Metric Geometry of Spaces of Persistence Diagrams
Explore metric geometry of persistence diagram spaces, focusing on synthetic curvature bounds and applications in non-smooth, infinite-dimensional contexts.
Non-commutative Optimal Transport - Spring 2025
Explore non-commutative optimal transport's applications in AI, quantum physics, and electronic structure theory. Delve into evolution equations, Wasserstein distances, and computational algorithms for density operators.
Supervised Quantile Normalization for Matrix Factorization Using Optimal Transport
Explore advanced matrix factorization techniques using optimal transport for quantile normalization. Learn applications in dimensionality reduction and genomics from expert Marco Cuturi.
Geometry of Covariance Matrices, Covariance Operators, and Gaussian Processes
Explore geometric approaches to covariance matrices, operators, and Gaussian processes. Gain insights into non-Euclidean distances, Fisher-Rao distance, and Wasserstein distance in infinite-dimensional settings.
DeepParticle: Learning Invariant Measure by Deep Neural Network Minimizing Wasserstein Distance
Explore DeepParticle: an integrated approach combining deep learning, optimal transport, and interacting particles to solve high-dimensional PDEs, demonstrated through Fisher-Kolmogorov-Petrovsky-Piskunov front speeds in incompressible flows.
Challenges and Breakthroughs in the Mathematics of Plasmas
Explore fundamental mathematical concepts in plasma physics, focusing on Vlasov equations, kinetic theory, and new Wasserstein-type distances for analyzing charged particle behavior.