In mathematics, the classifying space for the unitary group U(n) is a space BU(n) together with a universal bundle EU(n) such that any hermitian bundle on a paracompact space X is the pull-back of EU(n) by a map X → BU(n) unique up to homotopy. This space with its universal fibration may be constructed as either 1. * the Grassmannian of n-planes in an infinite-dimensional complex Hilbert space; or, 2. * the direct limit, with the induced topology, of Grassmannians of n planes. Both constructions are detailed here. (Wikipedia).
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Do physicists describe the world in 4D?
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From playlist Science Unplugged: Physics
From playlist Contributed talks One World Symposium 2020
From playlist Unlisted LA Videos
Minkowski Space-Time: Spacetime in Special Relativity
Includes discussion of the space-time invariant interval and how the axes for time and space transform in Special Relativity.
From playlist Physics
Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ...
Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Emily Riehl: On the ∞-topos semantics of homotopy type theory: The simplicial model of...- Lecture 2
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 22, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Topology
Charles Rezk - 3/4 Higher Topos Theory
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart3.pdf In this series of lectures I will give an introduction to the concept of "infinity
From playlist Toposes online
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture II
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Vincent LAFFORGUE - Stacks of Shtukas and spectral decompositions
https://ams-ems-smf2022.inviteo.fr/
From playlist International Meeting 2022 AMS-EMS-SMF
Definitions of null space, injectivity, range, and surjectivity. Fundamental theorem of linear maps. Consequences for systems of linear equations.
From playlist Linear Algebra Done Right
Clara Löh (5/28/22): Lower multiplicity bounds via classifying spaces
We consider variations of the Lusternik--Schnirelmann category, based on open covers satisfying constraints on the level of the fundamental group. Such LS-category invariants can be analysed through equivariant methods. For example, classifying spaces for families of subgroups can be used
From playlist Topological Complexity Seminar
Slopes in eigenvarieties for definite unitary groups - Lynnelle Ye
Joint IAS/Princeton University Number Theory Seminar Topic: Slopes in eigenvarieties for definite unitary groups Speaker: Lynnelle Ye Affiliation: Harvard University Date: December 6, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Symmetries in QFT and Their Relationship With Category Theory (Lecture 1) by Lakshya Bhardwaj
INFOSYS-ICTS STRING THEORY LECTURES SYMMETRIES IN QFT AND THEIR RELATIONSHIP WITH CATEGORY THEORY SPEAKER Lakshya Bhardwaj (Mathematical Institute, University of Oxford) DATE & TIME 10 October 2022 to 12 October 2022 VENUE Madhava Lecture Hall (Hybrid) Lecture 1: 10 October 2022 at 3:30 p
From playlist Infosys-ICTS String Theory Lectures
Linear Algebra - Lecture 28 - Null Space of a Matrix
In this video lecture, I define the null space of a matrix, and work through several examples.
From playlist Linear Algebra Lectures