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#Galois Theory

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Institut des Hautes Etudes Scientifiques (IHES)

Hidden Symmetries of the Work of Jan Nekovář

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Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Equações de Grau Cinco

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Explore a complexidade das equações de grau cinco e suas soluções, aprofundando-se em conceitos matemáticos avançados e suas implicações teóricas.
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1 Lesons
40 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 3

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Explore semisimple braided tensor categories, their structure, and classification. Delve into centralizers, non-degeneracy, equivariantizations, and the core of braided fusion categories.
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1 Lesons
53 minutes
On-Demand
Free-Video
CIMPA UCR

Contando Cuerpos de Números Algebraicos

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Explora la teoría de cuerpos de números algebraicos y sus aplicaciones en matemáticas avanzadas. Profundiza en conceptos fundamentales y técnicas de conteo.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Méthodes Galoisiennes Appliquées aux Équations Fonctionnelles

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Explorez les méthodes galoisiennes appliquées aux équations fonctionnelles en mathématiques avancées. Approfondissez vos connaissances avec cette conférence spécialisée du CIRM.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Le dernier théorème de Fermat

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Plongez dans l'histoire fascinante et la résolution du célèbre théorème de Fermat, un défi mathématique qui a intrigué les esprits pendant plus de trois siècles.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Advanced Study

Sheaves on Graphs, the Hanna Neumann Conjecture, and Algebraic Geometry Applications

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Explore advanced graph theory concepts through sheaf theory and the Hanna Neumann conjecture, featuring innovative problem-solving approaches and applications in discrete mathematics.
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1 Lesons
2 hours 6 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Class Field Theory Standpoint and Its Three Fundamental Generalisations - Lecture 2

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Delve into advanced class field theory concepts, exploring Takagi's existence theory, Mochizuki's IUT theory, and modern perspectives on Langlands program and anabelian geometry.
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1 Lesons
2 hours 2 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Tau of Ramanujan by Eknath Ghate

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Explore Ramanujan's tau-function, its significance in Number Theory, and recent developments. Discover intriguing patterns and open problems in this fascinating mathematical sequence.
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27 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program

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Explore the Langlands Program, connecting automorphic forms and representation theory in advanced mathematics, with insights from James Arthur of the University of Toronto.
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1 Lesons
59 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 18

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Explore the Langlands Program through automorphic forms and representation theory, delving into advanced mathematical concepts and their interconnections.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 14

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Explore the Langlands Program, connecting automorphic forms and representation theory in advanced mathematics, with insights from James Arthur of the University of Toronto.
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1 Lesons
53 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 3

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Explore the Langlands Program through automorphic forms and representation theory, delving into advanced mathematical concepts and their interconnections.
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1 Lesons
43 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 8

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Explore the Langlands Program, connecting automorphic forms and representation theory in advanced mathematics, with insights from James Arthur.
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1 Lesons
45 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 7

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Explore the Langlands Program through automorphic forms and representation theory, delving into advanced mathematical concepts and their interconnections.
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1 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 6

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Explore the Langlands Program, connecting automorphic forms and representation theory in advanced mathematics, with insights from James Arthur of the University of Toronto.
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1 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 5

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Explore the Langlands Program, connecting automorphic forms and representation theory in advanced mathematics, with insights from James Arthur of the University of Toronto.
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1 Lesons
53 minutes
On-Demand
Free-Video
Mathemaniac

Why You Can't Solve Quintic Equations - Galois Theory Approach

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Explore the fascinating world of Galois theory and discover why quintic equations can't be solved using a formula, with insights accessible to math enthusiasts of all levels.
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9 Lesons
45 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 1

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Explore advanced techniques for studying rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its theoretical and practical applications in arithmetic geometry.
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1 Lesons
1 hour 54 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Rational Points on Modular Curves - Lecture 2

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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 35 minutes
On-Demand
Free-Video
Insights into Mathematics

Galois Theory I - Introduction to Polynomial Equations and Symmetries

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Explore Galois theory's insights into solving polynomial equations, from quadratic to quartic, and the historical development of algebraic problem-solving techniques.
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7 Lesons
44 minutes
On-Demand
Free-Video
Insights into Mathematics

