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Séminaire d’Analyse Fonctionnelle

par PROCHAZKA Antonin, Yulia Kuznetsova - publié le , mis à jour le

Le séminaire a lieu le mardi à 13h45, en salle 316Bbis du bâtiment de
Métrologie (plan d’accès). Pour le moment, nous alternons des exposés virtuels (pour le lien, contactez la responsable) et classiques.

Vous trouverez ci-dessous le planning du séminaire d’Analyse
Fonctionnelle pour l’année universitaire en cours.
L’historique des séminaires des années précédentes se trouve
ici.

Pour contacter le responsable (Tony Prochazka) : antonin.prochazka univ-fcomte.fr.
Pour s’abonner au séminaire : ACM.

Exposés à venir



-Mardi 11 mai: Fabio Cipriani, Politecnico di Milano
(en ligne) On a noncommutative Sierpiński gasket

We illustrate the construction of a C*-algebra A that can be genuinely interpreed as a quantization of the classical Sierpiński gasket, the most studied instance of a self-similar fractal space. We further describe the discrete and continuous spectrum of A, the structure of the traces on A as well as the construction of a Dirichlet form E and of a spectral triple (A,D,H).

-Mardi 25 mai: David Kyed, University of Southern Denmark, Odense
(en ligne) The Podleś spheres converge to the sphere

The Podleś spheres, which are q-deformed analogues of the 2-sphere, are by now among the most classical objects in non-commutative geometry, but only recently their structure as non-commutative Riemannian manifolds has begun to unravel. In my talk, I will first provide an introduction to Rieffel’s notion of compact quantum metric spaces and his non-commutative counterpart to the Gromov-Hausdorff distance, and then present some recent progress within this field which shows that the quantised 2-spheres actually converge (in the quantum Gromov-Hausdorff distance) to the classical round 2-sphere as the deformation parameter q tends to 1. The talk is based on joint works with Konrad Aguilar and Jens Kaad.

-Mardi 8 juin: Haonan Zhang, IST Austria
(en ligne) Curvature-dimension conditions for symmetric quantum Markov semigroups

The curvature-dimension condition consists of the lower Ricci curvature bound and upper dimension bound of the Riemannian manifold, which has a number of geometric consequences and is very helplful in proving many functional inequalities. In this talk I will speak about two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet-Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz-Schur multipliers over group algebras and depolarizing semigroups. Joint work with Melchior Wirth (IST Austria).

Avril

  • Mardi 27 avril : Loris Arnold, LMB

Mars

  • Mardi 9 mars : Ryosuke Sato, Nagoya University
    (en ligne)
    Markov dynamics on unitary duals of compact quantum groups

In this talk, we will discuss Markov semigroups on unitary duals (i.e., the set of all irreducible representations) of compact quantum groups. First, we will construct quantum Markov semigroups on the group von Neumann algebra of compact quantum group based on its Hopf-algebra structure and characters of the compact quantum group. Then we will show the dynamics preserve the center of the group von Neumann algebra, and it gives the dynamics on the unitary dual. Moreover, the dynamics have generators, and we can describe it explicitly by the representation theory. In particular, we will deal with the case of quantum unitary groups.

  • Mardi 16 mars : Gilles Lancien, LMB
    Plongements non linéaires dans les duaux séparables

Le théorème d’Aharoni (1974) assure que tout espace métrique séparable se plonge de façon bi-Lipschitz dans $c_0$. C’est une question ouverte importante de savoir si tout Banach contenant une copie bi-Lipschitz de $c_0$ contient un sous-espace linéairement isomorphe à $c_0$. Dans cet exposé nous considérerons des questions similaires en relation avec la notion plus faible de plongement grossier. Dans un papier publié en 2007, un grand pas a été fait par N. Kalton, qui a prouvé qu’un Banach contenant grossièrement $c_0$ ne peut pas être réflexif. Cependant, on ignore encore si un tel espace peut être un dual separable. Dans cet exposé, nous discuterons de certains aspects de cette question. L’argument de Kalton est basé sur l’utilisation de graphes métriques particuliers, dits ``entrelacés’’. Nous donnerons des résultats sur les duaux contenant de façon équi-Lipschitz ou équi-grossière ces graphes, en relation avec leur indice de Szlenk et nous prouverons leur optimalité.
Travail en commun avec B. de Mendonça Braga, C. Petitjean and A. Procházka.

