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In this talk, we consider the limit multiplicity question (and some variants): how many automorphic forms of fixed infinity-type and level N are there as N grows? The question is well-understood when the archimedean representation is a discrete series, and we focus on non-tempered cohomological representations on unitary groups. Using an inductive argument which relies on the stabilization of the trace formula and the endoscopic classification, we give asymptotic counts of multiplicities, and prove the Sarnak-Xue conjecture at split level for (almost!) all cohomological representations of unitary groups. Additionally, for some representations, we derive an average Sato-Tate result in which the measure is the one predicted by functoriality. This is joint work with Rahul Dalal.[-]

In this talk, we consider the limit multiplicity question (and some variants): how many automorphic forms of fixed infinity-type and level N are there as N grows? The question is well-understood when the archimedean representation is a discrete series, and we focus on non-tempered cohomological representations on unitary groups. Using an inductive argument which relies on the stabilization of the trace formula and the endoscopic classification, ...[+]

11F55 ; 11F70 ; 11F72 ; 11F75 ; 22E50

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]

The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]

The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]

The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the deep structure of L-functions and also provides insights into advanced conjectures such as the Riemann hypothesis.[-]

The subconvexity of L-functions aims to refine estimates of central values, going beyond mere convexity. This is important in analytic number theory, especially in the study of the distribution of prime numbers. Researchers seek to establish more precise bounds for these L-functions to better understand prime numbers, particularly by exploring connections with automorphic forms. This approach offers an enriching perspective for understanding the ...[+]

11M41 ; 11F66 ; 11F72

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This is a work with Yves Colin de Verdière, Charlotte Dietze and Maarten De Hoop, motivated by recent works by M. De Hoop on inverse problems for sound wave propagation in gas giant planets. On such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with a boundary whose metric blows up near the boundary. With appropriate variable changes, we can reduce the study of the Laplacian?Beltrami to that of a kind of sub-Riemannian Laplacian. In this talk, I will explain how to approach the spectral analysis of such operators, and in particular how to calculate WeylÕs law.[-]

This is a work with Yves Colin de Verdière, Charlotte Dietze and Maarten De Hoop, motivated by recent works by M. De Hoop on inverse problems for sound wave propagation in gas giant planets. On such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with a boundary whose metric blows up near the boundary. With appropriate variable changes, we can reduce the study of ...[+]

11F72 ; 58C40 ; 53C22 ; 37D40 ; 53C65 ; 35R30

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11F67 ; 11F70 ; 11F72 ; 22E55

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After a brief introduction to the spectral theory of hyperbolic surfaces, we will focus on the problem of understanding the asymptotic distribution of resonances for hyperbolic surfaces. The theory of open quantum chaotic systems has inspired several interesting conjectures about this distribution. We will highlight the recent theoretical progress towards these conjectures, and present some of the latest numerical evidence.

58J50 ; 11F72 ; 11M36

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The metaplectic covering Mp(2n) of Sp(2n) affords an accessible yet nontrivial instance of the Langlands-Weissman program for covering groups. In order to use Arthur's methods in this setting, one needs a stable trace formula for Mp(2n). Thus far, only the elliptic terms have been stabilized. In this talk, I will report an ongoing work on the full stabilization, which is nearing completion. It will hopefully grant access to the whole genuine discrete automorphic spectrum of Mp(2n). Time permitting, I will also try to explain the similarities and subtle differences with the case of linear groups solved by Arthur.[-]

The metaplectic covering Mp(2n) of Sp(2n) affords an accessible yet nontrivial instance of the Langlands-Weissman program for covering groups. In order to use Arthur's methods in this setting, one needs a stable trace formula for Mp(2n). Thus far, only the elliptic terms have been stabilized. In this talk, I will report an ongoing work on the full stabilization, which is nearing completion. It will hopefully grant access to the whole genuine ...[+]

22E50 ; 11F70 ; 11F72

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Documents 11F72 14 résultats

Lecture 3: Period integrals of automorphic forms - Offen, Omer (Auteur de la conférence) | CIRM H Nouveau

Counting non-tempered automorphic forms using endoscopy - Gerbelli-Gauthier, Mathilde (Auteur de la conférence) | CIRM H Nouveau

Subconvexity of L-functions - Part 1 - Michel, Philippe (Auteur de la conférence) | CIRM H Nouveau

Subconvexity of L-functions - Part 2 - Michel, Philippe (Auteur de la conférence) | CIRM H Nouveau

Subconvexity of L-functions - Part 3 - Nelson, Paul (Auteur de la conférence) | CIRM H Nouveau

Subconvexity of L-functions - Part 4 - Nelson, Paul (Auteur de la conférence) | CIRM H Nouveau

From gas giant planets to the spectral theory of subelliptic Laplacians - Trélat, Emmanuel (Auteur de la conférence) | CIRM H Nouveau

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

Asymptotics of resonances for hyperbolic surfaces - Borthwick, David (Auteur de la conférence) | CIRM H Nouveau

Full stable trace formula for the group Mp(2n) - Li, Wen-Wei (Auteur de la conférence) | CIRM H Nouveau