In mathematics, a triangulated category is a category with the additional structure of a "translation functor" and a class of "exact triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short exact sequences in an abelian category, as well as fiber sequences and cofiber sequences in topology. Much of homological algebra is clarified and extended by the language of triangulated categories, an important example being the theory of sheaf cohomology. In the 1960s, a typical use of triangulated categories was to extend properties of sheaves on a space X to complexes of sheaves, viewed as objects of the derived category of sheaves on X. More recently, triangulated categories have become objects of interest in their own right. Many equivalences between triangulated categories of different origins have been proved or conjectured. For example, the homological mirror symmetry conjecture predicts that the derived category of a Calabi–Yau manifold is equivalent to the Fukaya category of its "mirror" symplectic manifold. (Wikipedia).
Radian Definition: Dynamic & Conceptual Illustrator
Link: https://www.geogebra.org/m/VYq5gSqU
From playlist Trigonometry: Dynamic Interactives!
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
Trigonometry 4 The Area of a Triangle
Various ways of using trigonometry to determine the area of a triangle.
From playlist Trigonometry
Projection of One Vector onto Another Vector
Link: https://www.geogebra.org/m/wjG2RjjZ
From playlist Trigonometry: Dynamic Interactives!
Trigonometry - Vocabulary of trigonometric functions
In this video will cover some of the basic vocabulary that you'll hear when working with trigonometric functions. Specifically we'll cover what is trigonometry, angles, and defining the trigonometric functions as ratios of sides. You'll hear these terms again as we dig deeper into the st
From playlist Trigonometry
Modeling with Trigonometric Functions! (Formative Assessment w/Feedback)
Link: https://www.geogebra.org/m/cuCwguXP BGM: Simeon Smith
From playlist Trigonometry: Dynamic Interactives!
3 Squares Problem: Trigonometric Identity (Proof Without Words)
Link: https://www.geogebra.org/m/w8r7rn9Q
From playlist Trigonometry: Dynamic Interactives!
Petar Pavešić (9/1/21): Category weight estimates of minimal triangulations
When one applies computational methods to study a specific manifold or a polyhedron it is often convenient to have as small triangulation of it as possible. However there are certain limitations on the size of a triangulation, depending on the complexity of the space under scrutiny. The de
From playlist AATRN 2021
Claire Amiot: Cluster algebras and categorification - Part 3
Abstract: In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of
From playlist Combinatorics
Generic bases for cluster algebras (Lecture 2) by Pierre-Guy Plamondon
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Pierre-Guy Plamondon, Research talk - 2 February 2015
Pierre-Guy Plamondon (Université de Paris Sud XI) - Research talk http://www.crm.sns.it/course/4463/ I will present a multiplication formula for cluster characters in 2-Calabi-Yau triangulated categories which generalizes the one proved by Palu. This formula enables one to reobtain, Domin
From playlist Lie Theory and Representation Theory - 2015
Alice Rizzardo: Enhancements in derived and triangulated categories
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: Derived and triangulated categories are a fundamental object of study for many mathematicians, both in geometry and in topology. Their structure is howeve
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Partially wrapped Fukaya categories of symmetric products of marked disks, Gustavo Jasso
Partially wrapped Fukaya categories of symmetric products of marked surfaces were in- troduced by Auroux so as to give a symplecto-geometric intepretation of the bordered Heegaard-Floer homology of Lipshitz, Ozsv ́ath and Thurston. In this talk, I will explain the equivalence between the p
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Claire Amiot: Cluster algebras and categorification - Part 2
Abstract: In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of
From playlist Combinatorics
Marc Levine - "The Motivic Fundamental Group"
Research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Catherine Meusburger: Turaev-Viro State sum models with defects
Talk by Catherine Meusburger in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 17, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Trig Reference Circle (2): Choose Your Own Radius
Trig circle (special angles): Quick reference. Radius modifiable: https://www.geogebra.org/m/rek7rd77 #GeoGebra #mtbos #iteachmath
From playlist Trigonometry: Dynamic Interactives!
Winter School JTP: Introduction to A-infinity structures, Bernhard Keller, Lecture 3
In this minicourse, we will present basic results on A-infinity algebras, their modules and their derived categories. We will start with two motivating problems from representation theory. Then we will briefly present the topological origin of A-infinity structures. We will then define and
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"