Antun Milas
University at Albany, NY·Mathematics & Statistics
Counting problems sit at the heart of mathematics. How many ways can a number be split into smaller parts?
- Fields
Mathematics & Statistics
Physics
- Topics
representation theory
number theory
quantum topology
- Grants
- 1 known grant, through Aug 2027
What they work on
- 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.
- Study Fourier coefficients of meromorphic Jacobi forms in several variables, functions with poles that generalize modular forms, extending existing results for a single variable.
- Investigate Gukov's conjecture that Z-hat invariants (homological blocks) of plumbed 3-manifolds show higher depth quantum modularity, linking topology of 3D spaces to modular forms.
- Prove rigorous formulas for Schur indices of certain 4d N=2 superconformal field theories, guided by BPS particle counting, and apply related methods to Hilbert-Poincaré series of arc spaces.
More about the research
How many states can a physical system occupy? The answers are often packaged into "partition functions" or generating functions, whose hidden symmetries reveal deep structure. This project sits where three fields meet. Representation theory studies symmetry using linear algebra. Number theory studies modular forms, special functions on the upper half-plane that keep their shape under certain transformations. Quantum topology links quantum physics to the shapes of low-dimensional spaces. The project aims to build new tools for the arithmetic and analytic behavior of these counting functions and use them on concrete problems.
Why it matters
This is pure mathematics. Its main contribution is a new understanding of how symmetry, modular forms and the topology of three-dimensional spaces fit together through counting functions. The new classes of modular objects and rigorous formulas could eventually guide mathematicians and theoretical physicists working on quantum field theory and low-dimensional topology.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
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.
Cris Negron
University of Southern California, CA·Mathematics & Statistics·Early-career
Build rigorous mathematical realizations of topological quantum field theories whose spaces of lowest-energy states (moduli of vacua) are non-compact, using homotopical methods in representation theory.
Ron Donagi
University of Pennsylvania, PA·Mathematics & Statistics
Attack the geometric Langlands conjecture, a proposed deep link between areas of mathematics, using non-abelian Hodge theory and ideas from quantum field theory.
The school
University at Albany: 15 labs on PI Pages, $472M a year on research, 144 research doctorates a year.
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