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SUMMARY:Tempered representations and K-theory
DTSTART:20250224T080000Z
DTEND:20250228T170000Z
DTSTAMP:20240908T230600Z
UID:indico-event-10857@indico.math.cnrs.fr
DESCRIPTION:Representation Theory and Noncommutative GeometryWorkshop: Tem
pered representations and K-theoryFebruary 24 to 28\, 2025 - IHP\, ParisSu
mmaryThe classification of tempered irreducible representations for real r
eductive groups was completed in the 1970s by Knapp and Zuckerman\, follow
ing Harish-Chandra's work on the Plancherel formula. But some aspects of t
he subject are now undergoing a re-examination\, following the discovery o
f new perspectives. C*-algebras and K-theory are valuable tools in Represe
ntation Theory\, as shown\, for instance\, by the Mackey bijection. Indeed
\, it was the Connes-Kasparov isomorphism in K-theory that motivated the s
earch for a natural bijection between the tempered dual of a real reductiv
e group and the unitary dual of its Cartan motion group\, as initially sug
gested by Mackey in the 1970s. The meeting will focus on recent developme
nts in which K-theoretic ideas have offered new perspectives on the temper
ed dual for reductive groups or symmetric spaces\, and conversely on new a
pproaches to operator-algebraic problems using contemporary tools in repre
sentation theory. Topics will include: New approaches to the Mackey bije
ction through pseudodifferential operator theory\, which has itself underg
one an extensive conceptual redesign in the past decade\, thanks again to
$C^*$-algebra $K$-theory connections.New perspectives on the the Connes--K
asparov isomorphism using Dirac cohomology and cohomological induction\;Hi
gher orbital intergrals\, which make it possible to go beyond the ``noncom
mutative topology of the tempered dual''\, hinting at something like the `
`differential geometry'' of this noncommutative space.Study of the Casselm
an--Schwartz algebras and their K-theory via Paley--Wiener theorems\, and
connections with the Connes--Kasparov isomorphism.$C^*$-algebraic analysis
of the tempered dual from the point of view of $G$ as a symmetric space f
or $G{\\times}G$\, and more generally of the tempered spectrum of symmetri
c spaces. Preliminary list of speakers:Anne-Marie AubertBachir BekkaYves
BenoistJacob BraddPeter HochsVincent LafforgueRoger PlymenAngel RománMaar
ten SolleveldXiang TangRobert YunckenOrganising Committee:Alexandre Afgous
tidis Pierre Clare Scientific Committee:Tyrone CrispClaire DebordToshi
yuki KobayashiHang WangBack to main page\n\nhttps://indico.math.cnrs.fr/ev
ent/10857/
IMAGE;VALUE=URI:https://indico.math.cnrs.fr/event/10857/logo-2252305829.pn
g
LOCATION:Amphithéâtre Hermite (Institut Henri Poincaré)
URL:https://indico.math.cnrs.fr/event/10857/
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