Logical Difficulties with Cyclotomic Fields - Famous Math Problems 20

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Explores logical issues in cyclotomic fields, focusing on the challenges of embedding roots of unity into complex numbers and the limitations of purely algebraic approaches.
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1 Lesons
29 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Linear Representations of the Grothendieck-Teichmuller Group

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Explore linear representations of the Grothendieck-Teichmuller group in this advanced mathematics lecture, delving into complex algebraic and geometric concepts.
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1 Lesons
46 minutes
On-Demand
Free-Video
Fields Institute

Ranks of Elliptic Curves in Cyclic Sextic Extensions of Q

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Explore elliptic curve ranks in cyclic sextic extensions of Q, delving into advanced number theory concepts and their applications in algebraic geometry.
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1 Lesons
22 minutes
On-Demand
Free-Video
Fields Institute

Artin's Primitive Root Conjecture

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Explore Artin's primitive root conjecture with Kumar Murty, delving into its mathematical significance and implications for number theory and algebraic structures.
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1 Lesons
44 minutes
On-Demand
Free-Video
Michael Penn

Solving Quintic Equations - Mathematical Misconceptions

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Discover the method to solve any quintic equation in this engaging tutorial. Learn advanced algebraic techniques and expand your mathematical problem-solving skills.
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1 Lesons
23 minutes
On-Demand
Free-Video
Fields Institute

Galois Groups of Lacunary Sparse Polynomial Systems

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Explore Galois groups in lacunary sparse polynomial systems, examining their properties and applications in algebraic geometry and number theory.
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1 Lesons
45 minutes
On-Demand
Free-Video
Fields Institute

Exponential Relations Among Algebraic Integer Conjugates

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Explore exponential relations between algebraic integer conjugates, delving into advanced number theory concepts and their implications in mathematical research.
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1 Lesons
17 minutes
On-Demand
Free-Video
Fields Institute

Essential Dimension in Algebra

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Explore the concept of essential dimension in algebra, its applications, and recent developments with renowned mathematician Alexander Merkurjev from UCLA.
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1 Lesons
41 minutes
On-Demand
Free-Video
Fields Institute

Iwasawa Theory in a Family of Z_p-Extensions

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Explore advanced number theory concepts, focusing on Iwasawa theory in Z_p-extensions families. Gain insights from expert Sujatha Ramdorai on this specialized mathematical topic.
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1 Lesons
44 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Locality Galois Group of Meromorphic Germs in Several Variables

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Explore the structure of meromorphic germs in several variables through locality algebras, focusing on multiple zeta functions and Feynman integrals. Discover applications in analytic renormalisation.
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1 Lesons
45 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Irreducibility of Random Polynomials

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Explore irreducibility of random polynomials in this advanced mathematical lecture, delving into probability theory and algebraic concepts.
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1 Lesons
49 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Galois Extensions and Galois Groups - Lecture 14

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Explore Galois extensions and groups, delving into fundamental concepts and initial examples in algebraic theory.
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1 Lesons
31 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Existence Theorem for Finite Fields

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Explore the existence theorem for finite fields, proving their existence for every prime power order.
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1 Lesons
15 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Subfields of a Finite Field

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Explore the concept of subfields within finite fields, understanding their properties and significance in abstract algebra and number theory.
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1 Lesons
12 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Solvable Groups: Polynomial Solvability and Galois Theory - Part 1

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Explore solvable groups, their connection to polynomial solvability, and their applications in Galois theory and field theory.
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1 Lesons
27 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

The Fundamental Theorem of Galois Theory - Lecture 1

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Explore the fundamental theorem of Galois Theory, delving into its core principles and applications in algebraic structures.
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1 Lesons
24 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Solvability by Radicals - Lecture 37

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Explore solvability by radicals, examining examples and radical extensions to deepen understanding of algebraic problem-solving techniques.
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1 Lesons
37 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Minimal Torsion Curves in Geometric Isogeny Classes

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Explore minimal torsion curves in geometric isogeny classes, delving into advanced number theory concepts and computational techniques.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Endomorphism Algebras of Geometrically Split Abelian Surfaces over Q

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Explore endomorphism algebras of geometrically split abelian surfaces over Q in this advanced mathematics talk. Delve into complex algebraic geometry and number theory concepts.
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1 Lesons
47 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Hecke Algebras for p-adic Groups and the Explicit Local Langlands Correspondence

