisms of free groups (2000) (36)
- Dynamics on free-by-cyclic groups (2013) (35)
- The Combination Theorem and Quasiconvexity (2001) (33)
- Detecting quasiconvexity: Algorithmic aspects (1995) (32)
- Algorithmic detectability of iwip automorphisms (2012) (32)
- McMullen polynomials and Lipschitz flows for free-by-cyclic groups (2013) (29)
- Stallings foldings and the subgroup structure of free groups (2002) (26)
- INVARIANT LAMINATIONS FOR IRREDUCIBLE AUTOMORPHISMS OF FREE GROUPS (2011) (25)
- Translation equivalence in free groups (2004) (24)
- On group-theoretic models of randomness and genericity (2007) (23)
- Freely Indecomposable Groups Acting on Hyperbolic Spaces (2002) (23)
- Quasiconvexity and Amalgams (1995) (21)
- Clusters, Currents, and Whitehead's Algorithm (2005) (20)
- Cannon–Thurston fibers for iwip automorphisms of FN (2012) (20)
- Small cancellation groups and translation numbers (1996) (20)
- On the structure of two-generated hyperbolic groups (1999) (20)
- DENSITIES IN FREE GROUPS AND Z k , VISIBLE POINTS AND TEST ELEMENTS (2005) (19)
- Spectral rigidity of automorphic orbits in free groups (2012) (19)
- Nielsen Methods and Groups Acting on Hyperbolic Spaces (2002) (19)
- Stabilizers of ℝ-trees with free isometric actions of FN (2009) (18)
- THE NON-AMENABILITY OF SCHREIER GRAPHS FOR INFINITE INDEX QUASICONVEX SUBGROUPS OF HYPERBOLIC GROUPS (2002) (17)
- Subgroup properties of fully residually free groups (2001) (17)
- Delzant's T-invariant, one-relator groups and Kolmogorov complexity (2003) (15)
- Howson property and one-relator groups 1 (1999) (15)
- Kleinian groups and the rank problem (2004) (15)
- Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups (2003) (15)
- Two-generated groups acting on trees (1999) (14)
- Densities in free groups and $\mathbb{Z}^k$, Visible Points and Test Elements (2005) (14)
- Cannon–Thurston maps for hyperbolic free group extensions (2015) (14)
- A train track directed random walk on Out(Fr) (2014) (14)
- Conical limit points and the Cannon-Thurston map (2014) (13)
- Subset currents on free groups (2011) (13)
- Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups (2012) (13)
- A note on the Poénaru condition (2001) (13)
- Domains of proper discontinuity on the boundary of Outer space (2009) (12)
- Random length-spectrum rigidity for free groups (2010) (11)
- On the failure of the co-hopf property for subgroups of word-hyperbolic groups (2001) (11)
- The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With the appendix by Khalid Bou–Rabee (2014) (11)
- Random quotients of the modular group are rigid and essentially incompressible (2006) (11)
- Amalgamated Products and the Howson Property (1997) (11)
- THE GEOMETRY OF RELATIVE CAYLEY GRAPHS FOR SUBGROUPS OF HYPERBOLIC GROUPS (2002) (10)
- The Frattini subgroup for subgroups of hyperbolic groups (2001) (10)
- Bounded Rank Subgroups of Coxeter Groups, Artin Groups and One‐Relator Groups with Torsion (2002) (10)
- Detecting Fully Irreducible Automorphisms: A Polynomial Time Algorithm (2016) (10)
- Geometric entropy of geodesic currents on free groups (2008) (9)
- Endomorphisms, train track maps, and fully irreducible monodromies (2015) (9)
- Acylindrical accessibility for groups acting on ℝ-trees (2005) (8)
- Stable Strata of Geodesics in Outer Space (2017) (7)
- A Non-quasiconvex Subgroup of a Hyperbolic Group with an Exotic Limit Set (1995) (7)