  • Mardi 30 mars : Hua Wang, LMB
    Exemples de biproduits croisés ayant propriété (RD)

Je vais d’abord parler rapidement la propriété (RD) pour les groupes
quantiques discrets de type Kac et dire quelques mots comme motivation. Puis
je vais présenter un critère pour voir si les biproduits croisés possèdent
cette propriété. Enfin, je vais introduire une procédure pour construire
explicitement exemples de biproduits croisés ayant ou sans cette propriété,
et parler la limitation de cette procédure.

Février

  • Mardi 23 février à 16h00 : Michael Brannan, Texas A&M University
    (en ligne)
    Complete logarithmic Sobolev inequalities and non-commutative Ricci curvature

I will give a brief introduction to the study of log-Sobolev type inequalities (LSI’s) for quantum Markov semigroups and some of their applications. In the context of classical heat semigroups on compact Riemannian manifolds, the famous Bakry-Emery theorem provides a beautiful connection between the geometry of the underlying manifold and the LSI, showing that a positive lower bound on the Ricci curvature implies an LSI for the heat semigroup. I will discuss an information-theoretic approach to obtain modified log-Sobolev inequalities based on non-positive non-commutative Ricci curvature lower bounds previously developed by Carlen and Maas. Using these tools, we are able to find new examples of quantum Markov semigroups satisfying a completely bounded version of the modified LSI, including heat semigroups on free quantum groups. This talk is based on joint work with Li Gao (TUM) and Marius Junge (UIUC).

Janvier

  • Mardi 12 janvier à 13h45 : Marek Bożejko, University of Wrocław
    Remarks on Generalized Gaussian processes and positive
    definite functions on some Coxeter groups

In my talk I will present the following topics :
1. Strong connections between generalized Gaussian processes and some class of positive definite functions on permutations group.
2. Type B Fock spaces and new Gaussian processes of type B , relations with q-Meixner-Pollaczek polynomials and Meixner probability measures like 1/cosh.
3. Thoma repsentation of central positive definite functions on Coxeter groups of type A and B and new classes of generalized Gaussian processes.
4. Open problems.

Novembre

  • Mardi 3 novembre à 13h30 : Tony Prochazka, LMB
    Compact reduction in Lipschitz-free spaces

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are : ℱ(X) is weakly sequentially complete for every superreflexive Banach space X, and ℱ(M) has the Schur property and the approximation property for every scattered complete metric space M. This is a joint work with R. Aliaga, C. Noûs and C. Petitjean.

Octobre

  • Mardi 6 octobre, 13:45 : Jean-Christophe Bourin, LMB
    Une décomposition pour les matrices partitionnées

On établit "un théorème de Pythagore" pour les matrices partitionnées qui entraîne de nombreuses inégalités.

  • Mardi 20 octobre, 13:45 (en ligne) : Jonas Wahl, Hausdorff Center for Mathematics, Bonn
    Markov dynamics on branching graphs of diagram algebras

Thoma’s famous theorem on the classification of characters on
the infinite symmetric group has been very influential in different
areas of mathematics such as combinatorics and probability theory. In
this talk, we explain versions of Thoma’s theorem for different diagram
algebras arising out of subfactor theory and Banica and Speicher’s
theory of easy quantum groups. As Thoma’s classical theorem, these
results can be formulated in a probabilistic language and we find
interesting new connections to random lattice paths and random walks on
trees.

Septembre

  • Mardi 8 septembre, 13:30 (en ligne) : Jacek Krajczok, IMPAN, Warsaw
    Type I locally compact quantum groups : coamenability and
    applications

We say that a locally compact quantum group is type I if its
universal C* algebra (which is equal to $C^u_0(\hatG)$) is type I.
This class of quantum groups can be though of as an intermediate step
between compact and general locally compact quantum groups ; they are
significantly more general than compact ones, but still have tractable
representation theory. Similarly to the compact case, one can define
"character-like" operators associated with suitable representations. I
will discuss a result which states that coamenability of G is equivalent
to a certain condition on spectra of these operators. If time permits, I
will also discuss how one can use theory of type I locally compact
quantum groups to show that the quantum space underlying the Toeplitz
algebra does not admit a quantum group structure (joint work with Piotr
Sołtan).

  • Mardi 22 septembre, 13:45 (en ligne) : Biswarup Das, Wroclaw University
    Towards quantizing separate continuity : A quantum version of Ellis joint continuity theorem

Let S be a topological space, which is also a semigroup with identity, such that the multiplication is separately continuous. Such semigroups are called semitopological semigroups. These type of objects occur naturally, if onestudies weakly almost periodic compactification of a topological group. Now if we assume the following : (a) The topology of S is locally compact. (b) Abstract algebraically speaking, S is a group (i.e. every element has an inverse). (c) The multiplication is separately continuous as above (no other assumption. This is the only assumption concerning the interaction of the topology with the group structure). Then it follows that S becomes a topological group i.e. : (a) The multiplication becomes jointly continuous. (b) The inverse is also continuous. This extremely beautiful fact was proven by R. Ellis in 1957 and is known in the literature as Ellis joint continuity theorem. In this talk, we will prove a non-commutative version of this result. Upon briefly reviewing the notion of semitopological semigroup, we will introduce ’’compact semitopological quantum semigroup’’ which were before introduced by M. Daws in 2014 as a tool to study almost periodicity of Hopf von Neumann algebras. Then we will give a necessary and sufficient condition on these objects, so that they become a compact quantum group. As a corollary, we will give a new proof of the Ellis joint continuity theorem as well. This is the joint work with Colin Mrozinski.

  • Mardi 29 septembre, 13:45, salle 316B : Uwe Franz, LMB
    Quelques applications de la cohomologie de Hochschild aux probabilités non commutatives

Les semi-groupes de convolution d’états sur un espace de probabilités non commutatif sont en général caractérisés par leur dérivée en t=0, qu’en appelle leur fonctionnelle génératrice. Une telle fonctionnelle $\psi$ peut être complétée en un triplet $(\rho,\eta,\psi)$, dont les composantes sont caractérisées par des relations cohomologiques. Dans mon expose je vais rappeler la cohomologie de Hochschild ainsi que cette construction. Ensuite nous allons regarder quelques applications du premier et deuxième groupes de cohomologie à l’étude des fonctionnelles génératrices.

Agenda

  • Mardi 7 juin 2016 13:45-14:45 - Beata Randrianantoanina - Miami University

    Embeddings of multi-diamonds into non-superreflexive spaces

    Lieu : 316Bbis


  • Mardi 14 juin 2016 13:45-14:45 - Mikael de la Salle - ENS Lyon

    Des questions sur une dualité espaces de Banach / opérateurs sur un espace $L_p$

    Résumé : Si $T\colon L_p \to L_p$ est une application linéaire bornée, et si $X$ est un espace de Banach, on peut considérer la norme (potentiellement infinie) de T sur l’espace $L_p$ à valeurs dans $X$. Cela a aussi un sens lorsque $T$ est seulement défini sur un sous-espace de $L_p$. Ainsi à toute paire $(T,X)$ on associe un nombre réel positif (ou l’infini), et cela permet de parler de dualité entre espaces de Banach et opérateurs entre sous-espaces d’espaces $L_p$. Pour cette dualité, le bipolaire d’un ensemble d’espaces de Banach est bien compris, tandis que le bipolaire d’un ensemble d’opérateurs est encore mystérieux. Je présenterai une approche élémentaire à cette question, qui permet de retrouver les résultats connus et qui mène à une description à moitié satisfaisante du cas inconnu. Ce sera surtout l’occasion de partager avec vous des questions qui me tiennent à coeur.

