Riemannian Geometry: Robot Motion Learning and Control

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Explores training robots through reinforcement learning and learning from demonstration, highlighting challenges in human-robot interaction and data collection.

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Riemannian Trust Regions framework

Introduces the Riemannian Trust Regions (RTR) framework, covering conjugate directions, Newton's method, and model improvement.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.