** Email: ** demarco at math dot northwestern dot edu

** Beginning September 1, 2014, I will be Professor at Northwestern University. **

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

** Primary research interests: ** Dynamical systems and complex
analysis.

CV, updated August 9, 2014.

** Preprints **

Bifurcation measures and quadratic rational maps, with Xiaoguang Wang and Hexi Ye.

Preprint, 2014, 35 pages. pdf

Torsion points and the Lattes family, with Xiaoguang Wang and Hexi Ye.

Submitted for publication, 2013, 30 pages. pdf (revised April 2014)

Degenerations of complex dynamical systems II: Analytic and algebraic stability,

with Xander Faber. Submitted for publication, 2013, 22 pages. pdf

The classification of polynomial basins of infinity, with K. Pilgrim.

Submitted for publication, 2012, 68 pages. pdf

** Publications **

Degenerations of complex dynamical systems, with Xander Faber.

To appear, *Forum of Mathematics, Sigma*. pdf

Special curves and postcritically-finite polynomials, with M. Baker.

*Forum of Mathematics, Pi*. **1** (2013), e3, 35 pages. pdf

Slides (pdf, 3.3 MB) from AMS Invited Address
at Joint Meetings, January 2013.

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

*Experimental Math.* **22** (2013), no. 1, 99-111. pdf

Combinatorics and topology of the shift locus.

*Conformal Dynamics and Hyperbolic Geometry,* AMS Contemporary Mathematics.

Volume in honor of Linda Keen's birthday. ** 573** (2012) 35-48.
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., Ser. A.* **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. Available upon request.