ICTS

This school aims to present the fascinating theory of gradient flows at the interface of analysis and probability. From an analysis perspective, several well-known partial differential equations can be formulated as gradient flows in the Wasserstein space. This formulation has resulted in a better understanding of the qualitative and quantitative behaviour of these equations. This gradient flow property has a natural variational structure that has led to the design of structure-preserving numerical schemes for numerous nonlinear partial differential equations. From a probabilistic perspective, it has been discovered that gradient flow structures arise in various cases from the large deviations of underlying stochastic particle systems. Since gradient flows are intimately connected to the ideas of optimization in energy landscapes, they have also found extensive applications in areas such as machine learning and image processing. The theory of gradient flows has had a tremendous impact on both pure and applied mathematics.

Topics covered during this school will include:

(1) Optimal Transport, Wasserstein gradient flows and the JKO scheme
(2) Gradient flows in Data Science
(3) Structure-preserving numerical schemes for gradient flows
(4) Gamma convergence for gradient systems
(5) Jump processes as generalized gradient flows
(6) Interacting particle systems and gradient flows

The organisers will run a five-day preparatory workshop in July at IIT Bombay. It is mandatory for all student/postdoc participants (faculty are welcome too) of our ICTS program to attend this preparatory workshop. This workshop aims to equip the participants with some essential tools from probability theory, convex analysis, and calculus of variations. This knowledge will prove valuable during the lectures and activities of our ICTS program.

Eligibility Criteria: PhD students, postdocs, and faculty members are all welcome to apply for this program.

Accommodation will be provided for outstation participants at our on campus guest house.

ICTS is committed to building an environment that is inclusive, non-discriminatory and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.