Homological algebra | Differential topology
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of the next. Associated to a chain complex is its homology, which describes how the images are included in the kernels. A cochain complex is similar to a chain complex, except that its homomorphisms are in the opposite direction. The homology of a cochain complex is called its cohomology. In algebraic topology, the singular chain complex of a topological space X is constructed using continuous maps from a simplex to X, and the homomorphisms of the chain complex capture how these maps restrict to the boundary of the simplex. The homology of this chain complex is called the singular homology of X, and is a commonly used invariant of a topological space. Chain complexes are studied in homological algebra, but are used in several areas of mathematics, including abstract algebra, Galois theory, differential geometry and algebraic geometry. They can be defined more generally in abelian categories. (Wikipedia).
Atoms, elements, molecules... What's the difference? This is part 3 in the Stated Clearly series: An Introduction to Chemistry. In it you will find a simplified definition of a molecule, you will learn how we model molecules, and you will see actual images of real molecules and their vibra
From playlist Introduction to Chemistry - Stated Clearly
Chemical Reaction (5 of 11) Synthesis Reactions, an Explanation
Describes the basics of synthesis reactions, how to identify them, predict the product and balance the chemical equation. Two examples are also shown, synthesis of MgO and ZnS. A chemical reaction is a process that leads to the chemical change of one set of chemical substances to another
From playlist Chemical Reactions and Stoichiometry
Chemical Reactions (4 of 11) Decomposition Reactions, An Explanation
Describes the basics of decomposition reactions, how to identify them, predict the products and balance the chemical equation. Two examples are also shown, decomposition of sugar and hydrogen peroxide. A chemical reaction is a process that leads to the chemical change of one set of chemic
From playlist Chemical Reactions and Stoichiometry
Chemical Reactions (6 of 11) Quick Review 5 Types of Chemical Reactions
Gives a quickened easy overview of the five types of chemical reactions. A chemical reaction is a process that leads to the chemical change of one set of chemical substances to another. Chemical reactions encompass changes that only involve the positions of electrons in the forming and b
From playlist Chemical Reactions and Stoichiometry
More Organic Chemistry Naming Examples 1
More Organic Chemistry Naming Examples 1
From playlist Organic Chemistry
Chemical Reactions (3 of 11) Combustion Reactions, An Explanation
Describes the basics of combustion reactions, how to identify them, predict the products and balance the chemical equation. Three explosions are included, methane mamba, whoosh bottle and hydrogen gas balloon. A chemical reaction is a process that leads to the chemical change of one set o
From playlist Chemical Reactions and Stoichiometry
Coordination Compounds: Geometry and Nomenclature
We have been learning a lot about a wide variety of compounds, but we haven't really looked much at the transition metals. These also form compounds called coordination compounds, and the types of bonds involved in these compounds is quite a bit different from what we are used to, as are t
From playlist General Chemistry
Chemical Bonding | Covalent Bond | Ionic Bonding | Class 11 Chemistry
A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bon
From playlist Chemistry Topics
Chemical Reactions (2 of 11) Single Replacement Reactions, An Explanation
Describes the basics of single replacement reactions, how to identify them, predict the product and balance the chemical equation. Two examples are also shown, Mg + AgNO3 and Al + CuCl2 You can see a listing of all my videos at my website, http://www.stepbystepscience.com A chemical reac
From playlist Chemical Reactions and Stoichiometry
Higher algebra 4: Derived categories as ∞-categories
In this video, we construct the ∞-categorical refinement of the derived category of an abelian category. This is the fourth video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA
From playlist Higher Algebra
Wojciech Chachólski (4/29/20): TDA invariants and model categories
Title: TDA invariants and model categories Abstract: Data analysis is a balancing act of simplification and ignoring most of the information available on the one hand, and retaining what might be meaningful for the particular task on the other. The same balancing act of extracting simplif
From playlist AATRN 2020
String topology coproduct: geometric and algebraic aspects - Manuel Rivera
Princeton/IAS Symplectic Geometry Seminar Topic: String topology coproduct: geometric and algebraic aspects Speaker: Manuel Rivera Affiliation: University of Miami Date: May 11, 2017 For more info, please visit http://video.ias.edu
From playlist Mathematics
Charles Weibel: K-theory of algebraic varieties (Lecture 2)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Charles Weibel: K theory of algebraic varieties Abstract: Lecture 1 will present definitions for the Waldhausen K-theory of rings, varieties, additive and exact categories, and dg c
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Sucharit Sarkar - Khovanov homotopy type
June 29, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry II
Barbara Giunti (5/6/2020): Invariants for tame parametrised chain complexes
Title: Invariants for tame parametrised chain complexes Abstract: Along the lines traced by Wojciech Chachólski in the previous talk, we will see that model structures for persistent chain complexes lead to constructions of new and old invariants. In my talk, I will illustrate the usefuln
From playlist AATRN 2020
Spatial refinements and Khovanov homology – Robert Lipshitz & Sucharit Sarkar – ICM2018
Topology Invited Lecture 6.11 Spatial refinements and Khovanov homology Robert Lipshitz & Sucharit Sarkar Abstract: We review the construction and context of a stable homotopy refinement of Khovanov homology. © International Congress of Mathematicians – ICM www.icm2018.org Os direi
From playlist Topology
Bradley Nelson (2/19/22): Parameterized Vietoris-Rips Filtrations via Covers
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression which restrict simplices to lie in open sets in a cove
From playlist Vietoris-Rips Seminar
The Free Energy Profile of Complexation of Two Oppositely Charged... by Arindam Kundagrami
DISCUSSION MEETING: 7TH INDIAN STATISTICAL PHYSICS COMMUNITY MEETING ORGANIZERS : Ranjini Bandyopadhyay, Abhishek Dhar, Kavita Jain, Rahul Pandit, Sanjib Sabhapandit, Samriddhi Sankar Ray and Prerna Sharma DATE: 19 February 2020 to 21 February 2020 VENUE: Ramanujan Lecture Hall, ICTS Ba
From playlist 7th Indian Statistical Physics Community Meeting 2020
Chemical Reactions (1 of 11) Double Replacement Reactions, An Explanation
Describes the basics of double replacement reactions, how to identify them, predict the products and balance the chemical equation. Two examples are also shown, AgNO3 + K2CrO4 and Pb(NO3)2 + KI You can see a listing of all my videos at my website, http://www.stepbystepscience.com A chemic
From playlist Chemical Reactions and Stoichiometry