Ringvorlesung
- Peter Smillie
- Felix Otto
- Daniel Roggenkamp
Abstract
This term, the Ringvorlesung is offered by Peter Smillie, Felix Otto, and Daniel Roggenkamp. Topics of the three parts are:
Part I (Peter Smillie): Harmonic maps
Abstract: A map between Riemannian manifolds that minimizes (or is a stationary point for) total (Dirichlet) energy is called a harmonic map. This is about the most natural PDE arising in Riemannian geometry, and several ubiquitous ideas in geometric analysis were first discovered in the study of harmonic maps. They have found many applications outside of geometric analysis, including in algebraic geometry and manifold topology. And they remain a hot subject, for instance in the context of the non-abelian Hodge correspondence.
In these lectures, I will explain just enough differential geometry to prove some foundational existence, uniqueness, and rigidity theorems for harmonic maps, and then highlight some of their applications to other fields.
Part II (Felix Otto): Convection-Enhanced Diffusion
Part III (Daniel Roggenkamp): Defects and higher categorical structures in quantum field theories
Recorded lecture
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Harmonic maps I
Peter Smillie -
Harmonic maps II
Peter Smillie -
Harmonic maps III
Peter Smillie -
Harmonic maps IV
Peter Smillie -
Convection-Enhanced Diffusion I
Felix Otto -
Convection-Enhanced Diffusion II
Felix Otto -
Convection-Enhanced Diffusion III
Felix Otto -
Convection-Enhanced Diffusion IV
Felix Otto
