The Noncommutative Geometry of Singular Foliations

Iakovos Androulidakis

*(National and Kapodistrian University of Athens)*

14:00-15:15, Oct 27-29, 2019 Science Building A510

__Abstract:__

Foliations are examples of dynamical systems that appear in abundance in
various fields of mathematics. The highly pathological topology of the
associated leaf space is crucial for the understanding of the foliation
itself. In the regular case, A. Connes gave the most successful treatment
of this space, by means of Noncommutative Geometry. Using the holonomy of
the foliation to model this space, he built pseudodifferential operators
which replace it successfully. The associated K-theory then accounts for
the topology of the leaf space.
In this series of lectures we will present the generalisation of all this
to singular foliations, which appear much more than often in applications.

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