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# Documents  Prasad, Dipendra | enregistrements trouvés : 13

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## The local Langlands correspondence: functoriality, $L$-functions, gamma functions and the epsilon factors Prasad, Dipendra | CIRM H

Post-edited

Research schools;Lie Theory and Generalizations;Number Theory

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

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## Beyond Endoscopy and elliptic terms in the trace formula Arthur, James Greig | CIRM H

Post-edited

Research talks;Lie Theory and Generalizations;Number Theory

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 ...

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Post-edited

Outreach;Mathematics Education and Popularization of Mathematics

Jean-Morlet Chair 2016: Cirm is delighted to welcome Dipendra Prasad (Tata Institute of Fundamental Research in Mumbai) and Volker Heiermann (I2M Marseille) for six months.
Five scientific events are scheduled at CIRM between January and June 2016 and a range of worldwide guests will be invited over this period.
CIRM - Chaire Jean-Morlet 2016 - Aix-Marseille Université

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## Lecture 1: Distinction and the geometric lemma Offen, Omer | CIRM H

Multi angle

Research schools;Lie Theory and Generalizations;Number Theory

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## Lecture 2: Distinction by a symmetric subgroup Offen, Omer | CIRM H

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Research schools;Lie Theory and Generalizations;Number Theory

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## Lecture 3: Period integrals of automorphic forms Offen, Omer | CIRM H

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Research schools;Lie Theory and Generalizations;Number Theory

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## Lecture 4: The relative trace formula Offen, Omer | CIRM H

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Research schools;Number Theory;Topology

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## Tame relatively supercuspidal representations Murnaghan, Fiona | CIRM H

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Research talks;Lie Theory and Generalizations;Number Theory

Let G be a connected reductive p-adic group that splits over a tamely ramified extension. Let H be the fixed points of an involution of G. An irreducible smooth H-distinguished representation of G is H-relatively supercuspidal if its relative matrix coefficients are compactly supported modulo H Z(G). (Here, Z(G) is the centre of G.) We will describe some relatively supercuspidal representations whose cuspidal supports belong to the supercuspidals constructed by J.K. Yu. Let G be a connected reductive p-adic group that splits over a tamely ramified extension. Let H be the fixed points of an involution of G. An irreducible smooth H-distinguished representation of G is H-relatively supercuspidal if its relative matrix coefficients are compactly supported modulo H Z(G). (Here, Z(G) is the centre of G.) We will describe some relatively supercuspidal representations whose cuspidal supports belong to the supe...

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## Congruent number problem and BSD conjecture Zhang, Shou-Wu | CIRM H

Multi angle

Research talks;Number Theory

A thousand years old problem is to determine when a square free integer $n$ is a congruent number ,i,e, the areas of right angled triangles with sides of rational lengths. This problem has a some beautiful connection with the BSD conjecture for elliptic curves $E_n : ny^2 = x^3 - x$. In fact by BSD, all $n= 5, 6, 7$ mod $8$ should be congruent numbers, and most of $n=1, 2, 3$ mod $8$ should not be congruent numbers. Recently, Alex Smith has proved that at least 41.9% of $n=1,2,3$ satisfy (refined) BSD in rank $0$, and at least 55.9% of $n=5,6,7$ mod $8$ satisfy (weak) BSD in rank $1$. This implies in particular that at last 41.9% of $n=1,2,3$ mod $8$ are not congruent numbers, and 55.9% of $n=5, 6, 7$ mod $8$ are congruent numbers. I will explain the ingredients used in Smith's proof: including the classical work of Heath-Brown and Monsky on the distribution F_2 rank of Selmer group of E_n, the complex formula for central value and derivative of L-fucntions of Waldspurger and Gross-Zagier and their extension by Yuan-Zhang-Zhang, and their mod 2 version by Tian-Yuan-Zhang. A thousand years old problem is to determine when a square free integer $n$ is a congruent number ,i,e, the areas of right angled triangles with sides of rational lengths. This problem has a some beautiful connection with the BSD conjecture for elliptic curves $E_n : ny^2 = x^3 - x$. In fact by BSD, all $n= 5, 6, 7$ mod $8$ should be congruent numbers, and most of $n=1, 2, 3$ mod $8$ should not be congruent numbers. Recently, Alex Smith has ...

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## The local Gan-Gross-Prasad conjecture for unitary groups Beuzart-Plessis, Raphaël | CIRM H

Multi angle

Research talks;Lie Theory and Generalizations;Number Theory

The local Gan-Gross-Prasad conjectures concern certain branching or restriction problems between representations of real or p-adic Lie groups. In its simplest form it predicts certain multiplicity-one results for "extended" L-packets. In a recent series of papers, Waldspurger has settled the conjecture for special orthogonal groups over p-adic field. In this talk, I will present a proof of the conjecture for unitary groups which has the advantage of working equally well over archimedean and non-archimedean fields. The local Gan-Gross-Prasad conjectures concern certain branching or restriction problems between representations of real or p-adic Lie groups. In its simplest form it predicts certain multiplicity-one results for "extended" L-packets. In a recent series of papers, Waldspurger has settled the conjecture for special orthogonal groups over p-adic field. In this talk, I will present a proof of the conjecture for unitary groups which has the ...

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## Theta lifts of tempered representations and Langlands parameters Gan, Wee Teck | CIRM H

Multi angle

Research talks;Lie Theory and Generalizations;Number Theory

In joint work with Hiraku Atobe, we determine the theta lifting of irreducible tempered representations for symplectic-metaplectic-orthogonal and unitary dual pairs in terms of the local Langlands correspondence. The main new tool for proving our result is the recently established local Gross-Prasad conjecture.

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## Relative aspects in representation theory, Langlands functoriality and automorphic forms.CIRM Jean Morlet Chair, Spring 2016 Heiermann, Volker ; Prasad, Dipendra | Springer;Société Mathématique de France 2018

Ouvrage

- vii; 361 p.
ISBN 978-3-319-95230-7

Lecture notes in mathematics , 2221

Localisation : Collection 1er étage

Chaire Jean-Morlet # CIRM # théorie des nombres # groupe topologique # structure ordonnée # variable complexe # géométrie algébrique

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## Sur les conjectures de Gross et Prasad. I Gan, Wee Teck ; Gross, Benedict H. ; Prasad, Dipendra ; Waldspurger, Jean-Loup | Société Mathématique de France 2012

Ouvrage

- xi; 318 p.
ISBN 978-2-85629-348-5

Astérisque , 0346

Localisation : Périodique 1er étage

Conjectures de Gross-Prasad # conjecture locale de Gross-Prasad # correspondence thêta # groupes classiques # groupes métaplectiques # groupes spéciaux orthogonaux # groupes unitaires # L-valeur centrale critique # lois de branchement # multiplicité 1 # nombres de racines locales # représentations tempérées # supercuspidales de profondeur zéro

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