Detecting quasiconvexity: Algorithmic aspects. - Ilya Kapovich (Geometric and Computational Perspectives on Infinite Groups, 1994)

Quasiconvexity and Amalgams. - Ilya Kapovich (Int. J. Algebra Comput., 1997)

The Combination Theorem and Quasiconvexity. - Ilya Kapovich (Int. J. Algebra Comput., 2001)

Generic-case complexity, decision problems in group theory and random walks - Ilya Kapovich; Alexei G. Myasnikov; Paul E. Schupp; Vladimir Shpilrain (CoRR, 2002)

Average-case complexity and decision problems in group theory - Ilya Kapovich; Alexei G. Myasnikov; Paul E. Schupp; Vladimir Shpilrain (CoRR, 2002)

Generic properties of Whitehead's Algorithm, stabilizers in Aut(Fk) and one-relator groups - Ilya Kapovich; Paul E. Schupp; Vladimir Shpilrain (CoRR, 2003)

Freely Indecomposable Groups Acting on Hyperbolic Spaces. - Ilya Kapovich; Richard Weidmann (Int. J. Algebra Comput., 2004)

The Frequency Space of a Free Group. - Ilya Kapovich (Int. J. Algebra Comput., 2005)

Foldings, Graphs of Groups and the Membership Problem. - Ilya Kapovich; Richard Weidmann; Alexei G. Myasnikov (Int. J. Algebra Comput., 2005)

Some Quantitative Aspects of Fractional Computability - Ilya Kapovich; Paul E. Schupp (CoRR, 2007)

Clusters, Currents, and Whitehead's Algorithm. - Ilya Kapovich (Exp. Math., 2007)

Musings on generic-case complexity. - Ilya Kapovich (CoRR, 2015)

A train track directed random walk on Out(Fr). - Ilya Kapovich; Catherine Pfaff (Int. J. Algebra Comput., 2015)

Cannon-Thurston fibers for iwip automorphisms of $F_N$. - Ilya Kapovich; Martin Lustig (J. Lond. Math. Soc., 2015)

Detecting Fully Irreducible Automorphisms: A Polynomial Time Algorithm. - Ilya Kapovich; Mark C. Bell (Exp. Math., 2019)

Primitivity index bounds in free groups, and the second Chebyshev function. - Ilya Kapovich; Zachary Simon (Int. J. Algebra Comput., 2023)