Category theory | Homotopy theory | Algebraic geometry | Homotopical algebra
In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If is a morphism of geometric or algebraic objects, the corresponding cotangent complex can be thought of as a universal "linearization" of it, which serves to control the deformation theory of . It is constructed as an object in a certain derived category of sheaves on using the methods of homotopical algebra. Restricted versions of cotangent complexes were first defined in various cases by a number of authors in the early 1960s. In the late 1960s, Michel André and Daniel Quillen independently came up with the correct definition for a morphism of commutative rings, using simplicial methods to make precise the idea of the cotangent complex as given by taking the (non-abelian) left derived functor of Kähler differentials. Luc Illusie then globalized this definition to the general situation of a morphism of ringed topoi, thereby incorporating morphisms of ringed spaces, schemes, and algebraic spaces into the theory. (Wikipedia).
Trigonometry X: the Law of Cotangents (and another lovely relation involving cotangents!)
Boy, oh boy this is a longish one. I prove the Law of Cotangents using the incenter of the triangle, after motivating the path with another way one might seek to prove the Law of Sines using the circumcenter of the triangle. After that, I demonstrate an equally lovely relationship betwee
From playlist Trigonometry
Trigonometry 8 The Tangent and Cotangent of the Sum and Difference of Two Angles.mov
Derive the tangent and cotangent trigonometric identities.
From playlist Trigonometry
Graphing the Cotangent Function
Illustrations the graph of the cotangent function using the cotangent segment. Explains how to graph cotangent using reciprocal values of the tangent function http://mathispower4u.wordpress.com/
From playlist Graphing Trigonometric Functions
integral of cot^4(x), integral of cot^4x, integral of (cot(x))^4, integral of cotangent, playlist: https://www.youtube.com/playlist?list=PLj7p5OoL6vGzK7feKUEtd_BUmTCCf5tlo blackpenredpen
From playlist Calculus: Sect 7.2 Trigonometric Integrals, Stewart Calculus Solution, 7th ET edition
Integral of cot^5x, cot(x) and csc(x) approach
integral of cot^5(x), integral of (cot(x))^5, integral of cotangent, playlist: https://www.youtube.com/playlist?list=PLj7p5OoL6vGzK7feKUEtd_BUmTCCf5tlo blackpenredpen
From playlist Calculus: Sect 7.2 Trigonometric Integrals, Stewart Calculus Solution, 7th ET edition
Monotone Lagrangians in cotangent bundles - Luis Diogo
Princeton/IAS Symplectic Geometry Seminar Speaker: Luis Diogo Affiliation: Columbia University Topic: Monotone Lagrangians in cotangent bundles Date: Oct 11, 2016 Description:* We show that there is a 1-parameter family of monotone Lagrangian tori in the cotangent bundle of the 3-sphere w
From playlist Mathematics
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. We define the cotangent sheaf of a scheme, and calculate it for the projective line and then for general projective space.
From playlist Algebraic geometry II: Schemes
Cotangent Graph Interpretation: Dynamic Illustration (Desmos)
Desmos Link: https://www.desmos.com/calculator/bmundg4zk5
From playlist Desmos Activities, Illustrations, and How-To's
Solve cot(x)=sqrt(3) (All Solutions): Degrees
This video explains how to find all of the solutions to a basic trigonometric equation using reference triangles and the unit circle.
From playlist Solving Trigonometric Equations
Winter School JTP: Introduction to Fukaya categories, James Pascaleff, Lecture 1
This minicourse will provide an introduction to Fukaya categories. I will assume that participants are also attending Keller’s course on A∞ categories. Lecture 1: Basics of symplectic geometry for Fukaya categories. Symplectic manifolds; Lagrangian submanifolds; exactness conditions;
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Digression: The cotangent complex and obstruction theory
We study the cotangent complex more in depth and explain its relation to obstruction theory. As an example we construct the Witt vectors of a perfect ring. This video is a slight digression from the rest of the lecture course and could be skipped. Feel free to post comments and questions
From playlist Topological Cyclic Homology
Integral fractional part tan(x)
In this video, I calculate the integral of the fractional part of tan(x) from 0 to pi/2. This beautiful integral will take us to the world of series, the triangle method, complex numbers, the Euler-Mascheroni constant, the Riemann zeta function, and finally the Gamma function, and it allow
From playlist Integrals
Inverting primes in Weinstein geometry - Oleg Lazarev
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Inverting primes in Weinstein geometry Speaker: Oleg Lazarev Affiliation: Harvard University Date: March 12, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
The Wltimate Integral, Part 3: The Closing Remarks - WACKY CALC WEDNESDAY
It's finally here...the ending you all saw coming. Despite that, the argument is still positively gorgeous, and I'm thrilled to finally have this finished for all of you wonderful people. Relevant Desmos graph: https://www.desmos.com/calculator/ogcfp6i8wd COMING SOON: the next part
From playlist Wacky Calc Wednesdays
Bertrand Toën - Deformation quantization and derived algebraic geometry
Bertrand TOËN (CNRS - Univ. de Montpellier 2, France)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Peter SCHOLZE (oct 2011) - 3/6 Perfectoid Spaces and the Weight-Monodromy Conjecture
We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q_p and over F_p((t)) are equivalent, generalizing to the relative situation a th
From playlist Peter SCHOLZE (oct 2011) - Perfectoid Spaces and the Weight-Monodromy Conjecture
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 2/5
The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Index Theory, survey - Stephan Stolz [2018]
TaG survey series These are short series of lectures focusing on a topic in geometry and topology. May_8_2018 Stephan Stolz - Index Theory https://www3.nd.edu/~math/rtg/tag.html (audio fixed)
From playlist Mathematics