# Laura DeMarco

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**Laura Grace DeMarco** is a professor of mathematics at [Harvard University](/source/Harvard_University), whose research concerns [dynamical systems](/source/Dynamical_system) and [complex analysis](/source/Complex_analysis).[1]

## Career

DeMarco received her Ph.D. from [Harvard University](/source/Harvard_University) in 2002 under the supervision of [Curtis T. McMullen](/source/Curtis_T._McMullen).[2] She held an NSF Postdoctoral Fellowship and was an L. E. Dickson Instructor at the [University of Chicago](/source/University_of_Chicago) from September 2002 to August 2005. She was also an assistant professor at the [University of Chicago](/source/University_of_Chicago), and then she moved to the [University of Illinois at Chicago](/source/University_of_Illinois_at_Chicago),[3] where she was tenured and promoted to professor. She moved to [Northwestern University](/source/Northwestern_University) in 2014,[4] and was promoted to Henry S. Noyes Professor of Mathematics in 2019, before she moved to [Harvard University](/source/Harvard_University) in 2020.[5] She has been appointed the [Hollis Professor of Mathematicks and Natural Philosophy](/source/Hollis_Chair_of_Mathematicks_and_Natural_Philosophy) as of 2026 [6]

DeMarco is an organizer of GROW (Graduate Research Opportunities for Women) [undergraduate](/source/Undergraduate) conference.[7]

## Awards and honors

In 2013, DeMarco became a fellow of the [American Mathematical Society](/source/American_Mathematical_Society) in the inaugural class of fellows.[8] In 2017, she received the AMS [Ruth Lyttle Satter Prize in Mathematics](/source/Ruth_Lyttle_Satter_Prize_in_Mathematics) in Mathematics for her contributions to [complex dynamics](/source/Complex_dynamics), [potential theory](/source/Potential_theory), and the emerging field of [arithmetic dynamics](/source/Arithmetic_dynamics).[9] In 2020, DeMarco was elected a member of the [National Academy of Sciences](/source/National_Academy_of_Sciences).[10]

She was an invited speaker at the 2018 [International Congress of Mathematicians](/source/International_Congress_of_Mathematicians), speaking in the section on [Dynamical Systems](/source/Dynamical_system) and Ordinary Differential Equations.[11][12] She is the 2023 [AWM-AMS Emmy Noether Lecturer](/source/Noether_Lecture) in recognition of her "fundamental and influential contributions to complex dynamics, arithmetic dynamics, and arithmetic geometry."[13]

Her work with [Holly Krieger](/source/Holly_Krieger) and Hexi Ye, "Uniform Manin–Mumford for a family of genus 2 curves", published in the *[Annals of Mathematics](/source/Annals_of_Mathematics)*, won the 2020 Alexanderson Award of the [American Institute of Mathematics](/source/American_Institute_of_Mathematics).[14]

## Research

DeMarco's research involves algebraic, [arithmetic](/source/Arithmetic_dynamics) and [complex dynamics](/source/Complex_dynamics) with an emphasis on their interactions with each other. She has studied dynamically meaningful [compactifications](/source/Compactification_(mathematics)) of the [moduli space](/source/Moduli_space) of [rational maps](/source/Rational_function) on \mathbb{P}^1. [15] [16] In joint work with [Curtis McMullen](/source/Curtis_McMullen), she showed how [simplicial](/source/Simplicial_complex) [metrized](/source/Metric_space) [trees](/source/Tree_(graph_theory)) can be used to compactify the moduli space of [polynomials](/source/Polynomials). [17] Together with Xander Faber, DeMarco has studied degenerations of complex dynamical systems from the viewpoint of [Berkovich spaces](/source/Berkovich_space). [18]

With Matthew Baker, DeMarco pioneered the study of [unlikely intersections](/source/Zilber-Pink_conjecture) in arithmetic dynamics [19] and formulated the dynamical [André-Oort conjecture](/source/Andr%C3%A9-Oort_conjecture). [20] Together with [Holly Krieger](/source/Holly_Krieger) and Hexi Ye, DeMarco proved the first instances of the uniform dynamical [Manin-Mumford conjecture](/source/Manin-Mumford_conjecture) for [Lattès maps](/source/Latt%C3%A8s_map) [21] and for [quadratic unicritical polynomials](/source/Complex_quadratic_polynomial). [22] In collaboration with Niki Myrto Mavraki, DeMarco studied the notion of non-degeneracy for polarized dynamical systems and its relation to stability. [23] Later with Niki Myrto Mavraki and Hexi Ye, DeMarco proved a uniform version of the dynamical André-Oort conjecture. [24]

