Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy
Organizers: Francesco Maggi (Austin), Claudio Arezzo (ICTP), Giovanni Bellettini (Siena), Carlo Sinestrari (Roma Tor Vergata)
The study of geometric flows is a fundamental branch of modern mathematical research which lies at the intersection of analysis and geometry, and which has led to spectacular achievements, such as the proof of the Poincaré conjecture by means of the Ricci flow. This school will focus on extrinsic flows, where the evolving object is a submanifold of an ambient space. The most fundamental example of extrinsic flow is the mean curvature flow which is deeply connnected to the theories of minimal surfaces and of diffusive partial differential equations. Extrinsic flows have important applications to the geometry of submanifolds, and their study provides an effective strategy for obtaining topological classification results and for proving sharp geometric inequalities. This two-week school will introduce students to the basic ideas and to the most recent breakthroughs in the field.