Higher Algebra 6: Derived Functors
In this video, we define and discuss derived functors between derived categories of abelian categories. Additionally we discuss the notion of adjoint functors and Kan extensions. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.
From playlist Higher Algebra
The differential calculus for curves, via Lagrange! | Differential Geometry 4 | NJ Wildberger
We rejuvenate the powerful algebraic approach to calculus that goes back to the work of Newton, Euler and particularly Lagrange, in his 1797 book: The Theory of Analytic Functions (english translation). The idea is to study a polynomial function p(x) by using translation and truncation to
From playlist Differential Geometry
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Geometric applications of derived categories - Alexander Perry
Short talks by postdoctoral members Topic: Geometric applications of derived categories Speaker: Alexander Perry Affiliation: Member, School of Mathematics Date: September 24 For more video please visit http://video.ias.edu
From playlist Mathematics
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
Maxima and Minima for Quadratic and Cubics | Algebraic Calculus One | Wild Egg
Tangents of algebraic curves are best defined purely algebraically, without recourse to limiting arguments! We apply our techniques for finding such tangents to derive some familiar results for quadratic and cubic polynomial functions and their maxima and minima. We compare also with the c
From playlist Algebraic Calculus One
Complex numbers and curves | Math History | NJ Wildberger
In the 19th century, the study of algebraic curves entered a new era with the introduction of homogeneous coordinates and ideas from projective geometry, the use of complex numbers both on the curve and at infinity, and the discovery by the great German mathematician B. Riemann that topolo
From playlist MathHistory: A course in the History of Mathematics
Isometry groups of the projective line (I) | Rational Geometry Math Foundations 138 | NJ Wildberger
The projective line can be given a Euclidean structure, just as the affine line can, but it is a bit more complicated. The algebraic structure of this projective line supports some symmetries. Symmetry in mathematics is often most efficiently encoded with the idea of a group--a technical t
From playlist Math Foundations
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
Dennis Gaitsgory - 1/4 Singular support of coherent sheaves
Singular support is an invariant that can be attached to a coherent sheaf on a derived scheme which is quasi-smooth (a.k.a. derived locally complete intersection). This invariant measures how far a given coherent sheaf is from being perfect. We will explain how the subtle difference betwee
From playlist Dennis Gaitsgory - Singular support of coherent sheaves
Pre-recorded lecture 16: Frolicher-Nijenhuis bracket and Frolicher-Nijenhuis cohomology
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Pre-recorded lecture 1: Introduction. What is Nijenhuis Geometry?
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Shane Farnsworth: Rethinking Connes' Approach to the Standard Model of Particle Physics via NCG
The preceding talk described a reformulation of Connes' non-commutative geometry (NCG), and some of its consequences for the NCG construction of the standard model of particle physics. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Ap
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Some directions in derived geometry - Gabriele Vezzosi
Gabriele Vezzosi March 10, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
In search of quantum geometry by Pranav Pandit
COLLOQUIUM IN SEARCH OF QUANTUM GEOMETRY SPEAKER: Pranav Pandit (ICTS - TIFR, Bengaluru) DATE: Mon, 29 November 2021, 15:30 to 17:00 VENUE: Online and Ramanujan Lecture Hall RESOURCES ABSTRACT Notions of geometry have evolved throughout the history of mathematics, often in parallel
From playlist ICTS Colloquia
Pre-recorded lecture 8: Differentially non-degenerate singular points and global theorems
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Shahn Majid: Quantum geodesic flows and curvature
Talk in the Global Noncommutative Geometry Seminar (23 February 2022)
From playlist Global Noncommutative Geometry Seminar (Europe)
The Miura operator at the M2-M5 Intersection by Miroslav Rapcak
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Infinitesimals in Synthetic Differential Geometry
In this video I describe the logic of Synthetic Differential Geometry. This is a non-constructive theory collapsing in the presence of the law of excluded middle. As a logic al theory, it can be realized in a topos and it has sheave models giving a nice representation of tangent bundles.
From playlist Algebra