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advanced_tools:stacks
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Stacks
Why is it interesting?
The development of modern physics in the first half of the 20th century was closely related to the development of differential geometry, first via Riemannian geometry in Einstein’s theory of gravity and then later via Cartan geometry in Yang-Mills’s theory of gauge fields. But, as highlighted by Grothendieck in the second half of the 20th century and as witnessed by a multitude of modern developments, a more natural mathematical description of many phenomena in geometry is obtained by re- fining from traditional geometric spaces to more refined kinds of spaces known as “stacks”. https://ncatlab.org/schreiber/files/Eggertsson2014.pdf
locality principle + gauge principle = stack principlehttps://ncatlab.org/schreiber/files/SchreiberTrento14.pdf
Layman
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Student
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
Researcher
The motto in this section is: the higher the level of abstraction, the better.
Examples
- Example1
- Example2:
FAQ
History
advanced_tools/stacks.1510160543.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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