The (algebraic) geometry of preperiodic points in P^N, in three lectures.
Lecture notes from CIRM France, January 2025. pdf
Bounded geometry for PCF-special subvarieties, with N. M. Mavraki and H. Ye.
To appear, Forum of Mathematics, Pi. arxiv
The geometry of preperiodic points in families of maps on P^N, with N. M. Mavraki.
To appear, L'Enseignement Mathematique. arxiv
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.
Alg. Number Th. 19 (2025), 2163-2183. arxiv
Elliptic surfaces and intersections of adelic R-divisors, with N. M. Mavraki.
J. Eur. Math. Soc. 26 (2024), 3639-3684. arxiv
Dynamics on P^1: preperiodic points and pairwise stability, with N. M. Mavraki.
Compositio Math., 160 (2024), no. 2, 356-387. arxiv
Variation of canonical height for Fatou points on P^1, with N. M. Mavraki.
J. Reine Angew. Math. (Crelle), 795 (2023), 183–220. arxiv
Common preperiodic points for quadratic polynomials, with H. Krieger and H. Ye.
Journal of Modern Dynamics, 18 (2022), 363-413. arxiv
Uniform Manin-Mumford for a family of genus 2 curves, with H. Krieger and H. Ye.
Annals of Math., 191 (2020), 949-1001. arxiv
Variation of canonical height and equidistribution, with N. M. Mavraki.
American J. Math., 142 (2020), 443-473. arxiv
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. arxiv
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. arxiv
Discontinuity of a degenerating escape rate, with Y. Okuyama.
Conform. Geom. Dyn. 22 (2018), 33-44. arxiv
KAWA Lecture Notes: Dynamical moduli spaces and elliptic curves.
Ann. Fac. Sci. Toulouse Math. 27 (2018), 389-420.
arxiv
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. arxiv
Bifurcations, intersections, and heights.
Algebra & Number Theory, 10 (2016), 1031-1056. arxiv
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. arxiv
Torsion points and the Lattes family, with X. Wang and H. Ye.
American J. of Math., 138 (2016), no. 3, 697-732. arxiv
Bifurcation measures and quadratic rational maps, with X. Wang and H. Ye.
Proc. London Math. Soc., 111 (2015), no. 1, 149-180. arxiv
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.
arxiv
The conformal geometry of billiards.
Bulletin of the AMS. 48 (2011), no. 1, 33-52.
pdf
Critical heights on the moduli space of polynomials, with K. Pilgrim.
Advances in Mathematics. 226 (2011) 350-372.
arxiv
Preperiodic points and unlikely intersections, with M. Baker.
Duke Math. Journal. 159 (2011), no. 1, 1-29. arxiv
Polynomial basins of infinity, with K. Pilgrim.
Geom. Funct. Anal. 21 (2011), no. 4, 920-950. arxiv
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. arxiv
Axiom A polynomial skew products of C^2 and their postcritical sets,
with S. Lynch Hruska.
Ergodic Theory Dynam. Systems. 28 (2008) 1729-1748.
arxiv, Erratum
Trees and the dynamics of polynomials, with C. T. McMullen.
Ann. Sci. Ecole Norm. Sup. 41 (2008) 337-383.
arxiv
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.
arxiv
Transfinite diameter and the resultant, with R. Rumely.
J. Reine Angew. Math. (Crelle). 611 (2007) 145-161.
arxiv
The boundary of the moduli space of quadratic rational maps.
Journal of the AMS. 20 (2007) 321-355.
arxiv
Iteration at the boundary of the space of rational maps.
Duke Math. Journal. 130 (2005) 169-197.
arxiv
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
Laura DeMarco
