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#Galois Representations

Showing: 26 courses
Institute for Advanced Study

First Explicit Reciprocity Law for Unitary Friedberg-Jacquet Periods

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Delve into the first explicit reciprocity law for unitary Friedberg-Jacquet periods. Explore its application to the Bloch-Kato conjecture and challenges arising from lack of local multiplicity one.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institute for Advanced Study

Exceptional Splitting of Reductions of Abelian Surfaces With Real Multiplication - Yunqing Tang

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Explore real multiplication in abelian surfaces, focusing on exceptional splitting of reductions. Delve into simple reduction, finite extension, and density zero concepts with insights on special devices and intersection numbers.
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18 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Advanced Study

A Derived Hecke Algebra in the Context of the Mod P Langlands Program - Rachel Ollivier

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Explore derived Hecke algebras in mod p Langlands program, covering super singular modules, involution, trace maps, and twisted duals with Rachel Ollivier.
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9 Lesons
56 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Galois Representations and Statistics - Lecture 1

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Explore Galois representations and statistics in arithmetic through an advanced mathematical lecture by René Schoof.
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1 Lesons
1 hour
On-Demand
Free-Video
Hausdorff Center for Mathematics

Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry

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Explore p-adic geometry through Riemann-Hilbert correspondence, covering local systems, Galois representations, Hodge theory, and cohomology in this advanced mathematics lecture.
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23 Lesons
53 minutes
On-Demand
Free-Video
ICTP Mathematics

Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art

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Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.
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10 Lesons
55 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Panorama of Mathematics - Peter Scholze

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Explore locally symmetric spaces and Galois representations with Peter Scholze, delving into hyperbolic 3-space, Bianchi manifolds, and non-abelian reciprocity laws in advanced mathematics.
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16 Lesons
50 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 3

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Exploring advanced techniques in arithmetic geometry for analyzing rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its practical applications.
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1 Lesons
1 hour 51 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 2

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Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 4

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Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.
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1 Lesons
1 hour 52 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Finite Slope Part of Overconvergent Cohomology & Coherent Sheaves on Spaces of

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Explores overconvergent cohomology, eigenvarieties, and coherent sheaves in p-adic automorphic forms. Discusses a conjecture on computing coherent sheaves using Galois representation stacks and its relation to p-adic Langlands program.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Weight Part of Serre's Conjecture and the Emerton-Gee Stack

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Explore the Breuil-Mezard conjecture's impact on local deformation rings and its connection to Serre's conjecture, focusing on recent advancements in moduli stack theory and p-adic Galois representations.
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1 Lesons
1 hour
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 3

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Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Fields Institute

Hypergeometric Functions, Galois Representations, and Modular Forms

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Explore connections between hypergeometric functions, Galois representations, and modular forms in advanced number theory and algebraic geometry.
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1 Lesons
39 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Modularity and Monodromy

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Explore the intricate relationship between modularity and monodromy in mathematics, delving into advanced concepts and their applications in number theory and algebraic geometry.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Motives and Automorphic Representations

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Explore motives and automorphic representations in advanced mathematics with James Arthur's insightful conference talk at CIRM.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Stony Brook Mathematics

Computing the Weil Representation of Superelliptic Curves

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Explore the Weil representation of superelliptic curves, focusing on local Galois representations and stable reductions in algebraic geometry.
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1 Lesons
57 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Modularity of Abelian Surfaces

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Explorez la preuve de la modularité d'une proportion positive de surfaces abéliennes sur les rationnels dans cette conférence mathématique avancée.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Sato-Tate Conjecture for Bianchi Modular Forms

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Explore potential automorphy results for Ramanujan and Sato-Tate conjectures in GL(2) over imaginary quadratic fields, extending previous work and introducing new mathematical concepts.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Eigenvarieties and Completed Cohomology in p-adic Automorphic Forms

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Explore connections between eigenvarieties and p-adic cohomology representation theory, focusing on p-adic families of finite slope automorphic eigenforms.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
BIMSA

The Langlands Project - Connecting Automorphic Forms and Number Theory

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Explore the Langlands project's deep connection between automorphic forms and arithmetic, tracing its roots and current challenges in mathematics.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Local Langlands Program and Characteristic p

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Explore the local Langlands program for GLn, focusing on representations in characteristic p and recent developments for GL2(K) in p-adic number theory.
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1 Lesons
58 minutes
On-Demand
Free-Video
BIMSA

Multivariable (φ, Γ)-Modules and Local-Global Compatibility

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Explore multivariable $(\varphi, \Gamma)$-modules, extending Colmez's construction to $\mathrm{GL}_2(K)$ representations and comparing with Galois representations in mod $p$ cohomology of Shimura curves.
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1 Lesons
54 minutes
On-Demand
Free-Video
BIMSA

Towards a Mod p Langlands Correspondence for GL2

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Explore the mod $p$ Langlands correspondence for $\mathrm{GL}_2(K)$, examining conjectures and recent progress in this open area of mathematical research.
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1 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Arithmetic Statistics and the Iwasawa Theory of Elliptic Curves

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Explore arithmetic statistics and Iwasawa theory of elliptic curves, covering Selmer groups, Greenberg's Conjecture, and p-adic Birch and Swinnerton-Dyer Conjecture in this advanced number theory seminar.
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12 Lesons
57 minutes
On-Demand
Free-Video
BunG Seminar

Moduli Spaces of Local Systems in Algebraic Varieties

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Delve into advanced mathematical concepts of local systems and Galois representations, exploring construction methods and parameter spaces in Betti, deRham, and l-adic settings.
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1 Lesons
1 hour 57 minutes
On-Demand
Free-Video