Laura DeMarco
Harvard University, MA·Mathematics & Statistics
Apply a simple rule over and over, and the results can either settle into order or scatter unpredictably. Systems built this way — repeated application of an algebraic rule — appear across science and technology, and a basic challenge is telling the two outcomes apart: when does a system hide extra structure, and when is its behavior essentially chaotic?
- Fields
Mathematics & Statistics
- Topics
algebraic dynamics
arithmetic dynamics
dynamical systems
- Grants
- 1 known grant, through Jul 2028
What they work on
- Characterize the special subvarieties — geometric pieces preserved by the map — that arise in families of dynamical systems built from endomorphisms of algebraic varieties, aiming at a general classification within a unifying conjectural framework.
- Develop the theory of generalized bifurcation currents, objects that record where a family's behavior becomes unstable, and establish criteria determining when such currents are positive.
- Obtain effective and uniform bounds controlling special loci and the geometry of periodic points, advancing dynamical analogues of the Manin–Mumford and André–Oort conjectures.
- Extend these methods to non-archimedean and p-adic settings using non-archimedean analysis, and build computational and algorithmic tools that yield explicit examples and quantitative bounds.
More about the research
This project develops mathematics to detect and describe those hidden structures, working where geometry, number theory, and dynamical systems meet.
Why it matters
This is foundational mathematics: it sharpens our understanding of when iterated algebraic processes are rigid and structured rather than chaotic, and it attacks long-standing open conjectures linking arithmetic and geometry. The effective and algorithmic bounds sought here would make such questions computable in concrete examples, and the underlying concepts belong to the mathematical groundwork used across modern computational and data-driven methods.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Ananth Shankar
Northwestern University, IL·Mathematics & Statistics·Early-career
Construct and study integral models of exceptional Shimura varieties, that is, descriptions by polynomial equations with whole-number coefficients for the varieties attached to exceptional symmetry groups.
John Lesieutre
Pennsylvania State University, PA·Mathematics & Statistics·Early-career
Study lower bounds on how fast the degrees of repeated rational maps grow, using methods from the Sarkisov program, a way of decomposing geometric transformations into simpler steps.
Claudio Gonzales
Carleton College, MN·Mathematics & Statistics
Advance the framework of "special points" using polar cones, geometric objects encoding convexity data, to sharpen bounds on the resolvent degree of finite groups and address related arithmetic questions.
The school
Harvard University: 42 labs on PI Pages, $1.5B a year on research, 712 research doctorates a year.
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