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
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
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
Igor Burban: Non commutative nodal curves and finite dimensional algebras
Abstract: Nodal rings are non-commutative analogues of the A_1-singularity k[[ u, v]]/(uv)$. I shall show that to any (non-commutative) rational projective curve {X} one can canonically attach a finite dimensional algebra \Lambda_{X} satisfying the following properties: •\mathsf{gl.dim}(\
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
AlgTopReview4: Free abelian groups and non-commutative groups
Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such
From playlist Algebraic Topology
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
algebraic geometry 15 Projective space
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It introduces projective space and describes the synthetic and analytic approaches to projective geometry
From playlist Algebraic geometry I: Varieties
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
Andrzej Sitarz: Spectral action for 3+1 geometries
I'll demonstrate a class of models, to illustrate a principle of evolution for 3-dimensional noncommutative geometries, determined exclusively by a spectral action. One particular case is a model, which allows evolution of noncommutativeness (deformation parameter) itself for a specific c
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Franz Luef: Noncommutative geometry and time-frequency analysis
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist 30 years of wavelets
Rainer Verch: Linear hyperbolic PDEs with non-commutative time
Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form (D + sW) f = 0 are studied, where D is a normal or prenormal hyperbolic differential operator on Minkowski spacetime, s is a coupling constant, and W i
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Ben Webster - Representation theory of symplectic singularities
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Dmytro Shklyarov: Semi-infinite Hodge structures in noncommutative geometry
Abstract: Homological mirror symmetry asserts that the connection, discovered by physicists, between a count of rational curves in a Calabi-Yau manifold and period integrals of its mirror should follow from an equivalence between the derived Fukaya category of the first manifold and the de
From playlist Algebraic and Complex Geometry
Masoud Khalkhali: Curvature of the determinant line bundle for noncommutative tori
I shall first survey recent progress in understanding differential and conformal geometry of curved noncommutative tori. This is based on work of Connes-Tretkoff, Connes-Moscovici, and Fathizadeh and myself. Among other results I shall recall the computation of spectral invariants, includi
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Anton Savin: Index problem for elliptic operators associated with group actions and ncg
Given a group action on a manifold, there is an associated class of operators represented as linear combinations of differential operators and shift operators along the orbits. Operators of this form appear in noncommutative geometry and mathematical physics when describing nonlocal phenom
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Yang Liu: Hypergeometric Functions and Heat Coefficients on Noncommutative Tori
Talk by Yang Liu in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/hypergeometric-functions-and-heat-coefficients-on-noncommutative-tori/ on April 16, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Walter van Suijlekom: Non-commutative geometry and spectral triples - Lecture 1
Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Our starting point is a spectral approach to geometry, starting with the simple ques tion ’can one hear the shape of a drum’. This was phrased by Mark Kac in t
From playlist Noncommutative geometry meets topological recursion 2021
Poisson tensors in non-commutative gravity
In this video I go through my master thesis. You can find all the links discussed here: https://gist.github.com/Nikolaj-K/ce2dd6b6da0fbd791529bc8dd9183a74 Links: http://othes.univie.ac.at/16190/ https://arxiv.org/abs/1111.2732 https://www.linkedin.com/in/nikolaj-kuntner-0138aa104/ http
From playlist Physics
Differential geometry with finite fields | Differential Geometry 7 | NJ Wildberger
With an algebraic approach to differential geometry, the possibility of working over finite fields emerges. This is another key advantage to following Newton, Euler and Lagrange when it comes to calculus! In this lecture we introduce the basics of finite (prime) fields, where we work mod
From playlist Differential Geometry