Power laws | Geometry

Spectral dimension

The spectral dimension is a real-valued quantity that characterizes a spacetime geometry and topology. It characterizes a spread into space over time, e.g. a ink drop diffusing in a water glass or the evolution of a pandemic in a population. Its definition is as follow: if a phenomenon spreads as , with the time, then the spectral dimension is . The spectral dimension depends on the topology of the space, e.g., the distribution of neighbors in a population, and the diffusion rate. In physics, the concept of spectral dimension is used, among other things, in quantum gravity, percolation theory, superstring theory, or quantum field theory. (Wikipedia).

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Dimensions (1 of 3: The Traditional Definition - Directions)

More resources available at www.misterwootube.com

From playlist Exploring Mathematics: Fractals

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What Is The Color Of Light?!?

How to observe the colors, wavelengths, and frequency of light waves, using physics!! #Quantum #Physics #Math #Science #NicholasGKK #Shorts

From playlist Quantum Mechanics

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Dimensions Chapter 5

Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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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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Dimensions Chapter 1

Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Dimensions Chapter 2

Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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Finding the Dimension of a Subspace

Description: How should we define the dimension of a subspace? In the past, we usually just point at planes and say duh its two dimensional. Here we give a precise definition, and use it to find the dimensions of the column space and null space of a matrix. Learning Objectives: 1) Define

From playlist Older Linear Algebra Videos

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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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Sven Bachmann: A classification of gapped Hamiltonians in d=1

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 SPECIAL 7th European congress of Mathematics Berlin 2016.

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Ginestra Bianconi (8/28/21): The topological Dirac operator and the dynamics of topological signals

Topological signals associated not only to nodes but also to links and to the higher dimensional simplices of simplicial complexes are attracting increasing interest in signal processing, machine learning and network science. Typically, topological signals of a given dimension are investig

From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021

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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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Stability of many-body localization in two and higher dimension by Sumilan Banerjee

29 May 2017 to 02 June 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore This program aims to bring together people working on classical and quantum systems with disorder and interactions. The extensive exploration, through experiments, simulations and model calculations, of growing cor

From playlist Correlation and Disorder in Classical and Quantum Systems

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Lisa Glaser: A picture of a spectral triple

Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: A compact manifold can be described through a spectral triple, consisting of a Hilbert space H, an algebra of functions A and a Dirac operator D. But what if we are g

From playlist Noncommutative geometry meets topological recursion 2021

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Is many-body localization stable in d greater than 1? by Sumilan Banerjee

PROGRAM: INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS ORGANIZERS: Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

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Lec 2 | MIT 6.451 Principles of Digital Communication II

Performance of Small Signal Constellations View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.451 Principles of Digital Communication II

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Toroidal Soap Bubbles: Constant Mean Curvature Tori in S3S3 and R3 - Emma Carberry

Emma Carberry University of Sydney April 14, 2014 Constant mean curvature (CMC) tori in S3S3, R3R3 or H3H3 are in bijective correspondence with spectral curve data, consisting of a hyperelliptic curve, a line bundle on this curve and some additional data, which in particular determines the

From playlist Mathematics

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Dimensions Chapter 6

Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.

From playlist Dimensions

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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)

Related pages

Frequency | Hausdorff dimension | Dimension | Superstring theory | Percolation critical exponents | Real number | Geometry | Topology | Fractal dimension | Sierpiński triangle