Polytopes | Incidence geometry | Algebraic topology

In mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely geometric properties such as points and lines. A geometric polytope is said to be a realization of an abstract polytope in some real N-dimensional space, typically Euclidean. This abstract definition allows more general combinatorial structures than traditional definitions of a polytope, thus allowing new objects that have no counterpart in traditional theory. (Wikipedia).

ðŸ‘‰ 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

ðŸ‘‰ 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

ðŸ‘‰ 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 are four types of polygons

From playlist Classify Polygons

What is the difference between a regular and irregular polygon

From playlist Classify Polygons

What is the definition of a regular polygon and how do you find the interior angles

From playlist Classify Polygons

What is a polygon and what is a non example of a one

From playlist Classify Polygons

From playlist Classify Polygons

What are the names of different types of polygons based on the number of sides

From playlist Classify Polygons

Dawid Kielak: Computing fibring of 3-manifoldsand free-by-cyclic groups

Abstract : We will discuss an analogy between the structure of fibrings of 3-manifolds and free-by-cyclic groups; we will focus on effective computability. This is joint work with Giles Gardam. Codes MSC : 20F65, 57K31, 20E36 Keywords : free-by-cyclic groups, fibering, Thurston norm, Thur

From playlist Virtual Conference

Tropical Geometry - Lecture 11 - Toric Varieties | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek

This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.

From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra

Generalizing GKZ secondary fan using Berkovich geometry by Tony Yue Yu

PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t

From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)

Tropical Geometry - Lecture 6 - Structure Theorem | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

Lars Martin Sektnan: Extremal PoincarÃ© type metrics and stability of pairs on Hirzebruch surfaces

Abstract: In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact KÃ¤hler manifolds, and stability of pairs, in the toric case. Using constructions of Legendre and Apostolov-Calderbank-Gauduchon, we completely c

From playlist Analysis and its Applications

Thibaut Delcroix : KÃ¤hler-Einstein metrics on group compactifications

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 Algebraic and Complex Geometry

Spectrahedral lifts of convex sets â€“ Rekha Thomas â€“ ICM2018

Control Theory and Optimization Invited Lecture 16.6 Spectrahedral lifts of convex sets Rekha Thomas Abstract: Efficient representations of convex sets are of crucial importance for many algorithms that work with them. It is well-known that sometimes, a complicated convex set can be expr

From playlist Control Theory and Optimization

Kolja Knauer : Posets, polynÃ´mes, et polytopes - Partie 1

RÃ©sumÃ© : Les posets (ensembles partiellement ordonnÃ©s) sont des structures utiles pour la modÃ©lisation de divers problÃ¨mes (scheduling, sous-groupes d'un groupe), mais ils sont aussi la base d'une thÃ©orie combinatoire trÃ¨s riche. Nous discuterons des paramÃ¨tres de posets comme la largeur,

From playlist Combinatorics

What is the difference between convex and concave

From playlist Classify Polygons

Rolf Schneider: Hyperplane tessellations in Euclidean and spherical spaces

Abstract: Random mosaics generated by stationary Poisson hyperplane processes in Euclidean space are a much studied object of Stochastic Geometry, and their typical cells or zero cells belong to the most prominent models of random polytopes. After a brief review, we turn to analogues in sp

From playlist Probability and Statistics