** 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

Events and seminars in the Harvard math department

** Teaching, Spring 2021 **

Math 295: Arithmetic Dynamics

MW 1:30-2:45 pm on Zoom

Begins Monday, January 25, 2021

** Upcoming conferences that I am organizing: **

Simons Symposium in Complex and Arithmetic Dynamics, Scotland, April 2-8, 2021

VIII Iberoamerican Congress on Geometry in Morelia, Mexico

POSTPONED, new dates TBA

Circle at Infinity: Celebrating the mathematics of Curtis T. McMullen, Harvard University

POSTPONED, new dates TBA

Midwest Dynamical Systems Conferences

To celebrate 50 years of Midwest Dynamics conferences, Northwestern University

POSTPONED, new dates TBA

Oberwolfach Workshop Diophantische Approximationen

POSTPONED, new dates TBA

** Preprints **

Elliptic surfaces and arithmetic equidistribution for R-divisors on curves, with N. M. Mavraki.

Preprint, 46 pages. pdf

Common preperiodic points for quadratic polynomials, with H. Krieger and H. Ye.

Preprint, 50 pages. pdf

** Publications **

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 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.