Title: Gradient flow for weak optimal transport.
Prof. Xin Zhang (NYU)
Abstract: Weak optimal transport is a relaxation of classical optimal transport in which the cost depends nonlinearly on the coupling through its disintegration. This framework is motivated by applications in transport inequalities, entropic optimal transport, and martingale optimal transport.
In this talk, we propose a gradient flow approach to weak optimal transport in the adapted Wasserstein space. We formally derive the corresponding adapted Wasserstein derivative, project it onto the tangent space of couplings, leading to a McKean-Vlasov SDE that characterizes the flow. We establish well-posedness of this dynamic, and prove its convergence to the optimal coupling for the weak optimal transport problem. This talk is based on the joint work with Nathan Sauldubois.
Time: Wed 2026-06-17 10.00 - 11.00
Location: Seminar Room 3721
Language: English
Participating: Prof. Xin Zhang (NYU)
Bio: Xin Zhang is a tenure-track assistant professor at the FRE department of NYU. Before that, he was a university assistant in the group of Prof. Mathias Beiglböck at the University of Vienna from 2021 to 2024. Zhang obtained his Ph.D. in Mathematics under the supervision of Prof. Erhan Bayraktar at the University of Michigan in 2021, and his B.S. in Mathematics at Fudan University in 2016.
His research focuses on optimal transport, stochastic analysis and control, as well as their applications in Finance and Machine Learning. More specifically, Zhang is interested in viscosity solution of nonlinear PDE, and optimal transport in robust finance. His research is partially funded by NSF Award DMS-2508556.