In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the subring Z[a] of K generated by a. Then OK is a quotient of the polynomial ring Z[X] and the powers of a constitute a power integral basis. In a monogenic field K, the field discriminant of K is equal to the discriminant of the minimal polynomial of α. (Wikipedia).
Ari Shnidman: Monogenic cubic fields and local obstructions
Recording during the meeting "Zeta Functions" the December 05, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http:
From playlist Number Theory
Monoclonal Antibodies | Health | Biology | FuseSchool
Antibodies are the warriors inside our body. They are part of our immune system, recognising and fighting against bad foreign invaders, called antigens. Antibodies can bind to a broad range of antigens, and are produced by cells of the immune system, known as B-cells. To learn more about
From playlist BIOLOGY: Health
On Class Groups of Monogenic Fields
Short Talks by Postdoctoral Members Topic: On Class Groups of Monogenic Fields Speaker: Artane Jeremie Siad Affiliation: Member, School of Mathematics September 30, 2022
From playlist Short Talks by Postdoctoral Members
Immunology wars: Monoclonal antibodies
Our immune systems are at war with cancer. This animation reveals how monoclonal antibodies can act as valuable reinforcements to shore up our defences – and help battle cancer. You can find more on this topic at http://www.nature.com/milestones/antibodies Nature Research has full resp
From playlist Health
Hank examines the zoological definition of monogamy, as well as some other breeding strategies that animals use. Like SciShow on Facebook: http://www.facebook.com/scishow Follow SciShow on Twitter: http://www.twitter.com/scishow References women give kids more genes than men: http://www.
From playlist Biology
Multivariable Calculus | What is a vector field.
We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
GCSE Science Biology "Monoclonal Antibodies" (Triple)
Find my revision workbooks here: https://www.freesciencelessons.co.uk/workbooks In this video, we look at monoclonal antibodies. We find out what is meant by a monoclonal antibody and then how these are produced. This is for Triple Biology Higher students. Image credit: Lab mouse "https
From playlist 9-1 GCSE Biology Paper 1 Infectious Diseases
Non-monogenic Division Fields of Elliptic Curves, Hanson Smith
Abstract: This talk will serve as an exposition of a recent preprint investigating the division fields of elliptic curves. In this work we show that for various positive integers n there exist of infinite families of elliptic curves over Q with n-division fields, Q(E[n]), that are not mono
From playlist My Students
Monogenic fields with odd class number - Artane Jeremie Siad
Joint IAS/Princeton University Number Theory Seminar Topic: Monogenic fields with odd class number Speaker: Artane Jeremie Siad Affiliation: Princeton University; Visitor, School of Mathematics Date: November 4, 2021 In this talk, we prove an upper bound on the average number of 2-torsi
From playlist Mathematics
Arul Shankar, Ordering elliptic curves by conductor
VaNTAGe seminar, on Oct 27, 2020 License: CC-BY-NC-SA. Closed captions provided by Rachana Madhukara.
From playlist Rational points on elliptic curves
Counting Low Degree Number Fields with Almost Prescribed Successive Minima - Sameera Vemulapalli
Joint IAS/PU Number Theory Seminar Topic: Counting Low Degree Number Fields with Almost Prescribed Successive Minima Speaker: Sameera Vemulapalli Affiliation: Princeton University Date: January 26, 2023 The successive minima of an order in a degree n number field are n real numbers encod
From playlist Mathematics
Kristin Lauter, Microsoft Research Redmond The Mathematics of Modern Cryptography http://simons.berkeley.edu/talks/kristin-lauter-2015-07-07
From playlist My Collaborators
Affine symmetric spaces and 2-torsion in the class group of unit-monogenized cubic... - Artane Siad
Spring Opportunities Workshop 2023 Topic: Affine symmetric spaces and 2-torsion in the class group of unit-monogenized cubic fields Speaker:Artane Siad Affiliation: IAS Date: January 13, 2023 Davenport’s lemma has been a crucial ingredient in recent applications of geometry of numbers
From playlist Spring Opportunities Workshop 2023
CTNT 2018 - "The Tsfasman-Vladut Generalization of the Brauer-Siegel Theorem" by Farshid Hajir
This is lecture on "The Tsfasman-Vladut Generalization of the Brauer-Siegel Theorem", by Farshid Hajir (UMass Amherst), during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - Guest Lectures
Category Theory 10.2: Monoid in the category of endofunctors
Monad as a monoid in the category of endofunctors
From playlist Category Theory
CTNT 2022 - Algebraic Number Theory (Lecture 4) - by Hanson Smith
This video is part of a mini-course on "Algebraic Number Theory" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Algebraic Number Theory (by Hanson Smith)
What is the definition of a monomial and polynomials with examples
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials