TODAY - Geometric Structures seminar - Steven Flynn - Dec 4 - 14:00 - Room 133

[Tommaso Rossi]

Dear All,

This is to remind you of today's seminar from the series "Geometric 
Structures".

*Speaker*: Steven Flynn

*Title*: A Microlocal Calculus on Filtered Manifolds

*Abstract*:**Sub-Riemannian geometries arise naturally in quantum 
mechanics and control theory, yet fundamental questions about quantum 
dynamics remain open, suggesting that new microlocal tools are needed to 
extend classical results to these singular geometries.

I will present a pseudodifferential calculus for filtered manifolds with 
operator-valued symbols built using representation theory of nilpotent 
groups. The key innovation is an explicit quantization procedure for 
noncommutative symbols adapted to the filtration, extending the Van 
Erp-Yuncken calculus while maintaining essential properties: closure 
under composition, parametrices, and Sobolev continuity.

This framework enables systematic microlocal analysis on equiregular 
sub-Riemannian manifolds. This is joint work with Véronique Fischer and 
Clotilde Fermanian-Kammerer.


More information can be found here: 
https://researchseminars.org/seminar/Geometric_Structures_SISSA