Research
Here is a list of my publications
Doubly sequencable groups, J. Combin. Design 32 no. 7 (2024), 371-387.
Upper Bound Residues of the Fibonacci Sequence Modulo Primes, Fibonacci Quart. 60 no. 1 (2022), 48--51.
The Distribution of Fibonacci Numbers Modulo Primes, Amer. Math. Monthly, 129 no. 1 (2022), 75--79. Joint with Stephanie Cambrea.
Permutations with a distinct divisor property, Internat. Electron. J. Algebra, 29 (2021), 1-14. Joint with N. Krylov.
On Sets Closed Under the Cross Product and a Property of the Octahedron, Amer. Math. Monthly, 127 (2020), 151-158.
Complete Generalized Fibonacci Sequences Modulo Primes, Moscow J. Comb. Number Theory, 9-1 (2020), 1-15. Joint with N.A. Krylov.
Cyclic composition operators on separable locally compact metric spaces, Topology Appl. 258 (2019), 126-141.
On the subgroup generated by solutions of Pell's equation, J. Number Theory 194 (2019), 356-371. Joint with E. Covill and N.A. Krylov.
A note on polynomial sequences modulo integers, J. Integer Sequences 22 (2019), Article 19.1.1.
Projective partitions of vector spaces, Electron. J. Linear Algebra 32 (2017), 125--130.
Loxodromes on hypersurfaces of revolution, Involve 10 (2017), no. 3, 465–472. Joint with Jacob B. & Adam D.
The correlation numerical range and trace-positive complex polynomials, Oper. Matrices 10 (2016), no. 3, 625-630. Joint with Eli B. & Jon B.
Cycle double covers of infinite planar graphs, Discuss. Math. Graph Theory 36 (2016), no. 3, 523--544.
On transitive polynomials modulo integers, Notes Number Theory Discrete Math. 22 (2016), no. 2, 23--35. Joint with Gili Rusak.
Dynamics of semigroups of linear fractional transformations, Dyn. Syst. 29 (4) (2014), 439--450.
Hypercyclic and topologically transitive semigroups of composition operators, Topology Appl. 164 (2014), 105--112.
Maximally transitive semigroups of nxn matrices, J. Math. Anal. Appl. 401 (2013), 743--753.
A Collatz-type conjecture on the set of rational numbers, J. Number Theory 132 (2012), no. 11, 2582--2594.
Dense 2-generator subsemigroups of 2x2 matrices, J. Math. Anal. Appl. 387 (2012), 103--113.
Semigroups of matrices with dense orbits, Dyn. Syst. 26 (3) (2011), 235--243.
Topologically transitive semigroup actions of real linear fractional transformations, J. Math. Anal. Appl. 368 (2010), 587--603.
Rigidity of conformally compact manifolds with the round sphere as the conformal infinity, Adv. Math. 224 (2010), 525--538. Joint with S. Dutta.
On a property of plane curves, J. Math. Anal. Appl. 361 (2010), 332--337.
Convergence of Ricci flow on R^2 to flat space, J. Geom. Anal. (2009), no. 19, 809--816. Joint with James Isenberg.
Chord theorems on graphs, Proc. Amer. Math. Soc. 137 (2009), 553--562.
A generalization of Dirichlet approximation theorem for the affine actions on real line, J. Number Theory 128 (2008), no. 5, 1146--1156.
Dirichlet problem on locally finite graphs, Discrete Appl. Math. 155 (2007), no. 18, 2496--2506.
A new arrangement inequality, J. Inequal. Pure Appl. Math. 7 (2006), no. 5, Article 162.