Ilya Kapovich

 Ilya Kapovich

Contact Information

Department of Mathematics
365 Altgeld Hall, MC-382
1409 W. Green Street
Urbana, IL 61801
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Research Description

--Geometric Group Theory Outer space and Geometric Topology

--Out(Fn) and group actions on R-trees

--3-dimensional Topology, mapping class groups, Teichmuller space and Kleinian Groups

--Manifolds of Non-positive Curvature and CAT(0)-spaces

--Ergodic theory and probabilistic aspects of group theory

--Logic, Computational Complexity, Computational and Algorithmic aspects of Algebra


  • B.Sc., Mathematics, Novosibirsk State University, Russia, 1992
  • Ph.D., Mathematics, City University of New York Graduate Center, 1996

Distinctions / Awards

Selected Publications

Journal Articles

Dowdall, Spencer, Ilya Kapovich, and Christopher J. Leininger McMullen polynomials and Lipschitz flows for free-by-cyclic groups Journal of the European Mathematical Society 19 11 2017, p. 3253–3353. preprint version.
Dowdall, Spencer, Ilya Kapovich, and Samuel J. Taylor Cannon-Thurston maps for hyperbolic free group extensions Israel Journal of Mathematics 216 2 2016, p. 753-797.
Dowdall, Spencer, Ilya Kapovich, and Christopher Leininger Dynamics on free-by-cyclic groups Geometry & Topology 19 5 2015, p. 2801-2899. preprint version. GoogleScholar link.
Kapovich, Ilya, and Richard Weidmann Nielsen equivalence in a class of random groups Journal of Topology 9 2 2016, p. 502-534.
Kapovich, Ilya Algorithmic detectability of iwip automorphisms Bulletin of the London Mathematical Society 46 2 2014, p. 279-290.
Kapovich, Ilya, and Kasra Rafi On hyperbolicity of free splitting and free factor complexes Groups, Geometry, and Dynamics 8 2 2014, p. 391-414.
Kapovich, Ilya, and Martin Lustig Intersection form, laminations and currents on free groups Geometric and Functional Analysis 19 5 2010, p. 1426–1467.
Kapovich, Ilya, and Paul Schupp Random quotients of the modular group are rigid and essentially incompressible Journal für die Reine und Angewandte Mathematik 628 2009, p. 91–119.
Kapovich, Ilya, and Martin Lustig Geometric intersection number and analogues of the curve complex for free groups Geometry & Topology 13 3 2009, p. 1805–1833.
Kapovich, Ilya, Paul Schupp, and Vladimir Shpilrain Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups Pacific Journal of Mathematics 223 1 2006, p. 113–140.
Kapovich, Ilya, and Paul Schupp Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups" Mathematische Annalen 331 1 2005, p. 1-19.
Kapovich, Ilya, Alexei G. Myasnikov, Paul Schupp, and Vladimir Shpilrain Generic-case complexity, decision problems in group theory and random walks Journal of Algebra 264 2 2003, p. 665–694.

Special Issues of a Journal

Book Contributions

Kapovich, Ilya Currents on free groups Topological and asymptotic aspects of group theory. Contemporary Mathematics, vol. 394 Currents on free groups Providence, RI American Mathematical Society 2006, p. 149–176.
Kapovich, Ilya, and Nadia Benakli Boundaries of hyperbolic groups Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001). Contemporary Mathematics, vol. 296 Boundaries of hyperbolic groups Providence, RI American Mathematical Society 2002, p. 39–93.


Kapovich, Ilya Open access policies: A legal quagmire Science, vol. 353, no. 6301 2016, p. 758-759.
Kapovich, Ilya Standards for publishing errata Notices of the American Mathematical Society, vol. 59, no. 10 2012, p. 1384.
Kapovich, Ilya The dangers of the ``author pays'' model in mathematical publishing Notices of the American Mathematical Society, vol 58, no. 9 2011, p. 1294-1295.