Cyclotomic fields | Algebraic number theory
In number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory because of their relation with Fermat's Last Theorem. It was in the process of his deep investigations of the arithmetic of these fields (for prime n) – and more precisely, because of the failure of unique factorization in their rings of integers – that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated congruences. (Wikipedia).
#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
Physics - E&M: Ch 36.1 The Electric Field Understood (1 of 17) What is an Electric Field?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an electric field. An electric field exerts a force on a charged place in the field, can be detected by placing a charged in the field and observing the effect on the charge. The stren
From playlist THE "WHAT IS" PLAYLIST
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
What is a cyclotron, the physics behind its working and why.
This video discusses the working of the cyclotron, the physics principles - the use of electric and magnetic fields to speed up charged particles - and uses the example of ANSTO National Research Cyclotron in Sydney in Australia. SEE MY VIDEO ON THE ANSTO CYCLOTRON : https://youtu.be/ot1
From playlist Electromagnetism
Physics 36 The Electric Field (5 of 18) The Electric Dipole
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the electric field of the electric dipole.
From playlist PHYSICS 22 E&M THE ELECTRIC FIELD
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
Electric Field (2 of 3) Calculating the Magnitude and Direction of the Electric Field
Explains how to calculate the electric field of a charged particle and the acceleration of an electron in the electric field. You can see a listing of all my videos at my website, http://www.stepbystepscience.com An electric field is an area that surrounds an electric charge, and exerts f
From playlist Electricity and Magnetism
Electric Field (1 of 3) An Explanation
Explains how to determine the direction and magnitude of the electric field from charged particles. You can see a listing of all my videos at my website, http://www.stepbystepscience.com An electric field is an area that surrounds an electric charge, and exerts force on other charges in t
From playlist Electricity and Magnetism
Iwasawa theory of the fine Selmer groups of Galois representations by Sujatha Ramdorai
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
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
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]
Inertia and Decomposition Groups (part 2)
A continuation of the previous video.
From playlist Anabelian Geometry
Field Theory - Cyclotomic Fields in CC - Lecture 12
In this video we define primitive roots of unity, explain why there are phi(n) primitive nth roots of unity, and show how to compute Phi_n(x) the nth cyclotomic polynomials.
From playlist Field Theory
A converse to a theorem of Gross--Zagier, Kolyvagin and Rubin, II - Ashay Burungale
Joint IAS/Princeton University Number Theory Seminar Topic: A converse to a theorem of Gross--Zagier, Kolyvagin and Rubin, II Speaker: Ashay Burungale Affiliation: Universite Paris 13; Member, School of Mathematics Date: May 1, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
CTNT 2020 - Infinite Galois Theory (by Keith Conrad) - Lecture 4
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Infinite Galois Theory (by Keith Conrad)
Physics - E&M: Magn Field Effects on Moving Charge & Currents (21 of 26) The Cyclotron
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the kinetic energy of an alpha particle in a cyclotron.
From playlist PHYSICS E&M 3: MAGNETIC FIELDS, MAGNETIC FORCES, MAGNETIC FIELD SOURCES, ELECTROMAGNETIC INDUCTION
Peter Stevenhagen: Character sums for primitive root densities
Find this video and 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, b
From playlist Jean-Morlet Chair - Shparlinski/Kohel
Non-commutative Twisted Euler characteristic in Iwasawa theory by Sudhanshu Shekhar
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Two mathematicians, their work and career experiences: Radhika Ganapathy and Purvi Gupta
OUTREACH ACTIVITY TWO MATHEMATICIANS, THEIR WORK AND CAREER EXPERIENCES: ON OCCASION OF INTERNATIONAL WOMEN IN MATHEMATICS DAY (ONLINE) SPEAKER: Radhika Ganapathy (Indian Institute of Science, Bangalore) and Purvi Gupta (Indian Institute of Science, Bangalore) WHEN: 9:30 am to 12:45 pm
From playlist OUTREACH ACTIVITY
Field Theory - Splitting Fields in CC - Lecture 11
In this video we compute some examples of splitting fields over CC. These include a Kummer field, a cyclotomic field, a quadratic field, and some real cubic field.
From playlist Field Theory