In mathematics, KK-theory is a common generalization both of K-homology and K-theory as an additive bivariant functor on separable C*-algebras. This notion was introduced by the Russian mathematician in 1980. It was influenced by Atiyah's concept of Fredholm modules for the Atiyah–Singer index theorem, and the classification of extensions of C*-algebras by Lawrence G. Brown, Ronald G. Douglas, and Peter Arthur Fillmore in 1977. In turn, it has had great success in operator algebraic formalism toward the index theory and the classification of nuclear C*-algebras, as it was the key to the solutions of many problems in operator K-theory, such as, for instance, the mere calculation of K-groups. Furthermore, it was essential in the development of the Baum–Connes conjecture and plays a crucial role in noncommutative topology. KK-theory was followed by a series of similar bifunctor constructions such as the E-theory and the , most of them having more category-theoretic flavors, or concerning another class of algebras rather than that of the separable C*-algebras, or incorporating group actions. (Wikipedia).
Arthur Bartels: K-theory of group rings (Lecture 1)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Arthur Bartels: K-theory of group rings The Farrell-Jones Conjecture predicts that the K-theory of group rings RG can be computed in terms of K-theory of group rings RV where V vari
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Guoliang Yu: Quantitative operator K-theory and its applications
Abstract: In this lecture, I will give an introduction to quantitative operator K-theory and apply it to compute K-theory of operator algebras which naturally arise from geometry. I will discuss applications to asymptotic behavior of positive scalar curvature when the dimension of the mani
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
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The framework in which quantum mechanics and special relativity are successfully reconciled is called quantum field theory. Heres how you can easily understand Quantum Field Theory. Support me on patreon so that i can keep on making videos! https://www.patreon.com/quantasy In theoretical
From playlist Quantum Field Theory
Clustering 1: monothetic vs. polythetic
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Alex Fok, Equvariant twisted KK-theory of noncompact Lie groups
Global Noncommutative Geometry Seminar(Asia-Pacific), Oct. 25, 2021
From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)
Arthur Bartels: K-theory of group rings (Lecture 3)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. The Farrell-Jones Conjecture predicts that the K-theory of group rings RG can be computed in terms of K-theory of group rings RV where V varies over the collection of virtually cycli
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Rufus Willett: Decomposable C*-algebras and the UCT
Talk by Rufus Willett in in Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/tba-25/ on March 11, 2022.
From playlist Global Noncommutative Geometry Seminar (Americas)
Ralf Meyer: On the classification of group actions on C*-algebras up to equivariant KK-equivalence
Talk by Ralf Meyer in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 10, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Quantum Theory - Full Documentary HD
Check: https://youtu.be/Hs_chZSNL9I The World of Quantum - Full Documentary HD http://www.advexon.com For more Scientific DOCUMENTARIES. Subscribe for more Videos... Quantum mechanics (QM -- also known as quantum physics, or quantum theory) is a branch of physics which deals with physica
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Jamie Gabe: A new approach to classifying nuclear C*-algebras
Talk in the global noncommutative geometry seminar (Europe), 9 February 2022
From playlist Global Noncommutative Geometry Seminar (Europe)
Koen van den Dungen: Localisations and the Kasparov product in unbounded KK-theory
Talk by Koen van den Dungen in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 19, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
(ML 16.1) K-means clustering (part 1)
Introduction to the K-means algorithm for clustering.
From playlist Machine Learning
Clustering is the process of grouping a set of data given a certain criterion. In this way it is possible to define subgroups of data, called clusters, that share common characteristics. Determining the internal structure of the data is important in exploratory data analysis, but is also u
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Christopher Schafhauser: On the classification of nuclear simple C*-algebras, Lecture 4
Mini course of the conference YMC*A, August 2021, University of Münster. Abstract: A conjecture of George Elliott dating back to the early 1990’s asks if separable, simple, nuclear C*-algebras are determined up to isomorphism by their K-theoretic and tracial data. Restricting to purely i
From playlist YMC*A 2021
José Carrión: "The abstract approach to classifying C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" José Carrión - Texas Christian University Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu/atc2021
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Christopher Schafhauser: "Non-stable extension theory and the classification of C∗-algebras"
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The KL Divergence : Data Science Basics
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