In differential geometry, the Euler characteristic of an orbifold, or orbifold Euler characteristic, is a generalization of the topological Euler characteristic that includes contributions coming from nontrivial automorphisms. In particular, unlike a topological Euler characteristic, it is not restricted to integer values and is in general a rational number. It is of interest in mathematical physics, specifically in string theory. Given a compact manifold quotiented by a finite group , the Euler characteristic of is where is the order of the group , the sum runs over all pairs of commuting elements of , and is the set of simultaneous fixed points of and . If the action is free, the sum has only a single term, and so this expression reduces to the topological Euler characteristic of divided by . (Wikipedia).
I explore the Euler Characteristic, and prove that it is equal to 2 for any convex polyhedra. I also discuss some cases when it is not equal to 2. FaceBook: https://www.facebook.com/MathProfPierce Twitter: https://twitter.com/MathProfPierce TikTok: https://www.tiktok.com/@professorheather
From playlist Summer of Math Exposition Youtube Videos
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Euler Pronunciation: In Depth Analysis
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From playlist Fun and Amazing Math
Topology | Math History | NJ Wildberger
This video gives a brief introduction to Topology. The subject goes back to Euler (as do so many things in modern mathematics) with his discovery of the Euler characteristic of a polyhedron, although arguably Descartes had found something close to this in his analysis of curvature of a pol
From playlist MathHistory: A course in the History of Mathematics
Algebraic geometry 45: Hurwitz curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses Hurwitz curves and sketches a proof of Hurwitz's bound for the symmetry group of a complex curve.
From playlist Algebraic geometry I: Varieties
Ian Agol, Lecture 1: Volumes of Hyperbolic 3-Manifolds
24th Workshop in Geometric Topology, Calvin College, June 28, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Euler’s method - How to use it?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,
From playlist Differential Equations
Alessandro Chiodo - Towards a global mirror symmetry (Part 1)
Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the i
From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten
There's a Donut in the Wallpaper: Topology, Symmetry, and Conway's Magic Theorem
Made for the 3Blue1Brown Summer of Math Exploration
From playlist Summer of Math Exposition Youtube Videos
Measuring shape with the Euler characteristic [Erik Amézquita]
The Euler characteristic is a simple yet quite powerful topological summary that can help us quantify shape nuances. In this tutorial, we will focus on the Euler Characteristic Transform which is mathematically rich and computationally very efficient, especially when used to extract shape
From playlist Tutorial-a-thon 2021 Spring
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
Submission for the Summer of Math Exposition (SoME1).
From playlist Summer of Math Exposition Youtube Videos
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Someone asked me a question about Euler's Identity (e^iπ = --1)...
...and despite it being almost entirely irrelevant to the lesson at hand, I couldn't resist spending 3 minutes talking about it because it's undiluted mathematical awesome.
From playlist Introduction to Complex Numbers
Orbifolds and Systolic Inequalities - Christian Lange
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Orbifolds and Systolic Inequalities Speaker: Christian Lange Affiliation: Mathematisches Institut der Universität München Date: January 13, 2023 In this talk, I will first discuss some instances in which orbi
From playlist Mathematics
Chris WENDL - 3/3 Classical transversality methods in SFT
There are easy examples showing that classical transversality methods cannot always succeed for multiply covered holomorphic curves, but the situation is not hopeless. In this talk I will describe two approaches that sometimes lead to interesting results: (1) analytic perturbation theory,
From playlist 2015 Summer School on Moduli Problems in Symplectic Geometry
Mandelbrot fractal zoom // featuring Euler bio
Mandelbrot fractal zoom // featuring Euler bio Come hang out and watch a fractal zoom through the Mandelbrot set. To celebrate Euler's contributions to mathematics, this video features a brief bio. of Leonhard Euler! ---------------------------------------------------------------------
From playlist Misc.
J. Demailly - Existence of logarithmic and orbifold jet differentials
Abstract - Given a projective algebraic orbifold, one can define associated logarithmic and orbifold jet bundles. These bundles describe the algebraic differential operators that act on germs of curves satisfying ad hoc ramification conditions. Holomorphic Morse inequalities can be used to
From playlist Ecole d'été 2019 - Foliations and algebraic geometry