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).
Dimensions (1 of 3: The Traditional Definition - Directions)
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From playlist Exploring Mathematics: Fractals
How to observe the colors, wavelengths, and frequency of light waves, using physics!! #Quantum #Physics #Math #Science #NicholasGKK #Shorts
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Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
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
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
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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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
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symplectic topology - Lev Buhovsky
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From playlist Mathematics
Stability of many-body localization in two and higher dimension by Sumilan Banerjee
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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
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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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From playlist Mathematics
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Hermann Schulz-Baldes: Computational K-theory via the spectral localizer.
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From playlist Global Noncommutative Geometry Seminar (Europe)