Linear algebra | Spectral theory

Spectral theory

In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of systems of linear equations and their generalizations. The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter. (Wikipedia).

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Ana Romero: Effective computation of spectral systems and relation with multi-parameter persistence

Title: Effective computation of spectral systems and their relation with multi-parameter persistence Abstract: Spectral systems are a useful tool in Computational Algebraic Topology that provide topological information on spaces with generalized filtrations over a poset and generalize the

From playlist AATRN 2022

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Elba Garcia-Failde - Quantisation of Spectral Curves of Arbitrary Rank and Genus via (...)

The topological recursion is a ubiquitous procedure that associates to some initial data called spectral curve, consisting of a Riemann surface and some extra data, a doubly indexed family of differentials on the curve, which often encode some enumerative geometric information, such as vol

From playlist Workshop on Quantum Geometry

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Raffaella Mulas - Spectral theory of hypergraphs

Hypergraphs are a generalization of graphs in which vertices are joined by edges of any size. In this talk, we generalize the graph normalized Laplace operators to the case of hypergraphs, and we discuss some properties of their spectra. We discuss the geometrical meaning of the largest an

From playlist Research Spotlight

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Teach Astronomy - Chemical Composition

http://www.teachastronomy.com/ Spectroscopy is the key to chemical composition to determining what a star is actually made of. There are two issues. One is detecting the presence of an element, and the second is the amount of that element. The presence of an element is determined by mea

From playlist 14. Stars

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(PP 6.1) Multivariate Gaussian - definition

Introduction to the multivariate Gaussian (or multivariate Normal) distribution.

From playlist Probability Theory

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Agnes Beaudry: An introduction to chromatic homotopy theory - Lecture 2

The goal of the minicourse will be to introduce the participants to the subject chromatic homotopy theory. This lecture series will require some familiarity with the stable homotopy category. I will first introduce some of the key players in chromatic homotopy theory, the Morava K-theories

From playlist Summer School: Spectral methods in algebra, geometry, and topology

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Oscar Bandtlow: Spectral approximation of transfer operators

The lecture was held within the framework of the Hausdorff Trimester Program "Dynamics: Topology and Numbers": Conference on “Transfer operators in number theory and quantum chaos” Abstract:The talk will be concerned with the problem of how to approximate spectral data oftra

From playlist Conference: Transfer operators in number theory and quantum chaos

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Spectral Sequences 02: Spectral Sequence of a Filtered Complex

I like Ivan Mirovic's Course notes. http://people.math.umass.edu/~mirkovic/A.COURSE.notes/3.HomologicalAlgebra/HA/2.Spring06/C.pdf Also, Ravi Vakil's Foundations of Algebraic Geometry and the Stacks Project do this well as well.

From playlist Spectral Sequences

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Introduction into spectral networks (Lecture 1) by Lotte Hollands

Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries

From playlist Quantum Fields, Geometry and Representation Theory

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Roberta Iseppi: The BV-BRST cohomology for U(n)-gauge theories induced by finitespectral triples

Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: The Batalin–Vilkovisky (BV) formalism provides a cohomological approach for the study of gauge symmetries: given a gauge theory, by introducing extra (non-existing) f

From playlist Noncommutative geometry meets topological recursion 2021

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Panorama of Mathematics: Andrew Neitzke

Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Andrew Neitzke: "Some new g

From playlist Panorama of Mathematics

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Dianel Isaksen - 3/3 Motivic and Equivariant Stable Homotopy Groups

Notes: https://nextcloud.ihes.fr/index.php/s/4N5kk6MNT5DMqfp I will discuss a program for computing C2-equivariant, ℝ-motivic, ℂ-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Far-from-Equilibrium Universality and Spectral Functions in the QGP by Kirill Boguslavski

DISCUSSION MEETING EXTREME NONEQUILIBRIUM QCD (ONLINE) ORGANIZERS: Ayan Mukhopadhyay (IIT Madras) and Sayantan Sharma (IMSc Chennai) DATE & TIME: 05 October 2020 to 09 October 2020 VENUE: Online Understanding quantum gauge theories is one of the remarkable challenges of the millennium

From playlist Extreme Nonequilibrium QCD (Online)

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Stable Homotopy Seminar, 12: The Atiyah-Hirzebruch Spectral Sequence (Caleb Ji)

Caleb Ji gives us an overview of spectral sequences, focusing on the example of the Leray-Serre spectral sequence which is used to prove the equivalence of cellular and singular homology. He then defines the Atiyah-Hirzebruch spectral sequence, which is used to compute extraordinary cohomo

From playlist Stable Homotopy Seminar

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Hermann Schulz-Baldes: Computational K-theory via the spectral localizer.

Talk by Hermann Schulz-Baldes in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 24, 2021

From playlist Global Noncommutative Geometry Seminar (Europe)

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Jord Boeijink: On globally non-trivial almost-commutative manifolds

The framework of Connes' noncommutative geometry provides a generalisation of ordinary Riemannian spin manifolds to noncommutative manifolds. Within this framework, the special case of a (globally trivial) almost-commutative manifold has been shown to describe a (classical) gauge theory ov

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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symplectic topology - Lev Buhovsky

IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: The Arnold conjecture, spectral invariants and C^0 symplectic topology Speaker: Lev Buhovsky Affiliation: Tel Aviv University Date: October 9, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

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Jeremy Hahn : Prismatic and syntomic cohomology of ring spectra

CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR

From playlist Topology

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Stefan Schwede: Equivariant stable homotopy - Lecture 2

I will use the orthogonal spectrum model to introduce the tensor triangulated category of genuine G-spectra, for compact Lie groups G. I will explain structural properties such as the smash product of G-spectra, and functors relating the categories for varying G (fixed points, geometric fi

From playlist Summer School: Spectral methods in algebra, geometry, and topology

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