Contact Information
Room 919/944 East
Hunter College
695 Park Avenue
New York, NY 10065
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
Education
B.Sc., Mathematics, Novosibirsk State University, Russia, 1992
Ph.D., Mathematics, City University of New York Graduate Center, 1996
Grants
Simons Foundation Collaboration Grant no. no. 279836 (2013-2014), Principal Investigator
NSF grant "Geodesic currents on free groups", DMS-0603921 (2006-2009), Principal Investigator
National Security Agency research grant DMA#H98230-04-1-0115 (2004-2005), Co-Principal Investigator
U.S.-Israel Binational Science Foundation Research Grant #1999298 (2000-2002), Co-Principal Investigator
Awards and Honors
Fellow of the American Mathematical Society, 2012--
Humboldt Foundation Fellow, 2006
Highlighted 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, vol. 19, no. 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, vol. 216, no. 2, 2016, p. 753-797.
Dowdall, Spencer, Ilya Kapovich, and Christopher Leininger. "Dynamics on free-by-cyclic groups." Geometry & Topology, vol.19, no. 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, vol. 9, no. 2, 2016, p. 502-534.
Kapovich, Ilya. "Algorithmic detectability of iwip automorphisms." Bulletin of the London Mathematical Society, vol. 46, no. 2, 2014, p. 279-290.
Kapovich, Ilya, and Kasra Rafi. "On hyperbolicity of free splitting and free factor complexes." Groups, Geometry, and Dynamics, vol. 8, no. 2, 2014, p. 391-414.
Kapovich, Ilya, and Martin Lustig. "Intersection form, laminations and currents on free groups." Geometric and Functional Analysis, vol. 19, no. 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, vol. 628, 2009, p. 91–119.
Kapovich, Ilya, and Martin Lustig. "Geometric intersection number and analogues of the curve complex for free groups." Geometry & Topology, vol. 13, no. 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, vol. 223, no. 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, vol. 331, no. 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, vol. 264, no. 2, 2003, p. 665–694.
Special Issues of a Journal
A collection of articles in honor of Wolfgang Haken. (Ilya Kapovich, Christopher Leininger and Walter Neumann, Editors). Illinois Journal of MathematicsI, vol. 60, no. 1, 2016.
A collection of articles in honor of Paul Schupp. (Ilya Kapovich and Walter Neumann, Editors). Illinois Journal of Mathematics, vol. 54, no. 1, 2010.
Book Contributions
Kapovich, Ilya. "Currents on free groups." Topological and asymptotic aspects of group theory. Contemporary Mathematics, vol. 394, 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, Providence, RI: American Mathematical Society, 2002, p. 39–93.
Essays
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.