Claire Debord - Microlocal and Global Analysis,...
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Claire Debord - Microlocal and Global Analysis, Interactions with Geometry
Index theory through Lie groupoids.
The aim of this lecture is to explain why Lie groupoids are very naturally linked to Atiyah-Singer index
theory. After introducing Lie groupoids, and giving various examples, I will explain how these geometrical objects
can be used:
- to construct the pseudodifferential calculus,
- to construct the index of pseudodifferential operators without using the pseudodifferential calculus,
- to prove and generalize index theorems.
This talk, inspired by ideas of A. Connes, will be based on joint works with JM. Lescure and with G. Skandalis.