Email: demarco at math.uic.edu

Associate Professor
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
851 S. Morgan St. (MC 249)
Chicago, IL 60607-7045

Office: SEO 501
Phone: (312) 413-7691

Teaching, Fall 2011:
Calculus 1 MATH 180, MWF 1 pm, Lecture Center F4
Complex Manifolds 1 MATH 554, MWF 2 pm, Taft Hall 321

Primary research interests: Dynamical systems and complex analysis

Publications

"The geometry of the critically-periodic curves in the space of cubic polynomials," with A. Schiff.
Submitted for publication, 2011. pdf

"The classification of polynomial basins of infinity," with K. Pilgrim.
Submitted for publication, 2011. pdf

"Combinatorics and topology of the shift locus."
To appear, in Conformal Dynamics and Hyperbolic Geometry, AMS Contemporary Mathematics.
Volume in honor of Linda Keen's birthday. Preprint, 2011. pdf

"The conformal geometry of billiards," pdf
Bulletin of the AMS. 48 (2011), no. 1, 33-52.

"Critical heights on the moduli space of polynomials," with K. Pilgrim.
Advances in Mathematics. 226 (2011) 350-372. pdf

"Preperiodic points and unlikely intersections," with M. Baker.
Duke Math. Journal. 159 (2011), no. 1, 1-29. pdf

"Polynomial basins of infinity," with K. Pilgrim.
Geom. Funct. Anal. 21 (2011), no. 4, 920-950. pdf

"Hausdorffization and polynomial twists," with K. Pilgrim.
Discrete Contin. Dyn. Sys. 29 (2011), no. 4, 1405-1417.
Special issue, Trends and developments in dynamical systems, Part III. pdf

"Enumerating the basins of infinity for cubic polynomials," with A. Schiff.
J. Difference Equ. Appl. 16 (2010) 451-461.
Special issue dedicated to Robert L. Devaney. pdf

"Axiom A polynomial skew products of C^2 and their postcritical sets," with S. Lynch Hruska.
Ergodic Theory Dynam. Systems. 28 (2008) 1729-1748. pdf, Erratum

"Trees and the dynamics of polynomials," with C. McMullen.
Ann. Sci. Ecole Norm. Sup. 41 (2008) 337-383. pdf

"Finiteness for degenerate polynomials."
Holomorphic Dynamics and Renormalization: A Volume in Honour of J. Milnor's 75th birthday.
Fields Institute Communications, AMS, 53 (2008) 89-104. pdf

"Transfinite diameter and the resultant," with R. Rumely.
J. Reine Angew. Math. 611 (2007) 145-161. pdf

"The moduli space of quadratic rational maps."
Journal of the AMS. 20 (2007) 321-355. pdf.

"Iteration at the boundary of the space of rational maps."
Duke Math. Journal. 130 (2005) 169-197. pdf.

"Dimension of pluriharmonic measure and polynomial endomorphisms of C^n," with Ilia Binder.
International Math. Research Notices. 11 (2003) 613-625. pdf.

"Dynamics of rational maps: Lyapunov exponents, bifurcations, and metrics on the sphere."
Mathematische Annalen. 326 (2003) 43-73. pdf.

"Dynamics of rational maps: a positive current on the bifurcation locus."
Math. Research Letters. 8 (2001) 57-66. pdf.

"Stability of H, D, and N atoms in solid ammonia above 100K," with A. Brill and D. Crabb.
J. Chem. Phys., 108 (1998) 1423-1428.

From graduate school

Holomorphic families of rational maps: dynamics, geometry, and potential theory
Ph.D. thesis, Harvard University, 2002. pdf

"Riemannian symmetric spaces and bounded domains in C^n."
Minor thesis, Harvard University, 1999. pdf