Melanie Wood
Harvard University, MA·Mathematics & Statistics
Some of the hardest questions in pure mathematics ask what happens on average when mathematical objects are chosen at random. The work recognized by this award sits at the interface of number theory, the study of whole numbers; algebraic geometry, the study of shapes defined by equations; topology, which studies properties of shapes preserved under stretching; and probability.
- Fields
Mathematics & Statistics
- Topics
number theory
algebraic geometry
topology
- Grants
- 1 known grant, through Aug 2027
What they work on
- Develop a nonabelian analogue of the Cohen-Lenstra heuristics, replacing class groups with Galois groups that encode symmetries of nonabelian extensions of a varying number field.
- Establish results on random matrices, random graphs and random sandpiles, models of randomly chosen algebraic and combinatorial structures, with expected downstream use in physics and statistics.
- Prove, and where appropriate disprove, conjectures and widely believed statements at the interface of number theory, algebraic geometry, topology and probability.
- Advance the understanding of quadratic forms, expressions built from squared and cross terms, including cases with arbitrarily strange coefficients.
More about the research
The award cites fundamental contributions across these areas, including deep results on random matrices and the proving, and in some cases disproving, of conjectures and widely believed statements.
Why it matters
This is foundational mathematics. It sharpens what is known about how number systems, their symmetries, and random discrete structures are distributed, and settles questions that had only been conjectured. The results on random matrices, random graphs and random sandpiles are expected to have downstream applications in physics and statistics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Aaron Landesman
Harvard University, MA·Mathematics & Statistics
Make progress on the Cohen-Lenstra conjectures about class groups of quadratic fields over function fields by computing relevant homology groups with new topological tools.
Ken Ono
University of Virginia, VA·Mathematics & Statistics
Develop algebraic, analytic and combinatorial tools for harmonic Maass forms, generalizations of modular forms that underlie Ramanujan's mock theta functions, for attacking open problems in number theory.
Frank Thorne
University of South Carolina-Columbia, SC·Mathematics & Statistics
Carry out finite Fourier transform computations for families of arithmetic objects, extending approaches the PI and collaborators have previously developed in arithmetic statistics.
The school
Harvard University: 42 labs on PI Pages, $1.5B a year on research, 712 research doctorates a year.
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