8-polytopes | E8 (mathematics)
In 8-dimensional geometry, there are 255 uniform polytopes with E8 symmetry. The three simplest forms are the 421, 241, and 142 polytopes, composed of 240, 2160 and 17280 vertices respectively. These polytopes can be visualized as symmetric orthographic projections in Coxeter planes of the E8 Coxeter group, and other subgroups. (Wikipedia).
What are four types of polygons
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Jeroen Schillewaert: Constructing highly regular expanders from hyperbolic Coxeter groups
Thursday 17 November 2022 Jeroen Schillewaert, University of Auckland Abstract: Given a string Coxeter system (W,S), we construct highly regular quotients of the 1-skeleton of its universal polytope P, which form an infinite family of expander graphs when (W,S) is indefinite and P has fin
From playlist SMRI Seminars
Geometry - Basic Terminology (12 of 34) Definition of Polygons (Continued)
Visit http://ilectureonline.com for more math and science lectures! In this video I will give examples of equiangular, quadrilateral, and regular polygons. Next video in the Basic Terminology series can be seen at: http://youtu.be/QpluDB1YApQ
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
Energy minimization by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Yang-Hui He (6/16/21): Universes as Bigdata: from Geometry, to Physics, to Machine-Learning
We briefly overview how historically string theory led theoretical physics first to algebraic/differential geometry, and then to computational geometry, and now to data science. Using the Calabi-Yau landscape - accumulated by the collaboration of physicists, mathematicians and computer sci
From playlist AATRN 2021
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is Polypropylene and what is it used for?
From wiki: Polypropylene, also known as polypropene, is a thermoplastic polymer used in a wide variety of applications. It is produced via chain-growth polymerization from the monomer propylene. Polypropylene belongs to the group of polyolefins and is partially crystalline and non-polar. W
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Geometry - Ch. 1: Basic Concepts (29 of 49) Equilateral, Equiangular, or Regular Polygon?
Visit http://ilectureonline.com for more math and science lectures! In this video I will show how to identify equilateral, equiangular or regular polygons. Equilateral: all sides are congruent. Equiangular: all angles in the interior are congruent. Regular polygon: is convex, equilateral,
From playlist GEOMETRY CH 1 BASIC CONCEPTS
Semidefinte programming bounds by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Representation theory and geometry – Geordie Williamson – ICM2018
Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor
From playlist Plenary Lectures
It is not always possible to carry around a DSLR for recording lectures or academic videos. The much smaller Canon EOS M, still allows for all Canon EF and EF-S lenses (via adapter) to be used and contains a large APS-C sized sensor, as in the Canon 650D. All-in-all a great portable came
From playlist Creating video tutorials - a series for academic personnel
Counting points on the E8 lattice with modular forms (theta functions) | #SoME2
In this video, I show a use of modular forms to answer a question about the E8 lattice. This video is meant to serve as an introduction to theta functions of lattices and to modular forms for those with some knowledge of vector spaces and series. -------------- References: (Paper on MIT
From playlist Summer of Math Exposition 2 videos
Modular forms: Theta functions in higher dimensions
This lecture is part of an online graduate course on modular forms. We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors
From playlist Modular forms
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is Polystyrene (styrofoam) and what is it used for?
from wiki: Polystyrene is a synthetic aromatic hydrocarbon polymer made from the monomer known as styrene. Polystyrene can be solid or foamed. General-purpose polystyrene is clear, hard, and rather brittle. It is an inexpensive resin per unit weight. Formula: (C8H8)n IUPAC ID: poly(1-phen
From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020
Stephan Weltge: Binary scalar products
We settle a conjecture by Bohn, Faenza, Fiorini, Fisikopoulos, Macchia, and Pashkovich (2015) concerning 2-level polytopes. Such polytopes have the property that for every facet-defining hyperplane H there is a parallel hyperplane H0 such that H and H0 contain all vertices. The authors con
From playlist Workshop: Tropical geometry and the geometry of linear programming
Classifying a polygon in two different ways ex 4
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Raman Sanyal: Polyhedral geometry of pivot rules
Geometrically, a linear program gives rise to a polyhedron together with an orientation of its graph. A simplex method selects a path from any given vertex to the sink and thus determines an arborescence. The centerpiece of any simplex method is the pivot rule that selects the outgoing edg
From playlist Workshop: Tropical geometry and the geometry of linear programming
