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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Lie Theory and Generalizations 54 results

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Space of actions of groups on the real line - Deroin, Bertrand (Author of the conference) | CIRM H

Multi angle

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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Random processes on symmetric spaces and discrete subgroups - Fraczyk, Mikolaj (Author of the conference) | CIRM H

Multi angle

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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Margulis-Zimmer's super-rigidity - Lee, Homin (Author of the conference) | CIRM H

Multi angle

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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2y

The local Langlands correspondence: functoriality, $L$-functions, gamma functions and the epsilon factors - Prasad, Dipendra (Author of the conference) | CIRM H

Post-edited

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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Lecture 1: Distinction and the geometric lemma - Offen, Omer (Author of the conference) | CIRM H

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11F67 ; 11F70 ; 11F72 ; 22E55

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Lecture 2: Distinction by a symmetric subgroup - Offen, Omer (Author of the conference) | CIRM H

Multi angle

11F67 ; 11F70 ; 11F72 ; 22E55

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2y

Beyond Endoscopy and elliptic terms in the trace formula - Arthur, James Greig (Author of the conference) | CIRM H

Post-edited

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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Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces - Boysal, Arzu (Author of the conference) | CIRM H

Post-edited

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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Homogeneous vector bundles over abelian varieties - Brion, Michel (Author of the conference) | CIRM H

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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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Descent in Bruhat-Tits theory - Prasad, Gopal (Author of the conference) | CIRM H

Post-edited

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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