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17/12/2025 14:00
Double Operator Integrals and Multiple Operator Integrals have a reputation of being quite technical objects of study in Functional Analysis, but in fact they appear in many places in noncommutative geometry. In this first part of the mini-course on MOIs I'll show the natural ways they arise, and explain two ways of constructing them. We will see that this gives us a handy tool for toying...
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17/12/2025 15:00
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17/12/2025 16:00
In this talk we will first introduce the notion of NΓ-Hilbert space as introduced by Wolfgang Lück in 1997. Then, we will introduce the notion of Γ-Fredholm operators defined between N Γ-Hilbert space. And finally, the goal of the presentation is to define nonparabolic Γ-near infinity operators and show how they induces Γ-Fredholmness on admissible domains
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17/12/2025 16:35
Using a going-down principle, Chabert, Echterhoff and Oyono-Oyono proved the injectivity of the assembly map for locally compact Hausdorff groups that are amenable at infinity. Bönicke proved the analogue for ample groupoids. In this talk we present the proof of the going-down principle for étale groupoids in general. It yields the injectivity of the assembly map for étale groupoids that are...
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17/12/2025 17:10
We present two distinct deformations of a given semisimple Lie group: the contraction onto the motion group, knwon as the Mackey-Higson deformation, and the quantisation of the symmetric pair related to a maximal compact subgroup, due to Letzter.
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For low dimensional examples, we explain how to assemble these two deformations into a continuous field of C*-algebras defined over a square, which... -
17/12/2025 17:45
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18/12/2025 09:00
Dans mon premier exposé, je présenterai le cadre usuel de la théorie.
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Dans le deuxième exposé, je présenterai des développements plus récents concernant l’existence de sous-algèbres de Cartan dans les C-algèbres nucléaires, les C-algèbres de groupoides non effectifs et les
C*-algèbres de groupoides non séparés. -
18/12/2025 10:00
A subspace of a Banach space E is said to be 1-complemented if it is the ra=
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nge of a contractive projection, and positively 1-complemented if the proje=
ction is, in addition, positive. In the commutative Lp spaces, the descript=
ion of contractive projections is well known (see, e.g., Ando's Theorem, 19=
66). In 1992, Arazy and Friedman provided a characterization of the... -
18/12/2025 11:00
We shall review basics facts about group actions on Banach spaces by affine isometries and explain latest result concerning the case of Schatten ideals.
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18/12/2025 11:30
To any sufficiently regular distribution $m$ on a locally compact group is associated, by the mean of the Fourier transform, some sort of « differential operator with symbol $m$ » on the dual of this group which in general is merely a quantum group. In 1970, M. Jodeit Jr. has shown that if a compactly supported distribution on $\mathbf R^d$ is the symbol of a continuous linear operator from...
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18/12/2025 14:00
With the framework of MOIs in mind from the first part of this mini-course, some arguments common in noncommutative geometry become recognisable as MOI identities. However, an adaptation is needed to deal with unbounded operators. I will discuss an abstract pseudodifferential calculus used in NCG and show a way of defining a functional calculus on this class of operators. This gives a...
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13. Cedric Arhancet: Classical harmonic analysis viewed through the prism of noncommutative geometry18/12/2025 15:00
This talk aims to connect noncommutative geometry with classical harmonic analysis on Banach spaces, with a particular emphasis on both classical and noncommutative Lp-spaces. The overarching goal is to show how the study of operators on Lp-spaces can be naturally integrated into the broader framework of noncommutative geometry, thereby opening new perspectives in...
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18/12/2025 16:00
When a group G acts properly on a tree T, it is a classical result that the action of G on the Gromov compactification X of the tree is amenable, i.e. the crossed product C(X)xG is nuclear. We will introduce an analogue of the crossed product C-algebra C(X)xG in the context of fundamental C-algebras of graph of C-algebras (Fima,Freslon 2013). This C-algebra has interesting features...
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19/12/2025 09:00
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19/12/2025 10:00
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19/12/2025 11:00
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19/12/2025 11:30
One can define a quantum analogue of Levy processes on involutive bialgebras. These processes can be studied through the convolution semigroup of states formed by their marginal distributions, which in turn is fully characterized by its generating functional.
Among those quantum Levy processes, we will focus on Gaussian processes and present the classification of their generating...
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