Broadly I am interested in the calculus of variations, functional analysis, PDEs and probability and how these areas interact. I am currently reading about Free Probability and Noncommutative Optimal Transport. More specifically I am interested in:
Optimal transport
Sliced Wasserstein metrics - particularly intrinsic and extrinsic geodesics in these spaces since I discovered some of them like this one -->
Non-commutative optimal transport and other generalizations of calculus of variations to operator algebras
Connections of the above to the quantum setting (particularly quantum informationa and quantum computing)
Recent Papers
John Hopper, Sliced Wasserstein Geodesics and Equivalence Wasserstein and Sliced Wasserstein metrics, arXiv (2024).
(arXiv link)
Araiza et al., White Paper: “Non-commutative Optimal Transport”, ipam reports and white papers (2025).
(link)
Talks and Posters
GPOTS 2026 talk, "Optimal control in noncommutative laws"
FoCM 2026 poster, "Sliced Wasserstein Geodesics and Metric equivalence"
Sliced Wasserstein metrics - particularly intrinsic and extrinsic geodesics in these spaces since I discovered some of them like this one -->
