Research
Geometric deep learning
I study:
- identifiability, expressivity, and the algebraic geometry of equivariant architectures
- trade-off between imposed equivariance and equivariance learned from data.
In a recent preprint, I show that there is in general impossible to polynomially constrain attention to express all equivariant maps expressible by the respective unconstrained attention layer, and nothing else.
Foundations of density functional theory
I’m also a mathematical physicist. I work on mathematical generalizations of density functional theory, with emphasis on the geometric aspects. A question that keeps me awake at night:
- In a generalized density functional theory, when the quantities we measure don’t commute but form a Lie algebra, Kirwan’s theorem says that the image of the density map still intersects a positive Weyl chamber in a convex polytope. What does this imply for the ground state physics described by that density functional theory?
Where I want to go next
I am looking for a PhD position in geometric deep learning, in a group that treats the mathematics as part of the work. Similarly, I’d also be interested in groups working on machine learning for the physical sciences.