- Generic properties of Whitehead's Algorithm, stabilizers in Aut(Fk) and one-relator groups (2003) (7)
- Random outer automorphisms of free groups: Attracting trees and their singularity structures (2018) (6)
- Corrigendum: “Spectral rigidity of automorphic orbits in free groups” (2011) (5)
- Relative Hyperbolicity and Artin Groups (2002) (5)
- Complexity and Randomness in Group Theory (2020) (5)
- A remark on mapping tori of free group endomorphisms (2002) (5)
- Unbounded asymmetry of stretch factors (2014) (5)
- On purely loxodromic actions (2015) (4)
- Random trees in the boundary of outer space (2019) (4)
- An integral weight realization theorem for subset currents on free groups (2012) (3)
- On the absence of McShane-type identities for the outer space (2006) (3)
- Detecting quasiconvexity: algorithmic aspects, from: “Geometric and (1995) (2)
- Erratum to “Subgroup properties of fully residually free groups” (2002) (2)
- Nielsen equivalence in a class of random groups (2013) (2)
- On the fibers of the Cannon-Thurston map for free-by-cyclic groups (2012) (2)
- Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space (2014) (2)
- Counting conjugacy classes of fully irreducibles: double exponential growth (2018) (2)
- Generalized geodesic currents on free groups (2011) (2)
- Nielsen equivalence in small cancellation groups (2010) (2)
- THE DANGERS OF THE "AUTHOR PAYS" MODEL IN MATHEMATICAL PUBLISHING (2011) (2)
- Cannon–Thurston maps for hyperbolic free group extensions (2016) (1)
- A note on the Ponaru condition (2001) (1)
- Musings on generic-case complexity (2015) (1)
- Primitivity rank for random elements in free groups (2021) (1)
- Acylindrical accessibility for groups acting on $\mathbf R$-trees (2002) (1)
- COUNTING CONJUGACY CLASSES IN $\text{Out}(F_{N})$ (2017) (0)
- Generic-case complexity of Whitehead's algorithm, revisited (2019) (0)
- Stabilizers of ℝ-trees with free isometric actions ofFN (2011) (0)
- S ep 2 00 2 RELATIVE HYPERBOLICITY AND ARTIN GROUPS (2002) (0)
- Wolfgang Haken: A biographical sketch (2016) (0)
- 2 5 A ug 2 00 4 KLEINIAN GROUPS AND THE RANK PROBLEM (0)
- Ju l 2 00 3 RELATIVE HYPERBOLICITY AND ARTIN GROUPS (2002) (0)
- On mathematical contributions of Paul E. Schupp (2010) (0)
- Asymptotic density in free groups and $\mathbb{Z}^k$, Visibile Points and Test Elements (2005) (0)
- Addendum to "Subset currents on free groups" (2012) (0)
- G R ] 1 9 M ay 2 00 6 THE ACTIONS OF Out ( F k ) ON THE BOUNDARY OFOUTER SPACE AND ON THE SPACE OF CURRENTS : MINIMAL SETS AND EQUIVARIANT INCOMPATIBILITY (2006) (0)
- Some Quantitative Aspects of Fractional Computability (2007) (0)
- Delzant's T-invariant and one-relator groups (2003) (0)
- K-groups and Rings of Integers (2019) (0)
- 2 7 Ju l 2 00 5 ASYMPTOTIC DENSITY IN FREE GROUPS AND Z k , VISIBILE POINTS AND TEST ELEMENTS (2005) (0)
- Open-access policies: A legal quagmire (2016) (0)
- Preprint servers: no author fees (2012) (0)
- EQUIVALENCE IN FREE GROUPS (2006) (0)
- Primitivity index bounds in free groups, and the second Chebyshev function (2020) (0)
- Rigidity of Length Functions over Strata of Flat Metrics (2014) (0)
- On purely loxodromic actions (2015) (0)
- An example of a non-quasiconvex subgroup of a word hyperbolic group with exotic limit set (1995) (0)
- Subset currents on free groups (2012) (0)
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