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Explore Hecke algebras for p-adic groups and the explicit Local Langlands Correspondence in this advanced mathematics lecture by Yujie Xu at CIRM's thematic meeting.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Finite Flat Group Schemes over Z

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Explore finite flat group schemes over Z with René Schoof in this advanced arithmetic geometry lecture from the CIRM Symposium.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Counting S4 and S5 Extensions Satisfying the Hasse Norm Principle

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Explore counting techniques for S4 and S5 extensions satisfying the Hasse norm principle in this advanced mathematical lecture by Rachel Newton.
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1 Lesons
56 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Beyond the Fontaine-Wintenberger Theorem

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Explore advanced mathematical concepts beyond the Fontaine-Wintenberger theorem in this in-depth conference talk by Konstantinos Kartas.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Arithmetic Statistics: Concepts and Applications

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Explore arithmetic statistics through an in-depth lecture, covering key concepts and recent developments in this mathematical field.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Class Field Theory - Lecture 1

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Explore fundamental concepts of class field theory in this advanced mathematics lecture, delving into algebraic number theory and Galois theory.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Frobenius Distributions - Lecture 1

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Explore Frobenius distributions in arithmetic statistics through an advanced mathematical lecture by Kiran Kedlaya at CIRM's Spring School.
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1 Lesons
50 minutes
On-Demand
Free-Video
Institute for Advanced Study

Determinants of Cohomology for Number Fields

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Explore determinants of cohomology in number fields, delving into advanced mathematical concepts and their applications in algebraic number theory.
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1 Lesons
18 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Prime, Knots and the Adele Class Space

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Explore geometric connections between primes and knots through scaling site theory, adele class space, and finite abelian extensions of Q, revealing insights into number theory and topology.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Motives and Super-Representation Theory: Principles and Case Studies

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Découvrez les principes et études de cas des motifs et de la (super-)théorie des représentations, explorant la théorie de Galois motivique abstraite.
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1 Lesons
56 minutes
On-Demand
Free-Video
Banach Center

Mathematical Grand Unification

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Explore the concept of mathematical grand unification through a thought-provoking lecture by Bartosz Naskręcki, delving into conjectures and potential connections across mathematical fields.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Kyoto-U OCW - Unofficial

Frobenius写像の周辺 - 第2回

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Delve into advanced mathematical concepts of Frobenius mappings, finite fields, and Witt vectors through an accessible exploration of number theory fundamentals and polynomial rings.
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6 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Math TAU

תורת גלואה - עבר ועתיד

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חקור את תורת גלואה, התפתחותה ההיסטורית והשלכותיה העתידיות בתחום המתמטיקה המתקדמת.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 5: Witt Equivalence and Categorical Witt Group

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Explore advanced concepts in braided fusion categories, including gauging, Picard groups, Witt equivalence, and categorical Witt groups. Suitable for graduate-level mathematics students.
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1 Lesons
50 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 4

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Explore algebraic theory of semisimple braided tensor categories, covering properties, examples, centralizers, equivariantizations, gauging, and Witt equivalence. Suitable for graduate students.
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9 Lesons
50 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 2

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Explore algebraic theory of semisimple braided tensor categories, covering structure, classification, and applications in quantum symmetries and topological quantum field theories.
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11 Lesons
53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 1

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Explore semisimple braided tensor categories, their structure, and classification. Learn about centralizers, non-degeneracy, equivariantizations, gauging, and Witt equivalence in fusion categories.
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1 Lesons
57 minutes
On-Demand
Free-Video
BunG Seminar

Shtukas and Global Langlands for Function Fields - Talk 37

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Delve into V. Lafforgue's groundbreaking proof of global Langlands correspondence, exploring shtukas, geometric Satake, and excursion operators in function fields through expert analysis.
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1 Lesons
2 hours 7 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Uniqueness of Splitting Fields

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Explore the concept of uniqueness in splitting fields, examining their properties and significance in abstract algebra.
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1 Lesons
15 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Separable Extensions: Multiple Roots, Derivatives, and Inseparable Polynomials - Part 1

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Explore separable extensions, multiple roots, derivatives, and inseparable polynomials in field theory, enhancing understanding of algebraic structures.
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1 Lesons
30 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

First Order Differential Equations in Characteristic Zero and Characteristic p

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Explore advanced mathematical concepts of first-order differential equations across characteristic zero and characteristic p, with insights from leading mathematician Marius van der Put.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video