Algebraic number theory

Cyclotomic character

In number theory, a cyclotomic character is a character of a Galois group giving the Galois action on a group of roots of unity. As a one-dimensional representation over a ring R, its representation space is generally denoted by R(1) (that is, it is a representation χ : G → AutR(R(1)) ≈ GL(1, R)). (Wikipedia).

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Cycloid

#Cycloid: A curve traced by a point on a circle rolling in a straight line. (A preview of this Sunday's video.)

From playlist Miscellaneous

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The Cycloid - The Helen of Geometry

This video defines, shows how a cycloid is formed, and explains 4 interesting properties of a cycloid. http://mathispower4u.com

From playlist Mathematics General Interest

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Typos noted by commenters: 7:45 - should be alpha is minimal over Q. 8:45 - Number 1, last line should read phi(alpha*beta) = phi(alpha)*phi(beta) Field Theory: We define cyclotomic polynomial as the minimal polynomials of roots of unity over the rationals. We show that the roots of t

From playlist Abstract Algebra

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Logical difficulties with cyclotomic fields | Famous Math Problems 20c | N J Wildberger

The irreducibility of the general cyclotomic polynomials goes back to a lot of 19th century work starting with Gauss -- but unfortunately there are serious logical problems, arising from the temptation to embed cyclotomic fields, generated by so called "roots of unity", into the complex nu

From playlist Famous Math Problems

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Calculus 2: Parametric Equations (10 of 20) What is a Cycloid? - Rolling Wheel

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain something unique to parametric equations for finding the positions of x and y. This involves a point on the edge of a rolling wheel tracing out a cycloid “shape” on a graph. Next video in the

From playlist CALCULUS 2 CH 17 PARAMETRIC EQUATIONS

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Trigonometry - Vocabulary of trigonometric functions

In this video will cover some of the basic vocabulary that you'll hear when working with trigonometric functions. Specifically we'll cover what is trigonometry, angles, and defining the trigonometric functions as ratios of sides. You'll hear these terms again as we dig deeper into the st

From playlist Trigonometry

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What are four types of polygons

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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What are the names of different types of polygons based on the number of sides

👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1

From playlist Classify Polygons

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Anabelian Geometry - Inertia and Decomposition Groups (Part 1)

We discuss the statements about the recovery of inertia and decomposition groups of cusps. We will give proofs in the number field case of some statements. Proofs for finite extensions of QQ_p appear later. Twitter: @DupuyTaylor

From playlist Anabelian Geometry

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Kevin Buzzard (lecture 12/20) 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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A converse to a theorem of Gross--Zagier, Kolyvagin and Rubin, II - Ashay Burungale

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From playlist Mathematics

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Peter Stevenhagen: Character sums for primitive root densities

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From playlist Jean-Morlet Chair - Shparlinski/Kohel

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Florian Herzig: On de Rham lifts of local Galois representations

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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Inertia and Decomposition Groups (part 2)

A continuation of the previous video.

From playlist Anabelian Geometry

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Kevin Buzzard (lecture 16/20) Automorphic Forms And The Langlands Program [2017]

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

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From playlist Perfectoid Spaces 2019

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From playlist Mathematics

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Group representation | Inverse limit | Algebraic torus | Group (mathematics) | Compatible system of ℓ-adic representations | Tate twist | Duality (mathematics) | Rational number | Projective variety | Projective line | Ring (mathematics) | Motive (algebraic geometry) | Tate module | Number theory | Absolute Galois group | Galois group | Prime number | Group homomorphism | Character (mathematics) | P-adic number | Étale cohomology