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
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem
In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers
Zeros of polynomial vs derivative
We will see how the zeros of the derivative of a polynomial are related to the zeros of the original polynomial. This is called the Gauss Lucas Theorem for zeros of derivatives, which is an elegant result from complex analysis that relates it with the convex hull of the original roots. I a
From playlist Complex Analysis
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Calculus 5.3 The Fundamental Theorem of Calculus
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Joint Distribution of Values of Integral Points under Pairs of Quadratic Forms....by Jiyoung Han
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Horocycle orbits in strata of translation surfaces
From playlist Mathematics Research Center
On Ratner's Theorem by M. S. Raghunathan
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Amir Mohammadi: Finitary analysis in homogeneous spaces and applications
Abstract: Rigidity phenomena in homogeneous dynamics have been extensively studied over the past few decades with several striking results and applications. In this talk, we will give an overview of recent activities related to quantitative aspect of the analysis in this context; we will a
From playlist Number Theory Down Under 9
Barak Weiss: Classification and statistics of cut-and-project sets
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 23, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
An effective version of Ratner’s equidistribution theorem for SL(3, R) by Lei Yang
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) An effective version of Ratner’s equidistribution theorem for SL(3, R) (Online) In this talk I will prove an effective version of Ratner’s equidistribution theorem for unipotent orbits in SL(3, R)/SL(3, Z). The proof relies on contr
From playlist Ergodic Theory and Dynamical Systems 2022
Effective equidistribution of some one-parameter unipotent flows with polynom...- Elon Lindenstrauss
Arithmetic Groups Topic: Effective equidistribution of some one-parameter unipotent flows with polynomial rates I & II Speaker: Elon Lindenstrauss Affiliation: Hebrew University Date: February 23, 2022 A landmark result of Ratner states that if G is a Lie group, Γ a lattice in G and if
From playlist Mathematics
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
[BOURBAKI 2017] 21/10/2017 - 4/4 - Serge CANTAT
Progrès récents concernant le programme de Zimmer [d'après A. Brown, D. Fisher, et S. Hurtado] ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://tw
From playlist BOURBAKI - 2017
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Dynamics on the Moduli Spaces of Curves, III - Maryam Mirzakhani
Maryam Mirzakhani Stanford University March 30, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics