Ken Ono
University of Virginia, VA·Mathematics & Statistics
About a century ago, the self-taught mathematician Ramanujan recorded strange functions and insights that still fascinate mathematicians. Recent evidence suggests his ideas are connected to the mathematics behind Einstein's general relativity, the theory that underpins GPS.
- Fields
Mathematics & Statistics
Physics
- Topics
number theory
harmonic Maass forms
modular forms
- Grants
- 1 known grant, through Jun 2027
What they work on
- 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.
- Apply harmonic Maass form methods to arithmetic statistics questions, including the ranks of elliptic curves and torsion in class groups of number fields.
- Study how Fourier coefficients of modular forms are distributed, using the theory of harmonic Maass forms.
- Clarify the relationship between monstrous and umbral moonshine, which link special functions to symmetry groups, and determine its consequences for mathematical physics.
More about the research
This project aims to develop the theory behind that connection. It also aims to lay groundwork for future uses in mathematics, signal processing and physics.
Why it matters
This is basic mathematics. It adds tools for understanding how number-theoretic objects such as elliptic curves and class groups behave statistically. It also clarifies the link between Ramanujan's mock theta functions, moonshine and theoretical physics. According to the project, this foundation could eventually inform applications in signal processing and physics.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Antun Milas
University at Albany, NY·Mathematics & Statistics
Introduce and develop higher depth false and quantum modular forms, extensions of Zagier's quantum modular forms, to describe characters of vertex algebras that show higher depth behavior.
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.
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
University of Virginia: 43 labs on PI Pages, $814M a year on research, 413 research doctorates a year.
Reach out
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