CIRM - Videos & books Library - Lie Theory and Generalizations

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In these lectures, we will report on some properties of the space of actions of a left-orderable group on the real line. We will notably describe the almost-periodic actions, the harmonic actions and their spaces.

20F60 ; 22F50 ; 37B05 ; 37E10 ; 57R30

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I will explain how certain probabilistic methods can be used to study the discrete groups of semisimple Lie groups. I will define the space of subgroups with the Chabauty topology and introduce two useful classes of random subgroups - invariant ans stationary random subgroups. In higher rank thses classes admit nice classification witch can be usesd to prove that a confined subgroup of a simple higher rank group must be a lattice.

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We introduce Margulis' and Zimmer's superrigidity. Statements give heuristics in Zimmer program, that is higher rank lattice actions on smooth manifolds. After we state the statement, we mainly focus how it interacts with group actions. Finally, we will also discuss about open questions.

22E40 ; 57M60

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Spherical Hecke algebra, Satake transform, and an introduction to local Langlands correspondence.
CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

20C08 ; 22E50 ; 11S37

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11F67 ; 11F70 ; 11F72 ; 22E55

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11F67 ; 11F70 ; 11F72 ; 22E55

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Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it pertains to these terms.[-]

Beyond endoscopy is the strategy put forward by Langlands for applying the trace formula to the general principle of functoriality. Subsequent papers by Langlands (one in collaboration with Frenkel and Ngo), together with more recent papers by Altug, have refined the strategy. They all emphasize the importance of understanding the elliptic terms on the geometric side of the trace formula. We shall discuss the general strategy, and how it ...[+]

11F66 ; 22E50 ; 22E55

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Using Szenes formula for multiple Bernoulli series, we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.
This is joint work with V. Baldoni and M. Vergne.

11B68 ; 11M32 ; 11M41 ; 14D20 ; 17B20 ; 17B22 ; 32S22 ; 53D30

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The objects of the talk are the translation-invariant vector bundles over an abelian variety. We will present a representation-theoretic description of these vector bundles, which displays a remarkable analogy with finite-dimensional representations of a compact connected Lie group: the weight lattice is replaced with the dual abelian variety, the Weyl group with the Galois group of the ground field...

14J60 ; 14K05 ; 14L15 ; 20G05

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Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric group scheme. In the case of unramified extension, that descent has been achieved by Bruhat-Tits at the end of [BT2]. The tamely ramified case is due to G. Rousseau [R]. Recently, G. Prasad found a new way to investigate the descent part of the theory. This is available in the preprints [Pr1, Pr2] dealing respectively with the unramified case and the tamely ramified case. It is much shorter and the method is based more on fine geometry of the building (e.g. galleries) than algebraic groups techniques.[-]

Bruhat-Tits theory applies to a semisimple group G, defined over an henselian discretly valued field K, such that G admits a Borel K-subgroup after an extension of K. The construction of the theory goes then by a deep Galois descent argument for the building and also for the parahoric group scheme. In the case of unramified extension, that descent has been achieved by Bruhat-Tits at the end of [BT2]. The tamely ramified case is due to G. ...[+]

20G15 ; 20E42 ; 51E24

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Lie Theory and Generalizations 54 résultats

Space of actions of groups on the real line - Deroin, Bertrand (Auteur de la Conférence) | CIRM H Nouveau

Random processes on symmetric spaces and discrete subgroups - Fraczyk, Mikolaj (Auteur de la Conférence) | CIRM H Nouveau

Margulis-Zimmer's super-rigidity - Lee, Homin (Auteur de la Conférence) | CIRM H Nouveau

The local Langlands correspondence: functoriality, $L$-functions, gamma functions and the epsilon factors - Prasad, Dipendra (Auteur de la Conférence) | CIRM H Nouveau

Lecture 1: Distinction and the geometric lemma - Offen, Omer (Auteur de la Conférence) | CIRM H Nouveau

Lecture 2: Distinction by a symmetric subgroup - Offen, Omer (Auteur de la Conférence) | CIRM H Nouveau

Beyond Endoscopy and elliptic terms in the trace formula - Arthur, James Greig (Auteur de la Conférence) | CIRM H Nouveau

Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces - Boysal, Arzu (Auteur de la Conférence) | CIRM H Nouveau

Homogeneous vector bundles over abelian varieties - Brion, Michel (Auteur de la Conférence) | CIRM H Nouveau

Descent in Bruhat-Tits theory - Prasad, Gopal (Auteur de la Conférence) | CIRM H Nouveau