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X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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DTSTART:20251026T010000
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DTSTART:20260329T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20251126T110000
DTEND;TZID=Europe/Paris:20251126T120000
DTSTAMP:20260430T182524
CREATED:20251030T124425Z
LAST-MODIFIED:20251121T100921Z
UID:20441-1764154800-1764158400@www.math.ens.psl.eu
SUMMARY:« Omar Mohsen\, raconte-moi les groupoïdes de Lie et les opérateurs différentiels elliptiques ! »
DESCRIPTION:L’une des opérations les plus importantes en mathématiques est la multiplication de matrices. En permettant aux indices de devenir continus\, on obtient la convolution de fonctions. De manière analogue\, on peut définir la convolution de fonctions sur les groupes de Lie. Les groupoïdes de Lie offrent une généralisation et unification de ces différentes notions de convolution. Je présenterai une introduction aux groupoïdes de Lie\, suivie d’une discussion sur plusieurs de leurs applications à l’analyse des équations aux dérivées partielles.
URL:https://www.math.ens.psl.eu/evenement/omar-mohsen-raconte-moi-les-groupoides-de-lie-et-les-operateurs-differentiels-elliptiques/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20251210T110000
DTEND;TZID=Europe/Paris:20251210T120000
DTSTAMP:20260430T182524
CREATED:20251030T124601Z
LAST-MODIFIED:20251204T090833Z
UID:20444-1765364400-1765368000@www.math.ens.psl.eu
SUMMARY:« Amaury Hayat\, raconte-moi comment l'IA pourrait changer la pratique des mathématiques ! »
DESCRIPTION:Est-ce qu’un modèle d’IA peut démontrer un énoncé mathématique complexe ? Formaliser des preuves ? Une IA peut-elle développer une intuition mathématique plus puissante qu’un humain sur un problème spécifique et aider à la découverte de nouveaux théorèmes ? Les récentes avancées issues de la combinaison de différentes techniques de machine learning allant des modèles de langage aux méthodes d’apprentissage par renforcement posent de nombreuses questions sur l’avenir de la pratique des mathématiques. Pour explorer ces enjeux\, nous présenterons plusieurs exemples de travaux récents en IA pour les mathématiques et nous en discuterons les perspectives.
URL:https://www.math.ens.psl.eu/evenement/amaury-hayat-que-vas-tu-nous-raconter/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20251210T140000
DTEND;TZID=Europe/Paris:20251210T170000
DTSTAMP:20260430T182524
CREATED:20251127T144118Z
LAST-MODIFIED:20260109T083237Z
UID:20568-1765375200-1765386000@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes à l'ENS
DESCRIPTION:14.00 – 14.45 : François Thilmany (KU Leuven) « Finding ping-pong partners for finite subgroups of linear groups » \n\n\n\nIn his paper on free subgroups of linear groups\, Tits proved his famous alternative: a linear group is either virtually solvable\, or contains a free subgroup. Since then\, Tits’ work has been generalized and applied in many different ways. One remaining open question in this subject is the one asked by de la Harpe and his collaborators: let $G$ be a semisimple Lie group without compact factors and with trivial center\, and let $\Gamma$ be a Zariski-dense subgroup of $G$. Given a prescribed finite subset $F$ of $G$\, is it always possible to find an element $\gamma \in \Gamma$ such that for any $h \in F$\, the subgroup generated by $h$ and $\gamma$ is freely generated? (If so\, we say $h$ and $\gamma$ are ping-pong partners.)  In this talk\, we will discuss a variant of the question of de la Harpe\, where $F$ is a finite set of finite subgroups $H_i$ of $G$. Using careful refinements of the main steps of Tits’ proof of the alternative (which we will recall)\, we give sufficient conditions for the existence of ping-pong partners for the $H_i$ in any Zariski-dense subgroup $\Gamma$. We will then show that these conditions are satisfied for products of copies of $\mathrm{SL}_n$ over division $\mathbb{R}$-algebras. The existence of such free products has applications in the theory of integral group rings of finite groups\, which will be briefly mentioned.Joint work with G. Janssens and D. Temmerman.  \n\n\n\n15.00 – 15.45 : Milan Donvil (Ecole normale supérieure) « The quantum groups behind W*-superrigidity »  \n\n\n\nTo any countable group\, one can associate its group von Neumann algebra\, which is the closure of the group ring in a weak topology. A group is called W*-superrigid if its group von Neumann algebra cannot be isomorphic to the von Neumann algebra of another nonisomorphic group. One says that the group is ‘completely recoverable’ from its von Neumann algebra. To prove W*-superrigidity\, one actually needs tools from the theory of compact quantum groups\, which are von Neumann algebras with additional structure. Since group von Neumann algebras are in particular compact quantum groups\, it is natural to ask if there are groups which are also superrigid within this larger class. I will explain the link between W*-superrigidity and compact quantum groups\, as well as present a resent work of Stefaan Vaes and me which provides the first ‘quantum W*-superrigid’ (quantum) groups.  \n\n\n\n16.15 – 17.00 : Pegah Pournajafi (Collège de France) « Quantum automorphism groups of 0-hyperbolic graphs »Quantum groups and graph theory may seem like distant areas\, yet intriguing connections emerge when they intersect. After an introduction to the notion of quantum automorphism groups of finite graphs\, we will focus on 0-hyperbolic graphs and a computation of their quantum automorphism group. If time permits\, we will also show how their quantum symmetries can be fully understood through their classical properties\, due to their structural constraints. This talk is based on joint work with Amaury Freslon and Paul Meunier. 
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-a-lens/
LOCATION:ENS 45 rue d’Ulm salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260114T110000
DTEND;TZID=Europe/Paris:20260114T120000
DTSTAMP:20260430T182524
CREATED:20260112T095343Z
LAST-MODIFIED:20260112T095344Z
UID:20704-1768388400-1768392000@www.math.ens.psl.eu
SUMMARY:David Lilienfeldt\, raconte-moi la formule de Gross-Zagier !
DESCRIPTION:Dans les années 1980\, Gross et Zagier ont établi une formule reliant les hauteurs de points CM sur les courbes modulaires aux dérivées de certaines fonctions L\, ouvrant la voie à des applications spectaculaires à la conjecture de Birch et Swinnerton-Dyer (BSD) pour les courbes elliptiques. J’exposerai d’abord la trichotomie des points rationnels sur les courbes algébriques\, avant de présenter la conjecture de Birch et Swinnerton-Dyer. Je décrirai ensuite les quatre piliers qui sous-tendent la démonstration de Gross–Zagier–Kolyvagin de la conjecture BSD en rang analytique 1. Si le temps le permet\, je dirai quelques mots sur la théorie en dimension supérieure.
URL:https://www.math.ens.psl.eu/evenement/david-lilienfeldt-raconte-moi-la-formule-de-gross-zagier/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260128T140000
DTEND;TZID=Europe/Paris:20260128T170000
DTSTAMP:20260430T182524
CREATED:20260123T095019Z
LAST-MODIFIED:20260123T095020Z
UID:20853-1769608800-1769619600@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes à l'ENS : Naomi Andrew\, Basile Morando\, Nicolas de Saxcé
DESCRIPTION:14.00 – 14.45 : Naomi Andrew \n\n\n\n(Laboratoire de Mathématiques d’Orsay)Title: Automorphisms behaving badlyAbstract: Baumslag–Solitar groups are HNN extensions of the infinite cyclic group\, whose isomorphism type is controlled by two integers giving the two embeddings. They have provided many counterexamples over the years: for example\, they include groups which are not Hopfian and groups which are Hopfian but not residually finite. Later\, Collins and Levin showed that there are Baumslag–Solitar groups that do not have finitely generated automorphism group. \n\n\n\nMoving this construction to higher rank\, one can study « Leary–Minasyan groups »: these are HNN extensions of free abelian groups\, with both inclusions finite index. They are also sources of counterexamples\, such as groups which are CAT(0) but not biautomatic. We study their automorphism groups\, and in particular characterise when they are finitely generated; this includes some finitely presented metabelian groups with automorphism groups that are not finitely generated. This is joint work with Sam Hughes and Motiejus Valiunas. \n\n\n\n15.00 – 15.45 : Basile Morando (ENS – PSL) Title: On factoriality of the Neretin group von Neumann algebraAbstract: To any locally compact group G\, one can associate a von Neumann algebra L(G)\, generated by the image of G under its left regular representation. This algebra reflects decomposition properties of the representation: L(G) is a factor — i.e.\, has trivial center — if and only if the regular representation does not split as a direct sum of two disjoint subrepresentations. \n\n\n\nIn the discrete case\, Murray and von Neumann showed in 1943 that L(G) is a factor if and only if all non-trivial conjugacy classes are infinite. By contrast\, for non-discrete groups\, determining factoriality becomes more subtle. \n\n\n\nIn this talk\, we present a new sufficient criterion for factoriality of L(G)\, when G is a totally disconnected group. This criterion\, based on a growth condition for the conjugation orbits of cosets\, allows us to prove that the von Neumann algebra of the Neretin group is a factor — providing the first known example of a simple\, non-discrete group with this property. \n\n\n\nIf time permits\, we will also discuss implications of this criterion for determining the type of L(G)\, and for understanding factoriality of crossed product associated to G-actions on von Neumann algebras. \n\n\n\n16.15 – 17.00 : Nicolas de Saxcé (CNRS & Université Paris-Nord) \n\n\n\nTitle: Approximation diophantienne et flots diagonaux dans les espaces de réseauxAbstract: Dans un espace de réseaux on associe à toute orbite diagonale une suite d’éléments du groupe de Weyl satisfaisant certaines propriétés de convexité pour l’ordre de Bruhat\, et qui décrit la position de l’orbite à distance finie près. Ce codage des orbites permet d’étudier l’approximation par des points rationnels dans les variétés de drapeaux.
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-a-lens-naomi-andrew-basile-morando-nicolas-de-saxce/
LOCATION:Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260211T110000
DTEND;TZID=Europe/Paris:20260211T120000
DTSTAMP:20260430T182524
CREATED:20260205T084712Z
LAST-MODIFIED:20260205T084712Z
UID:20903-1770807600-1770811200@www.math.ens.psl.eu
SUMMARY:Pierre-Antoine Guihéneuf\, raconte-moi le graphe fin des courbes !
DESCRIPTION:Le graphe fin des courbes est un objet associé à (presque) toute surface S\, sur lequel le groupe des homéos de S agit fidèlement par isométries. C’est un outil tout neuf qui permet de dire de nouvelles choses de ce groupe des homéos de S. J’expliquerai en particulier comment l’action d’un homéo est déterminée par ses propriétés rotationnelles\, en quoi ce fait est intéressant et les mots compliqués de ce résumé.
URL:https://www.math.ens.psl.eu/evenement/pierre-antoine-guiheneuf-raconte-moi-le-graphe-fin-des-courbes/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260218T110000
DTEND;TZID=Europe/Paris:20260218T120000
DTSTAMP:20260430T182524
CREATED:20260213T100634Z
LAST-MODIFIED:20260213T100635Z
UID:21016-1771412400-1771416000@www.math.ens.psl.eu
SUMMARY:Cécile Huneau\, raconte-moi les conjectures de censure cosmique de Penrose !
DESCRIPTION:Dans cet exposé\, je parlerai des trous noirs en m’appuyant sur deux exemples\, présenterai le comportement générique des singularités de l’espace-temps conjecturé par Penrose dans ses conjectures de censure cosmique\, et ferai une petite revue des résultats récents autour de ces conjectures.
URL:https://www.math.ens.psl.eu/evenement/cecile-huneau-raconte-moi-les-conjectures-de-censure-cosmique-de-penrose/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260218T140000
DTEND;TZID=Europe/Paris:20260218T170000
DTSTAMP:20260430T182524
CREATED:20260213T094415Z
LAST-MODIFIED:20260213T094415Z
UID:21014-1771423200-1771434000@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes - Jean Lécureux\, Adrien Le Boudec\, Vadim Kaimanovich
DESCRIPTION:14.00 – 14.45 : Jean Lécureux (Université de Bordeaux)Title: A simple lattice in an affine building \n\n\n\nAbstract: Affine buildings appear naturally in the study of algebraic groups over local fields: the first example is the tree on which acts SL_2(Q_p). Lattices in these algebraic groups are\, in higher rank\, arithmetic\, and in every case\, residually finite (hence never simple). \n\n\n\nNevertheless\, the main result that I will present implies that there exists a simple group which acts properly discontinuously and cocompactly on an affine building. The construction of this group is due to Titz-Mite and Witzel\, and together with Witzel we are able to conclude to its simplicity. The main tool we use is a construction of an analogue of a « geodesic flow » on the building\, with an adequate measure\, and prove its ergodicity. I will try to present some ideas for these constructions\, focusing on the example of the tree.  \n\n\n\n15.00 – 15.45 : Adrien Le Boudec (CNRS & ENS de Lyon)  \n\n\n\nTitle: Solvable groups with a common cocompact envelope \n\n\n\nAbstract: A locally compact group $G$ is a cocompact envelope of a group $\Gamma$ if $G$ contains a copy of $\Gamma$ as a discrete and cocompact subgroup. We consider the problem that takes two finitely generated groups having a common cocompact envelope and asks what properties must be shared between them\, for the class of solvable groups of finite rank. In that setting we obtain both rigidity and flexibility results. We obtain in particular that the class of solvable groups of finite rank is not QI-rigid. Our flexibility results also allow for finitely presented groups\, and more generally groups with type $F_n$ for arbitrary $n$. \n\n\n\n16.15 – 17.00 : Vadim Kaimanovich (Université de Rennes) \n\n\n\nTitle: Collapsing harmonic measures for discrete subgroups of semisimple Lie groups \n\n\n\nAbstract: The Furstenberg boundary of a non-compact\, finite centre\, real semi-simple Lie group (equivalently\, of the associated Riemannian symmetric space) is its quotient by a minimal parabolic subgroup; for $SL(d\,\mathbb R)$ this is the complete flag variety in $\mathbb R^d$. It serves as a « skeleton » of various compactifications and is essential for understanding the large-scale geometry of the symmetric space. \n\n\n\nIt is known since the 1980s that\, under natural conditions\, a random walk on a discrete subgroup gives rise to a uniquely defined harmonic measure on the Furstenberg boundary. This measure makes the boundary isomorphic\, as a measure space\, to the Poisson boundary of the random walk. \n\n\n\nThere is also a canonical finite family of lower dimensional quotients of the Furstenberg boundary corresponding to non-minimal parabolic subgroups (partial flag varieties in the $SL(d\,\mathbb R)$ case). In general – for instance\, when the harmonic measure is absolutely continuous – these quotient maps yield non-trivial quotients of the Poisson boundary. \n\n\n\nThe purpose of the talk is to exhibit a new « collapsing » phenomenon: there are situations in which some of these quotient maps become measure-theoretic isomorphisms with respect to the harmonic measure. In such cases the Poisson boundary is effectively « smaller » than the full geometric Furstenberg boundary. The construction uses the work of Hochman- Solomyak on the dimension of the harmonic measure for countable\,non-discrete groups of isometries of the hyperbolic plane.
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-jean-lecureux-adrien-le-boudec-vadim-kaimanovich/
LOCATION:Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260311T110000
DTEND;TZID=Europe/Paris:20260311T120000
DTSTAMP:20260430T182524
CREATED:20260305T142750Z
LAST-MODIFIED:20260309T143738Z
UID:21049-1773226800-1773230400@www.math.ens.psl.eu
SUMMARY:Cathy Swaenepoel\, raconte-moi la méthode du cercle !
DESCRIPTION:La méthode du cercle\, introduite par Hardy et Littlewood dans les années 20\, est un outil majeur en théorie analytique des nombres. Constamment améliorée\, elle a conduit à des résultats remarquables\, en particulier sur des problèmes additifs concernant les nombres premiers. Dans cette direction\, Vinogradov l’a développée en 1937 pour montrer que tout entier impair assez grand est somme de trois nombres premiers. Récemment\, elle a connu de nouveaux raffinements\, notamment grâce à des travaux de Bourgain et Maynard\, conduisant à des résultats spectaculaires sur les chiffres des nombres premiers. Dans cet exposé\, je décrirai les idées principales de la méthode du cercle à travers le théorème de Vinogradov puis je présenterai certaines applications récentes à des problèmes sur les chiffres des nombres premiers.
URL:https://www.math.ens.psl.eu/evenement/cathy-swaenepoel-raconte-moi-la-methode-du-cercle/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260318T140000
DTEND;TZID=Europe/Paris:20260318T170000
DTSTAMP:20260430T182524
CREATED:20260312T110116Z
LAST-MODIFIED:20260312T110116Z
UID:21119-1773842400-1773853200@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes - Xenia Flamm\, Vlerë Mehmeti\, Anna Ben-Hamou
DESCRIPTION:14.00 – 14.45 : Xenia Flamm (MPI Leipzig – IHES)  \n\n\n\nTitle: Positive representations and non-Archimedean ordered fields \n\n\n\nSummary: Positive representations were introduced by Olivier Guichard and Anna Wienhard in their foundational work on higher Teichmüller theory. In this talk\, we propose a notion of positive representation from the fundamental group of a (possibly non-closed) hyperbolic surface into the k-points of a reductive algebraic group\, where k is an ordered field. Our approach provides a common framework that simultaneously extends the classical theory for closed surfaces and real Lie groups. We focus on the non-Archimedean case\, where new phenomena arise\, and explain how such representations can be understood as limits of real positive representations. This is joint work with Nicolas Tholozan\, Tianqi Wang and Tengren Zhang. \n\n\n\n15.00 – 15.45 : Vlerë Mehmeti (IMJ-PRG) \n\n\n\nTitle: Variation of the Hausdorff dimension and degenerating Schottky groups \n\n\n\nSummary: I will talk about the continuity of the Hausdorff dimension of limit sets of Schottky groups defined over arbitrary complete valued fields.The common ambient topology allowing one to vary at the same time the Schottky group and the base field is induced by analytic spaces over Banach rings (in the sense of Berkovich). As an application\, one can obtain information on the asymptotic behavior of families of degenerating complex Schottky groups\, which can be extended to a continuous family by a non-Archimedean counterpart. No non-Archimedean prerequisites will be necessary. This is based on joint work with Nguyen-Bac Dang. \n\n\n\n16.15 – 17.00 : Anna Ben-Hamou (Sorbonne Université) \n\n\n\nTitle: Mixing time of a random walk on binary matrices \n\n\n\nSummary: In this talk\, we will consider a Markov chain on n by n invertible binary matrices\, which moves by picking an ordered pair of distinct rows and adding one to the other mod 2. This chain was first studied by Diaconis and Saloff-Coste (1996)\, who showed that the mixing time was O(n^4). Then Kassabov (2003) improved it to O(n^3). Using this last result\, we will show that the logarithmic Sobolev constant is O(n^2)\, which yields an upper bound of O(n^2 log n) on the mixing time. Up to logarithmic terms\, this matches the lower bound.
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-xenia-flamm-vlere-mehmeti-anna-ben-hamou/
LOCATION:Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260325T110000
DTEND;TZID=Europe/Paris:20260325T120000
DTSTAMP:20260430T182524
CREATED:20260320T100558Z
LAST-MODIFIED:20260320T100559Z
UID:21144-1774436400-1774440000@www.math.ens.psl.eu
SUMMARY:Mingkun Liu\, raconte-moi les surfaces hyperboliques aléatoires !
DESCRIPTION:Après avoir précisé comment tirer au hasard une surface hyperbolique de genre g\, je décrirai la géométrie d’une telle surface aléatoire. En particulier\, on verra que\, lorsque g tend vers l’infini\, sa systole (la longueur de la plus courte géodésique fermée) est en moyenne d’environ 1\,61498.
URL:https://www.math.ens.psl.eu/evenement/mingkun-liu-raconte-moi-les-surfaces-hyperboliques-aleatoires/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260408T110000
DTEND;TZID=Europe/Paris:20260408T120000
DTSTAMP:20260430T182524
CREATED:20260402T124328Z
LAST-MODIFIED:20260402T124444Z
UID:21211-1775646000-1775649600@www.math.ens.psl.eu
SUMMARY:Basile Morando\, raconte-nous les groupes de Neretin !
DESCRIPTION:Les groupes de Neretin ont été définis par Yuri Neretin au début des années 90\, à l’origine comme analogues p-adiques du groupe des difféomorphismes du cercle. Depuis la preuve de leur simplicité par Kapoudjian en 1999\, ces groupes (localement compacts et totalement discontinus) suscitent un intérêt croissant: ils présentent de remarquables propriétés qui contrastent avec celles des groupes localement compacts simples connexes. Dans cet exposé\, on s’intéressera notamment au fait qu’ils n’admettent aucun réseau\, ainsi qu’aux propriétés remarquables de leurs représentations unitaires.