    Lieu : 316Bbis


  • Jeudi 16 juin 2016 15:00-16:00 - Michael Brannan - Texas A&M University

    On the structure of exotic quantum group C*-algebras

    Résumé : Given a compact quantum group G, there are often many ways to complete the Hopf *-algebra of polynomial functions Pol(G) to a quantum group C*-algebra. For instance, one could take the minimal C*-completion $C_r(G)$ coming from the GNS construction for the Haar state, or the maximal completion $C^u(G)$ by taking the universal C*-completion of Pol(G). Any quantum group C*-algebra C(G) lying as an intermediate quotient $C^u(G) \to C(G) \to C_r(G)$ is called exotic.
    In this talk, I will discuss a class of exotic quantum group C*-algebras, called $L_p$-C*-algebras, which are obtained by completing Pol(G) with respect to the C*-norm induced by all unitary representations of the discrete dual of G satisfying a certain $L_p$-integrability condition for their matrix coefficient functions (with respect to the Haar weight). In the case of free orthogonal quantum groups, it turns out that we can say a lot about these $L_p$ C*-algebras : they are all distinct for different exponents p, they admit unique tracial states, and they fail to have any nice local properties such as local reflexivity, the local lifting property, amenable traces, or the weak expectation property.
    This is based on joint work with Zhong-Jin Ruan and Matthew Wiersma.

    Lieu : 324-2B

    Notes de dernières minutes : Changement de salle —>324-2B


  • Mardi 21 juin 2016 10:30-11:30 - Piotr M. Hajac - IMPAN (Varsovie) et University of New Brunswick

    From classical to quantum quaternionic projective spaces

    Lieu : 316Bbis


  • Mardi 28 juin 2016 13:45-14:45 - Stephen Wills - Université de Cork, Irlande

    Construction of quantum stochastic cocycles

    Résumé : Quantum stochastic cocycles generalise (semi)groups of automorphisms of operator algebras in two ways - the automorphism condition is weakened to a positivity preservation condition, and the time evolution law of a semigroup is suitably modified. I will survey known results that show the correspondence between cocycles and solutions of the Evans-Hudson quantum stochastic differential equation for bounded generators, before outlining two distinct approaches to the problems of constructing such cocycles when the generator is unbounded, detailing the advantages and disadvantages of the two methods.

    Lieu : 316Bbis


  • Mardi 13 septembre 2016 13:45-14:45 - Marek Cúth - Université Charles, Prague

    Embedding of ℓ1 into Lipschitz-free Banach spaces and ℓ∞ into their duals

    Résumé : Given a metric space M, it is possible to construct a Banach space ℱ(M) in such a way that the Lipschitz structure of M corresponds to the linear structure of ℱ(M). This space ℱ(M) is sometimes called the "Lipschitz-free space over M". The study of Lipschitz-free Banach spaces became an active field of study. I will present our recent result with M. Johanis that ℓ∞ embeds isometrically into the dual of every infinite-dimensional Lipschitz-free Banach space and that it is often the case that a Lipschitz-free Banach space contains a 1-complemented subspace isometric to ℓ1. We do not know whether the later is true for every infinite-dimensional Lipschitz-free Banach space.

