Last year I had the opportunity to give the first talk at the The Dutch Differential Topology & Geometry seminar (DDT&G). This was a 3 hour long event in which I had the chance to give a high-level introduction to sub-Riemannian geometry and present some interesting results and open questions partly related to my research.
In the first part of the seminar I introduced what are sub-Riemannian structures, where do they come from and what are some of the major properties and open questions, using some famous examples to drive the discussion. For this part of the talk I assumed basic knowledge of Riemannian geometry and calculus of variation and took time to provide a reading list for the interested reader.
In the second part of the talk, I discussed recent advances in sub-Riemannian spectral geometry, focussing in particular on the research around the meaning(s) of intrinsic sub-Laplacians, their self-adjointness and what we can learn from studying their spectra. I tried to provide the main ideas and touch upon some of the major open questions, again giving a more or less detailed list of reading material. For this part of the talk I assumed also some knowledge of functional analysis and operator theory.
My slides are also available for download but, beware, they are big (99Mb) and handwritten…
Keep an eye out for the DDT&G, they have a lot of very interesting micro courses already, and more are coming!
I hope you enjoy. I should have posted them here much earlier.
I recently gave one more talk on this subject, giving more emphasis the connections to the physics of magnetic systems. I link it here for future reference: