Linear algebra | 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).
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
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
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
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
(PP 6.1) Multivariate Gaussian - definition
Introduction to the multivariate Gaussian (or multivariate Normal) distribution.
From playlist Probability Theory
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
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
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
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
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
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
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
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)
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
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)
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"
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
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
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