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SUMMARY:Quid seminar
DTSTART:20240703T160000Z
DTEND:20240703T173000Z
DTSTAMP:20241103T101000Z
UID:indico-event-12247@indico.math.cnrs.fr
DESCRIPTION:Speakers: Gabriel Duez\, Guilherme Sobreira\, Mathis Alleysson
\n\nMathis Alleysson : Quid of index theory?\nPast development of index th
eory led to the introduction of index morphisms in K-theory. Unfortunately
\, these indices are not induced by the classical K-theory functor\, as th
ey go in the "wrong-way". In this presentation\, our goal is to introduce
push-forwards in K-theory\, a functor solving this "wrong-way" issue. To d
o so\, we will have to introduce some notions and examples of Lie groupoid
s\, such as the deformation to normal cone. We might also have time to dis
cuss the functoriality of push-forwards and how it can be applied to rewri
ting a proof of one of Atiyah-Singer's famous theorems.\n \nGuilherme Sob
reira : Quid of Anosov surfaces?\nAnosov surfaces can be seen as a dynamic
al generalization of surfaces of negative curvature. It turns out that the
se surfaces display a lot of rigidity phenomena: invariants defined using
the metric\, like the spectrum of the Laplacian or lengths of geodesics\,
may often determine the metric. This is the case of the marked length spe
ctrum\, which we will discuss in this seminar. To understand why this inva
riant determines the underlying Anosov metric\, we will come across a beau
tiful interplay between the complex structure of our surface and the dynam
ical/analytical behavior of its geodesic flow.\n \nDuez Gabriel : Quid of
Cartan subalgebras in C*-algebras?\nCartan subalgebras are particular max
imal abelian subalgebras which exist in various theories. The most basic e
xample is the subalgebra of diagonal matrices in a matrix algebra. For ope
rator algebras\, Cartan subalgebras were first defined in the von Neumann
case and were proved to be equivalent to some particular measured equivale
nce relations. By analysing groupoid C*-algebras\, Renault defined in 2008
Cartan subalgebras in C*-algebras and proved that they are equivalent to
some groupoid structures. We propose to (re)discover this fundamental theo
rem\, a bridge between dynamical systems and operator algebras.\n\nhttps:/
/indico.math.cnrs.fr/event/12247/
LOCATION:Room Picard (1R2 )
URL:https://indico.math.cnrs.fr/event/12247/
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