## Further reading

- Hartnett, Kevin (3 January 2017), ["3-D Fractals Offer Clues to Complex Systems"](https://www.quantamagazine.org/20170103-fractal-dynamics-from-3d-julia-sets/), *[Quanta Magazine](/source/Quanta_Magazine)*

## References

1. [Laura DeMarco Home Page at Harvard](http://people.math.harvard.edu/~demarco/)

1. ["Laura DeMarco"](http://www.nasonline.org/member-directory/members/20049441.html). *www.nasonline.org*. Retrieved 2020-11-06.

1. ["2017 Ruth Lyttle Satter Prize"](https://www.ams.org/journals/notices/201704/rnoti-p316.pdf). *Notices of the AMS*. **64**: 316.

1. ["Math Department announces three new faculty members"](https://news.harvard.edu/gazette/story/2020/06/math-department-announces-three-new-faculty-members/). *Harvard Gazette*. 2020-06-23. Retrieved 2020-08-12.

1. [https://www.math.harvard.edu/laura-demarco-appointed-hollis-professor-of-mathematicks-and-natural-philosophy/](https://www.math.harvard.edu/laura-demarco-appointed-hollis-professor-of-mathematicks-and-natural-philosophy/)

1. ["Graduate Research Opportunities for Women 2020 | Department of Mathematics | The University of Chicago"](https://mathematics.uchicago.edu/grow2020/). *mathematics.uchicago.edu*. Retrieved 2020-10-27.

1. [List of Fellows of the American Mathematical Society](https://www.ams.org/profession/fellows-list)

1. [Ruth Lyttle Satter Prize 2017](https://www.ams.org/news?news_id=3222)

1. ["NAS Election 2020"](http://www.nasonline.org/news-and-multimedia/news/2020-nas-election.html)

1. ["Speakers"](https://web.archive.org/web/20171215001530/http://www.icm2018.org/portal/en/icm-speakers), *ICM 2018*, archived from [the original](http://www.icm2018.org/portal/en/icm-speakers) on 2017-12-15, retrieved 2018-02-24

1. [Laura DeMarco](https://www.youtube.com/HClk4YiDRns) on YouTube

1. ["2023 AWM-AMS Emmy Noether Lecture"](https://awm-math.org/2023-awm-ams-emmy-noether-lecture/). 26 April 2022.

1. ["Alexanderson Award 2020"](https://aimath.org/anderson-award-2020/), American Institute of Mathematics, retrieved November 17, 2020

1. "Iteration at the boundary of the pace of rational maps". *Duke Mathematical Journal*. '***(130): 607-637. 2005.***

1. "The moduli space of quadratic rational maps". *Journal of the American Mathematical Society*. '***(20): 321-355. 2007.***

1. "Trees and the dynamics of polynomials". *Annales Scientifique de l'ENS*. '***(41): 337-383. 2008.***

1. "Degenerations of Complex Dynamical Systems". *Forum of Mathematics Sigma*. '***(2): 36. 2014.***

1. "Preperiodic points and unlikely intersections". *Duke Mathematical Journal*. '***(159(1)): 1-29. 2011.***

1. "Special curves and post-critically finite curves". *Forum of Mathematics Pi*. '***(1): 35. 2013.***

1. "Uniform Manin-Mumford for a family of genus 2 curves". *Annals of Mathematics*. '***(191(3)): 949-1001. 2020.***

1. "Common preperiodic points for quadratic polynomials". *Journal of Modern Dynamics*. '***(18): 363-413. 2022.***

1. "Dynamics on \mathbb{P}^1: preperiodic points and pairwise stability". *Compositio Mathematica*. '***(160(2)): 356-387. 2024.***

1. ["Bounded geometry for PCF-special subvarieties"](https://arxiv.org/abs/2405.17343). 2024.

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