    Lieu : 316Bbis


  • Mardi 20 septembre 2016 13:45-14:45 - Safoura Jafar-Zadeh - UFC

    Isometric isomorphisms of the annihilator of $C_0(G)$ in $LUC(G)^*$

    Résumé : For a locally compact group $G$, let $C_b(G)$ be the space of all complex-valued, continuous and bounded functions on $G$ equipped with the sup-norm, and $LUC(G)$ be the subspace of $C_b(G)$ consisting of all functions $f$ such that the map $G\to C_b(G) ;x\mapsto l_xf$ is continuous, where $l_xf$ is the function defined by $l_xf(y)=f(xy)$, for each $y\in G.$
    In this talk, I will show that if $G$ is a locally compact group and $H$ is a discrete group then whenever there exists a weak-star continuous isometric isomorphism between $C_0(G)^\perp$ (the annihilator of $C_0(G)$ in $LUC(G)^*$) and $C_0(H)^\perp$, then $G$ is isomorphic to $H$ as a topological group. Several related results will also be discussed.

    Lieu : 316Bbis


  • Mardi 27 septembre 2016 13:45-14:45 - Uwe Franz - UFC

    HUNT FORMULA FOR SUq(n) AND Uq(n)

    Résumé : Joint work with Anna Kula, Martin Lindsay, and Michael Skeide.
    We provide a Hunt type formula for the infinitesimal generators of Lévy process on the compact quantum groups SUq(N )and Uq(N ). In particular, we obtain a decomposition of such generators into a gaussian part and a "jump" type part, similar to the classical Hunt formula.

    Lieu : 316Bbis


  • Mardi 4 octobre 2016 13:45-14:45 - François Netillard - UFC

    Plongements grossièrement Lipschitz entre espaces de James

    Résumé : Il est connu que $\ell_q$ ne se plonge pas grossièrement Lipschitz dans $\ell_p$ pour $q\neq p$ ($p, q \geq 1$). On essaie d’adapter les méthodes utilisées alors au cas des espaces de James.

    Lieu : 316Bbis


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  • Mardi 5 novembre 2019 13:30-15:00 - Alexandre Nou

    Théorème de Marcinkiewicz (Groupe de travail)

  • Lundi 27 novembre 2017 09:00-17:00 - Journée thematique de NC-Geom-FA

    Analyse fonctionnelle et information quantique

    Résumé : Benoit Collins (Universite de Kyoto)
    Guillaume Aubrun (Universite de Lyon)
    Participants du projet I-QUINS


  • Du 26 mars 2018 14:00 au 27 mars 2018 17:30 - Journées en Analyse Fonctionnelle

    Journées en Analyse Fonctionnelle

  • Du 29 mai 2018 13:30 au 1er juin 2018 12:30 - Guillaume Aubrun (Lyon), Marek Cúth (Prague) et Sophie Grivaux (Lille)

    Ecole de printemps 2018 du GdR AFHP

    Résumé : Voir le programme ici.


  • Mercredi 19 décembre 2018 09:00-17:30 -

    Journée de jeunes analystes non commutatifs

    Résumé :

    • Guixiang Hong (Wuhan University) :
      Vector-valued Littlewood-Paley theorem for sum and difference sets
    • Chao Zhang (Universidad Autonoma de Madrid)
      On some properties of the differential transforms related to the fractional parabolic Poisson
      semigroups
    • Haonan Zhang (UFC) :
      Carlen-Frank-Lieb conjecture and monotonicity of α-z Renyi relative entropy
    • Simeng Wang (Université Paris Sud) :
      Factoriality and type classification for q-deformed Araki-Woods algebras
    • Sheng Yin (Universitat des Saarlandes) :
      Free analysis : zero divisors and Atiyah properties
    • Isabelle Baraquin (UFC) :
      Random walks on finite quantum groups
    • Xumin Wang (UFC) :
      Fourier multipliers on some discrete groups

    Lieu : 316Bbis


  • Du 27 mai 2019 13:30 au 28 mai 2019 16:30 - Journées Besançon-Neuchâtel

    Journées Besançon-Neuchâtel

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