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Local Langlands conjectures

In mathematics, the local Langlands conjectures, introduced by Robert Langlands , are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups. (Wikipedia).

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David Ben-Zvi - Between Coherent and Constructible Local Langlands Correspondences

(Joint with Harrison Chen, David Helm and David Nadler.) Refined forms of the local Langlands correspondence seek to relate representations of reductive groups over local fields with sheaves on stacks of Langlands parameters. But what kind of sheaves? Conjectures in the spirit of Kazhdan

From playlist 2022 Summer School on the Langlands program

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Olivier Taïbi - 1/3 The Local Langlands Conjecture

We formulate the local Langlands conjecture for connected reductive groups over local fields, including the internal parametrization of L-packets. Olivier Taïbi (ENS Lyon)

From playlist 2022 Summer School on the Langlands program

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Olivier Taïbi - 3/3 The Local Langlands Conjecture

We formulate the local Langlands conjecture for connected reductive groups over local fields, including the internal parametrization of L-packets. Olivier Taïbi (ENS Lyon)

From playlist 2022 Summer School on the Langlands program

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The Weil-Deligne group, and Langlands parameters.

In this video exploring the local Langlands conjectures, we dive deeper into the definitions of the Langlands L group, and the definition of the Weil-Deligne group, allowing us to get a better sense of what Langlands parameters are, and their connection to Galois representations.

From playlist The local Langlands correspondence

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 16

SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro

From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 18

SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro

From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 21

SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro

From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

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The Geometric Langlands conjecture and non-abelian Hodge theory (Lecture 1) by Ron Donagi

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

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David Helm: Whittaker models, converse theorems, and the local Langlands correspondence for ...

Find other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies,

From playlist Algebraic and Complex Geometry

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Yiannis Sakellaridis - 1/2 Local and Global Questions “Beyond Endoscopy”

The near-completion of the program of endoscopy poses the question of what lies next. These talks will take a broad view of ideas beyond the program of endoscopy, highlighting the connections among them, and emphasizing the relationship between local and global aspects. Central among thos

From playlist 2022 Summer School on the Langlands program

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Kevin Buzzard (lecture 10/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 22

SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro

From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 20

SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro

From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

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The Geometric Langlands conjecture and non-abelian Hodge theory (Lecture 3) by Ron Donagi

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

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Kevin Buzzard (lecture 17/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

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[BOURBAKI 2018] 13/01/2018 - 2/4 - Raphaël BEUZART-PLESSIS

Progrès récents sur les conjectures de Gan-Gross-Prasad [d'après Jacquet-Rallis, Waldspurger, W. Zhang, etc.] Les conjectures de Gan-Gross-Prasad ont deux aspects: localement elles décrivent de façon explicite certaines lois de branchements entre représentations de groupes de Lie réels ou

From playlist BOURBAKI - 2018

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Peter Scholze - 5/6 On the local Langlands conjectures for reductive groups over p-adic fields

Hadamard Lectures 2017 Abstract: Consider a reductive group G over a p-adic field F. The local Langlands conjecture relates the irreducible smooth representations of G(F) with the set of (local) L-parameters, which are maps from the Weil group of F to the L-group of G; refinements of the

From playlist Hadamard Lectures 2017 - Peter Scholze - On the local Langlands conjectures for reductive groups over p-adic fields

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Peter Scholze - 6/6 On the local Langlands conjectures for reductive groups over p-adic fields

Hadamard Lectures 2017 Abstract: Consider a reductive group G over a p-adic field F. The local Langlands conjecture relates the irreducible smooth representations of G(F) with the set of (local) L-parameters, which are maps from the Weil group of F to the L-group of G; refinements of the

From playlist Hadamard Lectures 2017 - Peter Scholze - On the local Langlands conjectures for reductive groups over p-adic fields

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Peter Scholze - 4/6 On the local Langlands conjectures for reductive groups over p-adic fields

Hadamard Lectures 2017 Abstract: Consider a reductive group G over a p-adic field F. The local Langlands conjecture relates the irreducible smooth representations of G(F) with the set of (local) L-parameters, which are maps from the Weil group of F to the L-group of G; refinements of the

From playlist Hadamard Lectures 2017 - Peter Scholze - On the local Langlands conjectures for reductive groups over p-adic fields

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Geordie Williamson: Langlands and Bezrukavnikov II Lecture 19

SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro

From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence

Related pages

Galois group | Langlands group | Langlands–Deligne local constant | Algebraic group | Symplectic group | Mathematics | Weil group | Langlands classification | Local class field theory | (g,K)-module | Langlands program | Bernstein–Zelevinsky classification