URL:https://www.math.ens.psl.eu/evenement/basile-morando-raconte-nous-les-groupes-de-neretin/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20260408T140000
DTEND;TZID=Europe/Paris:20260408T170000
DTSTAMP:20260430T182524
CREATED:20260403T082003Z
LAST-MODIFIED:20260403T082112Z
UID:21215-1775656800-1775667600@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes - Adrien Boyer\, Julien Marché\, Greg Patchell
DESCRIPTION:14:00-14:45 Adrien Boyer (IMJ-PRG): Property RD and Boundary Representations for A2 Buildings  \n\n\n\n15:00-15:45 Julien Marché (ENS – PSL): Action of endomorphisms of free groups on their SL_2-character varieties  \n\n\n\n16:15-17:00 Greg Patchell (University of Oxford): Selfless Inclusions of C*-Algebras and Quantum Groups \n\n\n\n \n\n\n\nAbstracts: \n\n\n\nGreg Patchell: Selfless Inclusions of C*-Algebras and Quantum Groups \n\n\n\nRecently\, strong asymptotic freeness\, or selflessness\, in C-algebras has emerged as a powerful technique to prove important regularity properties including simplicity\, unique trace\, stable rank 1\, and strict comparison. In particular\, in Fall 2024\, Amrutam\, Gao\, Kunnwalkam Elayavalli\, and I showed that the reduced group C-algebras of all hyperbolic groups with trivial finite radical are selfless\, which resolved the open problem of strict comparison for the reduced group C-algebra of the free group on two generators. Since then\, our result has been expanded to include a much larger class of groups. Work has also begun on isolating selflessness for C-algebras not arising from groups\, including the result of Hayes\, Kunnawalkam Elayavalli\, and Robert on selflessness of the reduced free product of a large class of C-algebras (see also Flores-Klisse-Ó Cobhthaigh-Pagliero). I will introduce the general notion of a selfless inclusion of C-algebras\, with which we will see the selflessness of the reduced unitary compact matrix quantum groups. This work is joint with Ben Hayes\, Srivatsav Kunnawalkam Elayavalli\, and Leonel Robert. \n\n\n\n \n\n\n\nAdrien Boyer: Property RD and Boundary Representations for A2 Buildings \n\n\n\nI will discuss an approach based on boundary representations to prove property RD for discrete groups acting properly and cocompactly on affine buildings of type A2. This result is due to Robertson\, Ramagge\, and Steger in the late 1990s. I will emphasize geometric arguments involving the Furstenberg boundary that can be used to establish property RD\, in particular the notion of “foldings” or “confluences\,” as suggested by V. Kaimanovich. Along the way\, I will also mention a conjecture of Robertson\, Ramagge\, and Steger concerning the optimal bound\, and propose a possible approach toward resolving it. If time permits\, I will also explain what happens in the C2 case. This is joint work with Thang Nguyen. \n\n\n\n \n\n\n\nJulien Marché: Action of endomorphisms of free groups on their SL_2-character varieties. \n\n\n\nLet phi : F_n->F_n be an endomorphism and let phi^* denote its action on the character variety X_n=Hom(F_n\,SL_2(C))/SL_2(C). Cantat-Gelander-Souto raised the question whether phi^* is an automorphism of the affine variety X_n if and only if phi is an automorphism of F_n. I will describe work in progress which relates directly this question to the action of endomorphisms on the outer space CV_n through a compactification of X_n with special valuations.
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-adrien-boyer-julien-marche-greg-patchell/
LOCATION:Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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DTSTART;TZID=Europe/Paris:20260506T110000
DTEND;TZID=Europe/Paris:20260506T120000
DTSTAMP:20260430T182524
CREATED:20260430T081744Z
LAST-MODIFIED:20260430T081744Z
UID:21515-1778065200-1778068800@www.math.ens.psl.eu
SUMMARY:Matteo Tamiozzo\, raconte-moi les groupes de Golod-Shafarevich !
DESCRIPTION:Les groupes de Golod-Shafarevich\, découverts dans les années 60\, ont trouvé des applications en théorie des nombres\, théorie des groupes et topologie. Dans cet exposé j’introduirai ces groupes\, et j’expliquerai le rôle qu’ils jouent dans l’étude des groupes fondamentaux des anneaux des entiers des corps de nombres et des variétés de dimension 3.
