Email: demarco at math dot harvard dot edu

Professor of Mathematics
Radcliffe Alumnae Professor at the Radcliffe Institute for Advanced Study
Department of Mathematics
Harvard University
1 Oxford Street
Cambridge, MA 02138

Office: Science Center 337

Primary research interests:
Dynamical systems, arithmetic geometry, and complex analysis
CV (short version), updated October 2023.

Algebraic Dynamics Seminar

Events and seminars in the Harvard math department

Upcoming events:

Hamilton Day, Royal Irish Academy
Dublin, Ireland, October 16, 2024.

Algebra and Number Theory Day
Johns Hopkins University, Maryland, November 23, 2024.

Arithmetic, Algebraic, and Analytic Dynamics
CIRM, Luminy, France, January 20-24, 2025.

DeLong Lectures
University of Colorado, Boulder, February 2025.

Bloomington Geometry Workshop
Indiana University, Bloomington, April 2025.

University of Waterloo Women in Mathematics Day
Waterloo, Canada, May 2025.

Workshop on Model Theory, Algebraic Dynamics, and Differential-Algebraic Geometry
Fields Institute, Toronto, June 16-20, 2025.

Diophantine approximation and transcendence
CIRM, Luminy, France, November 10-14, 2025.

Publications and Preprints

The geometry of preperiodic points in families of maps on P^N, with N. M. Mavraki.
Preprint, August 2024, 27 pages. pdf

Bounded geometry for PCF-special subvarieties, with N. M. Mavraki and H. Ye.
Preprint, revised August 2024, 30 pages. pdf

Multiplier spectrum of maps on P^1: theorems of Ji-Xie and Ji-Xie-Zhang, with N. M. Mavraki.
Notes, revised April 2024, 12 pages. pdf

Geometry of PCF parameters in spaces of quadratic polynomials, with N. M. Mavraki.
Preprint, revised Sept 2024, 24 pages. pdf

Dynamics on P^1: preperiodic points and pairwise stability, with N. M. Mavraki.
Compositio Math., 160 (2024), no. 2, 356-387. pdf

Elliptic surfaces and intersections of adelic R-divisors, with N. M. Mavraki.
To appear, J. Eur. Math. Soc., 48 pages. pdf

Variation of canonical height for Fatou points on P^1, with N. M. Mavraki.
J. Reine Angew. Math. (Crelle), 795 (2023), 183–220. pdf

Common preperiodic points for quadratic polynomials, with H. Krieger and H. Ye.
Journal of Modern Dynamics, 18 (2022), 363-413. pdf



Uniform Manin-Mumford for a family of genus 2 curves, with H. Krieger and H. Ye.
Annals of Math., 191 (2020), 949-1001. pdf

Variation of canonical height and equidistribution, with N. M. Mavraki.
American J. Math., 142 (2020), 443-473. pdf

On the postcritical set of a rational map, with S. Koch and C. T. McMullen.
Math. Annalen, 377 (2020), 1-18. pdf

Critical orbits and arithmetic equidistribution.
Proceedings of the ICM 2018, Vol III, 1867-1886. pdf

Rationality of dynamical canonical height, with D. Ghioca.
Ergodic Theory Dynam. Systems, 9 (2019), 2507-2540. pdf

Bounded height in families of dynamical systems,
with D. Ghioca, H. Krieger, K. D. Nguyen, T. J. Tucker, and H. Ye.
Int. Math. Res. Notices, 8 (2019), 2453-2482. 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 X. Faber and an Appendix by J. Kiwi.
Math. Ann., 365 (2016), 1669-1699. pdf

Torsion points and the Lattes family, with X. Wang and H. Ye.
American J. of Math., 138 (2016), no. 3, 697-732. pdf

Bifurcation measures and quadratic rational maps, with X. Wang and H. Ye.
Proc. London Math. Soc., 111 (2015), no. 1, 149-180. pdf

Degenerations of complex dynamical systems, with X. 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. T. 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. (Crelle). 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.

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