Research

My research focuses on combinatorial aspects of complex dynamics and their applications to topological, geometric and group theoretic problems.

Publications & Professional Activity

1. "A new partition identity coming from complex dynamics".
   (With G. Andrews)
   Ann. Comb, 9 #3, (2005), p. 245–257.
2. "A count of maximal small copies in Multibrot sets".
   (With A. Bridy)
   Nonlinearity, 18 #5, (2005), p. 1945–1953.
3. "Quadratic polynomials and combinatorics of the principal nest".
   Indiana Univ. Math. J, 54 #6, (2005), p. 1661–1695.
4. "On the Growth of Iterated Monodromy Groups".
   (With K.-U. Bux)
   Contemp. Math. 394, (2006), p. 61–76.
5. "Compositions versus cyclic compositions".
   JP J. Algebra Number Theory Appl, 12 #1, (2008), p. 41–48.
6. "Real saddle-node bifurcation from the complex viewpoint".
   (With M. Misiurewicz)
   Conf. Geom. Dyn, 12, (2008), p. 97–108.
7. "Existence of limit cycles in the repressilator equations".
   (With O. Buse and A. Kuznetsov)
   Internat. J. Bifur. Chaos Appl. Sci. Engrg, 19 #12, (2009), p. 4097–4106.
8. "Dynamical properties of the repressilator model".
   (With O. Buse and A. Kuznetsov)
   Phys. Rev. E, 81066206, (2010).
9. "A brief but historic article of Siegel".
   Notices Amer. Math. Soc. 58 #4, (2011), p. 558–566.
10. "Control of cancellations that restrain the growth of a binomial recursion".
    (With M. Aspenberg)
    Submitted.