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SUMMARY:Connes' trace theorem on Carnot manifolds [Oberseminar Global Anal
 ysis and Operator Algebras]
DTSTART:20260421T121500Z
DTEND:20260421T134500Z
DTSTAMP:20260420T222500Z
UID:indico-event-1227@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ed McDonald (MI (Uni Bonn))\n\nA Carnot manifold (al
 so called a filtered manifold\, among other\nnames) is a manifold $M$ whos
 e tangent bundle $TM$ is equipped with a\nnested family of sub-bundles $0=
 H_0\,H_1\,...\,H_N=TM$ with the property that\nthe Lie bracket of a sectio
 n of $H_j$ and a section of $H_k$ belongs to\n$H_{j+k}$ for $j+k\\leq N.$ 
 We should think of differentiation in the\ndirections of $H_j$ as having `
 `order $j$"\, and the tangent spaces of $M$\ncan be given the structure of
  a nilpotent Lie group built from\n$H_0\,...\,H_N.$ The prototypical examp
 le is a contact structure. There are\nvarious ways to associate a pseudodi
 fferential calculus to a Carnot\nmanifold\, and I will describe the approa
 ch of van Erp and Yuncken based on\na modification of the tangent groupoid
 . I will explain some of the spectral\ntheory of pseudodifferential operat
 ors on a Carnot manifold\, in particular\nthe analogy of Connes' trace the
 orem for this setting. Time permitting\, I\nwill also explain some recent 
 progress relating to operators on singular\nfoliations. This talk is based
  mostly on my paper arXiv:2601.17794.\n\nhttps://math-events.uni-bonn.de/e
 vent/1227/
LOCATION:Endenicher Allee 60/1-008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1227/
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