Email: demarco at uic dot edu

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
Office Hours: Mondays 1-3 pm

Teaching, Spring 2013:
Complex Analysis MATH 535
MWF 11 am

Upcoming events
Conference, June 5-7, 2013, here at UIC: Complex Dynamics (and Arithmetic Geometry)
AMS Math Research Community, June 9-15, 2013, Snowbird, Utah. Description (pdf).

Primary research interests: Dynamical systems and complex analysis.
CV, updated May 2013.
Here is a movie of the bifurcation locus in Per_1(A), inside the space of quadratic rational maps with marked critical points, as the multiplier A moves along a curve from A=2 to A=-4. The picture below is for A = 1.1 i. All images were generated with Dynamics Explorer, a program developed by Suzanne and Brian Boyd.

Publications

Degenerations of complex dynamical systems, with Xander Faber.
Submitted for publication, February 2013. pdf

Critical bifurcation measures on curves, with Xiaoguang Wang and Hexi Ye.
In preparation, 2013.

Profinite groups and polynomial basins of infinity, with Kevin Pilgrim.
In preparation, 2013.

Special curves and postcritically-finite polynomials, with M. Baker.
Submitted for publication, 2012. pdf
Slides (pdf, 4.2 MB) from AMS Invited Address at Joint Meetings, January 2013.

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

The geometry of the critically-periodic curves in the space of cubic polynomials, with A. Schiff.
To appear, Experimental Math. 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