advanced_tools:stacks
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advanced_tools:stacks [2017/11/08 18:02] jakobadmin created |
advanced_tools:stacks [2017/11/09 09:52] (current) jakobadmin [History] |
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| by Grothendieck in the second half of the 20th century and as | by Grothendieck in the second half of the 20th century and as | ||
| witnessed by a multitude of modern developments, a more natural mathematical | witnessed by a multitude of modern developments, a more natural mathematical | ||
| - | description of many phenomena in geometry is obtained by re- | + | description of many phenomena in geometry is obtained by refining from traditional geometric spaces to more refined kinds of spaces |
| - | fining from traditional geometric spaces to more refined kinds of spaces | + | |
| known as “stacks”. | known as “stacks”. | ||
| + | |||
| + | [...] | ||
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| + | 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.** | ||
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| <cite>https://ncatlab.org/schreiber/files/Eggertsson2014.pdf</cite></blockquote> | <cite>https://ncatlab.org/schreiber/files/Eggertsson2014.pdf</cite></blockquote> | ||
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| <tabbox Researcher> | <tabbox Researcher> | ||
| - | <note tip> | + | * See section 6 in [[https://arxiv.org/abs/0802.0999|Mirror Symmetry, Hitchin's Equations, And Langlands Duality]] by Edward Witten |
| - | The motto in this section is: //the higher the level of abstraction, the better//. | + | |
| - | </note> | + | |
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| <tabbox Examples> | <tabbox Examples> | ||
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| <tabbox History> | <tabbox 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 | ||
| </tabbox> | </tabbox> | ||
advanced_tools/stacks.1510160543.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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