**Iterations of Polynomial Maps, with Applications to Group Theory:**

Geometrically Nilpotent Subvarieties. * Finite Fields Appl.* ** 50** (2018), 366--371.

Iterations of Integer Polynomial Maps Modulo Primes. *J. Integer Sequences* ** 16 ** (2013), no. 8, Article 13.8.3.

Polynomial maps over p-adics and residual properties of mapping tori of group endomorphisms (with M. Sapir). * Int. Math. Res. Not. IMRN * ** (2009) ** no.16, 3002--3015.

Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms (with M. Sapir). *Inventiones Math. * ** 160 ** (2005) no.2, 341--356.

**Toric Varieties and Lattice Polytopes:**

On the log discrepancies in Mori contractions (with Valery Alexeev). *Proc. Amer. Math. Soc.* ** 142 ** (2014), no. 11, 3687--3694.

On Empty Lattice Simplices in Dimension 4 (with Margherita Barile, Dominique Bernardi, and Jean-Michel Kantor). * Proc. Amer. Math. Soc. * ** 139 ** (2011), no. 12, 4247--4253.

Quotient singularities, integer ratios of factorials and the Riemann Hypothesis. *Int. Math. Res. Not. IMRN * ** 2008 ** (2005) no.15, Art. ID rnn052.

Directional rational approximations with some applications to algebraic geometry (with V.V. Shokurov). [Russian]* Tr. Mat. Inst. Steklova * ** 240 ** (2003), Biratsion. Geom. Linein. Sist. Konechno Porozhdennye Algebry, 73--81; translation in * Proc. Steklov Inst. Math.* 2003, no. 1 (240), 66--74.

Convex lattice polytopes and cones with few lattice points inside, from a birational geometry viewpoint.
Preprint (1999).

On classification of toric singularities. Algebraic Geometry. 9. *J. Math. Sci. (New York)* **94 **(1999), no. 1, 1111--1113.

Minimal discrepancies of toric singularities. *Manuscripta Math.* **92 **(1997), no. 1, 33--45.

Singular toric Fano varieties (with Lev Borisov). [Russian] * Mat. Sbornik* ** 183** (1992), no. 2, 134--141; translation in * Russian Acad. Sci. Sb. Math.* ** 75** (1993), no. 1, 277--283.

**Two-dimensional Jacobian Conjecture and Related Topics:**

Frameworks for Two-dimensional Keller Maps. * Electronic Journal of Combinatorics * ** 27 (3) ** (2020), 3.54.

On the Stein factorization of resolutions of two-dimensional Keller maps. * Beitr. Algebra Geom. * ** 56 ** (2015), no. 1, 299--312.

On two invariants of divisorial valuations at infinity. * J. Algebraic Combinatorics* ** 39 ** (2014), no. 3, 691--710.

On Resolution of Compactifications of Unramified Planar Self-maps. Preprint (2011-12). Unpolished, will not be submitted.

**Applications of Harmonic Analysis to Number Theory:**

Positive positive-definite functions and measures on locally compact abelian groups. Preprint (1999).

Convolution structures and arithmetic cohomology. *Compositio Math.* **136** (2003), no. 3, 237--254.

**Fano Varieties:**

Boundedness of Fano threefolds with log-terminal singularities of given index. *J. Math. Sci. Univ. Tokyo* **8** (2001), no. 2, 329--342.

Boundedness theorem for Fano log-threefolds. * J. Algebraic Geom.* **5 **(1996), no. 1, 119--133.

**Rational Polynomials:**

Corrigendum to "Quantum integers and cyclotomy'' [J. Number Theory 109 (1) (2004) 120–135] [MR2098480]. *J. Number Theory* ** 145 ** (2014), 632--634.

Quantum integers and cyclotomy (with Melvyn Nathanson and Yang Wang). * J. Number Theory * ** 109 ** (2004), no. 1, 120--135.

On a Question of Craven and a Theorem of Belyi. *Proc. Amer. Math. Soc.* ** 131 ** (2003), no. 12, 3677--3679.

Classes of polynomials having only one non-cyclotomic
irreducible factor (with M.
Filaseta, T.-Y. Lam, and O. Trifonov). *Acta Arithmetica* **90 **(1999), no. 2, 121--153.

On some polynomials allegedly related to the abc conjecture. *Acta Arithmetica*, **84 **(1998), no. 2, 109--128.

**Miscellaneous:**

A congruence Problem for Polyhedra (with Mark Dickinson and Stuart Hastings) *Amer. Math. Monthly* ** 131** (2010) 232--249.