** Email: ** demarco at northwestern dot edu

Professor

Department of Mathematics

Northwestern University

2033 Sheridan Road

Evanston, IL 60208-2730

** Office: ** Lunt 304

** Primary research interests: **

Dynamical systems, complex analysis, arithmetic geometry

CV, updated January 2019.

** Teaching, Spring 2018: **

Math 354 Chaotic Dynamical Systems

MWF 2-2:50pm, Tech F281

Complex/Arithmetic Dynamics informal seminar

Midwest Dynamical Systems Conferences

** Preprints **

Uniform Manin-Mumford for a family of genus 2 curves, with H. Krieger and H. Ye.

Preprint, 44 pages. pdf

A uniform bound on the number of common preperiodic points of quadratic polynomials, with H. Krieger and H. Ye.

In preparation; draft available upon request. Abstract

** Publications **

Critical orbits and arithmetic equidistribution.

Proceedings of the ICM 2018, 19 pages. pdf

Variation of canonical height and equidistribution, with N.M. Mavraki.

To appear, *American J. Math.*, 34 pages. pdf

On the postcritical set of a rational map, with S. Koch and C.T. McMullen.

To appear, *Math. Annalen*, 21 pages. pdf

Rationality of dynamical canonical height, with D. Ghioca.

To appear, *Ergodic Theory Dynamical Systems*, 35 pages. pdf

Bounded height in families of dynamical systems,

with D. Ghioca, H. Krieger, K.D. Nguyen, T.J. Tucker, and H. Ye.

To appear, *Int. Math. Res. Notices*, 25 pages. pdf

Discontinuity of a degenerating escape rate, with Y. Okuyama.

* Conform. Geom. Dyn.* **22** (2018), 33-44. pdf

KAWA Lecture Notes: Dynamical moduli spaces and elliptic curves.

*Ann. Fac. Sci. Toulouse Math.* **27** (2018), 389-420.
pdf

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

*Ann. Sci. Ecole Norm. Sup.* **50** (2017), 799-877. pdf

Convex shapes and harmonic caps, with K. Lindsey.

*Arnold Math. J.*, **3** (2017), 97-117. Special volume for 25th anniversary of IMS. pdf

Bifurcations, intersections, and heights.

*Algebra & Number Theory*, **10** (2016), 1031-1056. pdf

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

with Xander Faber and an Appendix by Jan Kiwi.

*Math. Ann.*, **365** (2016), 1669-1699. pdf

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

*American J. of Math.*, **138** (2016), no. 3, 697-732. pdf

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

*Proc. London Math. Soc.*, **111** (2015), no. 1, 149-180. pdf

Degenerations of complex dynamical systems, with Xander Faber.

*Forum of Mathematics, Sigma*. **2** (2014), e6, 36 pages. Available from the publisher

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

*Forum of Mathematics, Pi*. **1** (2013), e3, 35 pages. Available from the publisher

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.