URL:https://www.math.ens.psl.eu/evenement/matteo-tamiozzo-raconte-moi-les-groupes-de-golod-shafarevich/
LOCATION:Salle W toits du DMA
CATEGORIES:Algèbre et géométrie,Séminaire Raconte-moi
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DTSTART;TZID=Europe/Paris:20260506T140000
DTEND;TZID=Europe/Paris:20260506T170000
DTSTAMP:20260430T182524
CREATED:20260430T080415Z
LAST-MODIFIED:20260430T081156Z
UID:21503-1778076000-1778086800@www.math.ens.psl.eu
SUMMARY:Un après-midi de théorie des groupes - Elia Fioravanti\, Enrico Le Donne\, Catherine Pfaff
DESCRIPTION:14.00 – 14.45   Elia Fioravanti (KIT – Karlsruhe) « Generators for automorphisms of special groups »15.00 – 15.45   Enrico Le Donne (University of Fribourg) « Asymptotic geometry of Riemannian nilpotent groups »16.15 – 17.00   Catherine Pfaff (Queen’s University) « A « cubist » decomposition of the Handel-Mosher axis bundle » \n\n\n\n \n\n\n\nAbstracts: \n\n\n\nElia Fioravanti: Generators for automorphisms of special groups  \n\n\n\nGiven a family F of finitely generated groups\, do all groups in F have “tame” automorphisms\, or can there be “wild” examples? More concretely\, is Out(G) finitely generated for all groups G in the family F? Rips and Sela showed in the 90s that Out(G) is finitely generated for all Gromov-hyperbolic groups G\, while Baues and Grunewald showed in the 00s that Out(G) is arithmetic over Q (and hence finitely generated) for all virtually polycyclic groups G. This essentially exhausts our limited understanding of general phenomena of this kind\, with the structure of automorphisms of non-positively curved groups remaining a fundamental open problem. I will discuss the recent result that Out(G) is finitely generated for all (cocompact) special groups of Haglund and Wise. This is already new for most finite-index subgroups of right-angled Artin and Coxeter groups. \n\n\n\nEnrico Le Donne: Asymptotic geometry of Riemannian nilpotent groups. \n\n\n\nAsymptotic cones of Riemannian nilpotent Lie groups are Carnot groups. The volume of balls in Carnot groups grows exactly as a power of the radius. Heuristically\, the better the asymptotic cone approximates a Riemannian group\, the closer the volume growth approaches a polynomial growth. I will discuss several results obtained over the last few years in collaboration with Breuillard\, Nalon\, Nicolussi Golo\, and Ryoo. \n\n\n\nCatherine Pfaff: A “cubist” decomposition of the Handel-Mosher axis bundle \n\n\n\nA hyperbolic isometry acts on the compactified hyperbolic plane with North-South dynamics and a single invariant axis. The same is true for a pseudo-Anosov mapping class acting on a Teichmuller space and other hyperbolic-like settings. However\, while a fully irreducible free group outer automorphism acts on compactified Outer space with North-South dynamics\, there can be many axes for a single fully irreducible φ ∈ Out(F_r). With this in mind\, Handel and Mosher define the axis bundle for a fully irreducible φ ∈ Out(F_r). And then Handel-Mosher and Bridson-Vogtmann ask about the geometry of the axis bundle. In joint work with Chi Cheuk Tsang\, we show that the axis bundle of a nongeometric fully irreducible outer automorphism admits a canonical “cubist” decomposition into branched cubes that fit together with special combinatorics. From this structure\, we locate a canonical finite collection of periodic fold lines in each axis bundle. This can be considered as an analogue of results of Hamenstadt and Agol from the surface setting\, which state that the set of trivalent train tracks carrying the unstable lamination of a pseudo-Anosov map can be given the structure of a CAT(0) cube complex\, and that there is a canonical periodic fold line in this cube complex. Our “cubist” decomposition also gives a “hands on” solution to the fully irreducible
URL:https://www.math.ens.psl.eu/evenement/un-apres-midi-de-theorie-des-groupes-elia-fioravanti-enrico-le-donne-catherine-pfaff/
LOCATION:Salle W
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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