Theorems about prime numbers | Theorems in analytic number theory
In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes). (Wikipedia).
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
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
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
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
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
algebraic geometry 3 Bezout, Pappus, Pascal
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives more examples and applications of algebraic geometry, including Bezout's theorem, Pauppus's theorem, and Pascal's theorem.
From playlist Algebraic geometry I: Varieties
What is the max and min of a horizontal line on a closed interval
👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Lizhi Chen: Triangulation Complexity of Hyperbolic Manifolds and Asymptotic Geometry
Lizhi Chen, Lanzhou University Title: Triangulation Complexity of Hyperbolic Manifolds and Asymptotic Geometry The triangulation complexity is related to volume of hyperbolic manifolds via simplicial volume. On the other hand, Gromov showed that simplicial volume is related to topological
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Metrics of constant Chern scalar curvature - Xi Sisi Shen
Seminar in Analysis and Geometry Topic: Metrics of constant Chern scalar curvature Speaker: Xi Sisi Shen Affiliation: Columbia University Date: May 03, 2022 We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estima
From playlist Mathematics
Frank Gounelas : Rational curves on K3 surfaces
Bogomolov and Mumford proved that every complex projective K3 surface contains a rational curve. Since then, a lot of progress has been made by Bogomolov, Chen, Hassett, Li, Liedtke, Tschinkel and others, towards the stronger statement that any such surface in fact contains infinitely many
From playlist Algebraic and Complex Geometry
Calculus - The Fundamental Theorem, Part 3
The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.
From playlist Calculus - The Fundamental Theorem of Calculus
Metrics of constant Chern scalar curvature and a Chern-Calabi flow
Speaker: Sisi Shen (Northwestern) Abstract: We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the
From playlist Informal Geometric Analysis Seminar
Ricci Curvature: Some Recent Progress and Open Questions - Jeff Cheeger [2016]
Slides for this talk: https://drive.google.com/open?id=1p9JK7EXKLyy_WxIfbrw02wjjoRm5E1je Name: Jeff Cheeger Event: Simons Collaboration on Special Holonomy Workshop Event URL: view webpage Title: Ricci Curvature: Some Recent Progress and Open Questions Date: 2016-09-09 @1:15 PM Location:
From playlist Mathematics
Multivariable Calculus | The Squeeze Theorem
We calculate a limit using a multivariable version of the squeeze theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Johannes Nicaise: The non-archimedean SYZ fibration and Igusa zeta functions - part 3/3
Abstract : The SYZ fibration is a conjectural geometric explanation for the phenomenon of mirror symmetry for maximal degenerations of complex Calabi-Yau varieties. I will explain Kontsevich and Soibelman's construction of the SYZ fibration in the world of non-archimedean geometry, and its
From playlist Algebraic and Complex Geometry
Fundamental Theorem of line integrals
In this video, I present the fundamental theorem for line integrals, which basically says that if a vector field ha antiderivative, then the line integral is very easy to calculate. This illustrates why conservative vector fields are so important! I also provide a proof of the FTC, which u
From playlist Multivariable Calculus
Vinberg’s theorem on hyperbolic reflection groups - Chen Meiri
Speaker: Chen Meiri (Technion) Title: Vinberg’s theorem on hyperbolic reflection groups Abstract: In this talk we will expalin the main ideas of the proof of the following theorem of Vinberg: Let f be an integral quadratic form of signature (n, 1). If n ≥ 30 then the subgroup of SO(n, 1)(
From playlist Mathematics
Plenary Lecture 1 Some recent developments in Kähler geometry and exceptional holonomy Simon Donaldson Abstract: This article is a broad-brush survey of two areas in differential geometry. While these two areas are not usually put side-by-side in this way, there are several reasons for d
From playlist Plenary Lectures
This lecture gives an introductory overview of the Chow ring of a nonsingular variety. The idea is to define a ring structure related to subvarieties with the product corresponding to intersection. There are several complications that have to be solved, in particular how to define intersec
From playlist Algebraic geometry: extra topics
How We Should Vote (Range Voting)
In the last video, we looked at how Arrow's Theorem proves that the way we vote is fundamentally flawed. But all hope isn't lost! We take a look at range voting, and how it seemingly does the impossible and satisfies all of the criterion put forth by Arrow's Theorem. Created by: Cory Chan
From playlist Voting and Election Reform