


Welcome to my page.
LD224R
Dept. of Math. Sci.
I U P U I
Indianapolis, IN 46202
(317) 2786977




I am an associate professor at IUPUI.
My research focuses on combinatorial aspects of complex dynamics
and their applications to topological, geometric and group theoretic
problems.
 Teaching.
 Publications:

"A new partition identity coming from complex
dynamics".
(With G. Andrews)
Ann. Comb,
9 #3, (2005),
pp. 245–257.

"A count of maximal small copies in Multibrot
sets".
(With A. Bridy)
Nonlinearity,
18 #5, (2005),
pp. 1945–1953.

"Quadratic polynomials and combinatorics of the
principal nest".
Indiana Univ. Math. J,
54 #6, (2005),
pp. 1661–1695.

"On the Growth of Iterated Monodromy
Groups".
(With K.U. Bux)
Contemp. Math. 394,
(2006),
pp. 61–76.

"Compositions versus cyclic
compositions".
JP J. Algebra Number Theory Appl,
12 #1, (2008),
pp. 41–48.

"Real saddlenode bifurcation from the complex
viewpoint".
(With M. Misiurewicz)
Conf. Geom. Dyn,
12, (2008),
pp. 97–108.

"Existence of limit cycles in the repressilator
equations".
(With O. Buse and A. Kuznetsov)
Internat. J. Bifur. Chaos Appl. Sci. Engrg,
19 #12, (2009),
pp. 4097–4106.

"Dynamical properties of the repressilator
model".
(With O. Buse and A. Kuznetsov)
Phys. Rev. E,
81 066206, (2010).

"A brief but historic article of
Siegel".
Notices Amer. Math. Soc.
58 #4, (2011),
pp. 558–566.
 Book review:
"Early Days in Complex Dynamics: a History of Complex Dynamics in One Variable During 1906–1942"
(by D. S. Alexander, F. Iavernaro and A. Rosa)
Bull. Amer. Math. Soc. (N.S.),
50 #3, (2013),
pp. 503–511.

"Control of cancellations that restrain the growth
of a binomial recursion".
(With M. Aspenberg)
J. Geom. Anal.
Accepted.

"Examples of Rational Maps of CP^2 with Equal
Dynamical Degrees and No Invariant
Foliation".
(With S. Kaschner and R. Roeder)
Submitted.
 