A gentle introduction to Gamma-convergence (Lecture 4) by Swarnendu Sil @ICTStalks

Uploaded September 2026 | Updated September 2026, 2 weeks ago

Program : A School on Gradient Flows

ORGANIZERS : Jose A Carrillo (University of Oxford, Oxford, UK), Harsha Hutridurga (IIT Bombay, India), Saikat Mazumdar (IIT Bombay, India), Mark A Peletier (TU/e, Eindhoven, Netherlands) and Upanshu Sharma (UNSW, Sydney, Australia)

DATE : 31 August 2026 to 11 September 2026

VENUE : Ramanujan Lecture Hall, ICTS Bengaluru

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.

CONTACT US: sgflows@icts.res.in
PROGRAM LINK : icts.res.in/program/sgflows

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