Irreducibility (Eisenstein's Irreducibility Criterion)
Given a polynomial with integer coefficients, we can determine whether it's irreducible over the rationals using Eisenstein's Irreducibility Criterion. Unlike some our other technique, this works for polynomials of high degree! The tradeoff is that it works over the rationals, but need not
From playlist Modern Algebra - Chapter 11
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
Alina Ostafe: Dynamical irreducibility of polynomials modulo primes
Abstract: In this talk we look at polynomials having the property that all compositional iterates are irreducible, which we call dynamical irreducible. After surveying some previous results (mostly over finite fields), we will concentrate on the question of the dynamical irreducibility of
From playlist Number Theory Down Under 9
Abstract Algebra | Irreducible polynomials
We introduce the notion of an irreducible polynomial over the ring k[x] where k is any field. A proof that p(x) is irreducible if and only if (p(x)) is maximal is also given, along with some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal W
From playlist Abstract Algebra
RNT2.6.2. Eisenstein's Criterion
Ring Theory: Continuing with Gauss' Lemma, we prove Eisenstein's Criterion for Irreducibility and that R UFD implies R[x] UFD. As an example of EC, we show that f(x) = x^4+x^3+x^2+x+1 is irreducible over the integers using substitution.
From playlist Abstract Algebra
Anthony Licata: Hilbert Schemes Lecture 7
SMRI Seminar Series: 'Hilbert Schemes' Lecture 7 Kleinian singularities 2 Anthony Licata (Australian National University) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students inter
From playlist SMRI Course: Hilbert Schemes
The cohomology groups...Jacobians of planar curves - Luca Migliorini
Luca Migliorini University of Bologna; Member, School of Mathematics February 18, 2015 I will first discuss a relation between the cohomology groups (with rational coefficients) of the compactified Jacobian and those of the Hilbert schemes of a projective irreducible curve CC with planar
From playlist Mathematics
Symplectic forms in algebraic geometry - Giulia Saccà
Giulia Saccà Member, School of Mathematics January 30, 2015 Imposing the existence of a holomorphic symplectic form on a projective algebraic variety is a very strong condition. After describing various instances of this phenomenon (among which is the fact that so few examples are known!)
From playlist Mathematics
This lecture is part of an online course on rings and modules. We prove Hilbert's theorem that poynomial rings over fields are Noetherian, and use this to prove Hilbert's theorem about finite generation of algebras of invariants, at least for finite groups over the complex numbers. For
From playlist Rings and modules
Lecture 24. Hilbert basis theorem
From playlist Abstract Algebra 2
Brent Pym: Holomorphic Poisson structures - lecture 3
The notion of a Poisson manifold originated in mathematical physics, where it is used to describe the equations of motion of classical mechanical systems, but it is nowadays connected with many different parts of mathematics. A key feature of any Poisson manifold is that it carries a cano
From playlist Virtual Conference
Serre's Conjecture for GL_2 over Totally Real Fields (Lecture 2) by Fred Diamond
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
MAST30026 Lecture 20: Hilbert space (Part 3)
I prove that L^2 spaces are Hilbert spaces. Lecture notes: http://therisingsea.org/notes/mast30026/lecture20.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For
From playlist MAST30026 Metric and Hilbert spaces
Ekaterina Amerik: Rational curves and contraction loci on holomorphic symplectic manifolds
VIRTUAL LECTURE RECORDED DURING SOCIAL DISTANCING Recording during the meeting "Varieties with Trivial Canonical Class " the April 06, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by
From playlist Virtual Conference
Factors of sparse polynomials: structural results and some algorithms - Shubhangi Saraf
Computer Science/Discrete Mathematics Seminar II Topic: Factors of sparse polynomials: structural results and some algorithms Speaker: Shubhangi Saraf Affiliation: Member, School of Mathematics Date: March 26, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Davesh Maulik - Stable Pairs and Gopakumar-Vafa Invariants 4/5
In the first part of the course, I will give an overview of Donaldson-Thomas theory for Calabi-Yau threefold geometries, and its cohomological refinement. In the second part, I will explain a conjectural ansatz (from joint work with Y. Toda) for defining Gopakumar-Vafa invariants via modul
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Stefaan Vaes: Cohomology and L2-Betti numbers for subfactors and quasi-regular inclusions
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 Analysis and its Applications
Algebraic and Convex Geometry of Sums of Squares on Varieties (Lecture 4) by Greg Blekherman
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study o
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Title: Revisiting the Model Theory of Painlevé Equations
From playlist Spring 2017