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--- advanced_tools:stacks [2017/11/08 18:04]
jakobadmin [Researcher]
+++ advanced_tools:stacks [2017/11/08 18:05]
jakobadmin [Why is it interesting?]
@@ Line 9: / Line 9: @@
 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-
+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”.
+[...]
+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.**
 <cite>https://ncatlab.org/schreiber/files/Eggertsson2014.pdf</cite></blockquote>