User Tools

Site Tools


Sidebar


Add a new page:

advanced_tools:stacks

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 refining from traditional geometric spaces to more refined kinds of spaces known as “stacks”.

[…]

Our main motivation to consider sheaves and stacks is to provide a nonperturbative framework in which we can do physics. Much of gauge theory is done in perturbation theory, but in fact non-perturbative effects such as Dirac monopoles and Yang-Mills instantons play a crucial role in fundamental physics [5]. The language of stacks is the natural language for these phenomena.

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

Examples

Example1
Example2:

FAQ

History

The idea of using stacks goes back to a manuscript titled Pursuing Stacks by Alexander Grothendieck in 1983. For some more information, see https://ncatlab.org/nlab/show/Pursuing+Stacks

Contributing authors:

Jakob Schwichtenberg
advanced_tools/stacks.txt · Last modified: 2017/12/04 07:01 (external edit)