Email: demarco at northwestern dot edu
Department of Mathematics
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
Department Seminar Calendar
Complex/Arithmetic Dynamics informal seminar
Midwest Dynamical Systems Conferences
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
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.
J. Difference Equ. Appl. 16 (2010) 451-461.
Special issue dedicated to Robert L. Devaney. pdf
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.