Aaron Landesman
Harvard University, MA·Mathematics & Statistics
How often does a random whole number avoid repeated prime factors? Questions like this belong to arithmetic statistics, the study of how numbers and number-like objects behave on average.
- Fields
Mathematics & Statistics
- Topics
arithmetic statistics
number theory
function fields
- Grants
- 1 known grant, through May 2029
What they work on
- 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.
- Study Malle's conjecture, which predicts how many global field extensions have a given Galois group, using stable and unstable homology computations.
- Address the Poonen-Rains conjectures on ranks and Selmer groups of elliptic curves over function fields by combining algebraic geometry with topology and higher algebra.
- Pursue related open problems, including the Putman-Wieland conjecture, using the methods developed in this project.
More about the research
Many of the central predictions in this area are still open. This project attacks them by bringing in tools from topology, the mathematics of shapes and spaces, and from higher algebra.
Why it matters
This is basic research in pure mathematics. It aims to explain the statistical behavior of integers and related objects, such as class groups and elliptic curves, by connecting number theory with topology. Progress on these long-standing conjectures could give mathematicians new tools that link distant areas of the field.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Melanie Wood
Harvard University, MA·Mathematics & Statistics
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.
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.
Peter Patzt
University of Oklahoma, OK·Mathematics & Statistics
Study cohomological and representation stability for general linear groups and their principal congruence subgroups, which are matrix groups defined by a divisibility condition. Describe how the cohomology behaves as matrix size grows.
The school
Harvard University: 42 labs on PI Pages, $1.5B a year on research, 712 research doctorates a year.
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