In 2004, mathematicians Edward Frenkel, Dennis Gaitsgory, Kari Vilonen, and Mark Goresky were awarded millions of dollars in the form of a grant by DARPA (Defense Advanced Research Projects Agency). The project being funded was to relate the geometric Langlands program to quantum field theory.
According to DARPA’s Wikipedia page, the agency is “a research and development agency of the United States Department of Defense responsible for the development of emerging technologies for use by the military.” In other words, it seems unlikely that an agency dedicated to researching military technology would fund anything with no chance of being applicable to its goal.
Now anyone who has spent any time trying to understand the mathematics related to the geometric Langlands program knows that it’s a highly abstract field. Although the program has roots in number theory, its central conjectures are certain equivalences of DG categories whose definitions take literal books to write out fully. Even the program’s connections to physics (via S-duality a la Witten) seem too deep to have any real impact on “real world” issues.
My question is as stated in the title. Why is the US military interested in funding research related to highly abstract subfields of math and physics?
Two possibilities spring to mind:
1) DARPA has no understanding of the project; it just knows that it’s a hot topic and hopes that some practical application will come of it in the future
2) There are actual concrete applications the military has in mind but they’re classified.
Any thoughts?
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