Optimal transport: stochastics, projections, and applications

This workshop brings together two exciting new directions in research: stochastic transport and Wasserstein projections. Stochastic transport studies how processes evolve over time rather than as instant shifts, making it particularly useful for dynamic systems where decisions depend on the flow of information. This perspective connects probability, geometry, and partial differential equations and has proven powerful in understanding learning in neural networks, development of cells, and the performance of algorithms. It also underpins important advances in finance, risk management, and optimization, where choices must be made sequentially and uncertainty plays a major role. Recent work has introduced causal and adapted transport, which ensures models respect time and available information, leading to robust ways of comparing systems. These methods have already found wide-ranging applications and promise further breakthroughs in dynamic, information-driven settings.

Wasserstein projections, on the other hand, address the problem of finding the best-fitting model for observed data within a chosen class of models. This approach is particularly important when robustness is required, such as in economics or risk management. Though seemingly distinct from stochastic transport, surprising connections have emerged, linking Wasserstein projections to geometric inequalities, stochastic ordering of probability distributions, and computational tools like the Sinkhorn algorithm. These intersections suggest rich opportunities for advancing both theory and applications. The workshop’s central aim is to create a platform where these two communities—often working separately—can exchange ideas, spark collaborations, and explore their common ground. By bringing together experts, early-career researchers, and students, the workshop will foster new insights and collaborations that could reshape classical areas of mathematics while also driving innovation in modern applied fields.

Main Event Site: Optimal transport: stochastics, projections, and applications | Fields Institute for Research in Mathematical Sciences