Timeline for Mirror symmetry mod p?! ... Physics mod p?!
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Jan 15, 2010 at 1:32 | comment | added | Kevin H. Lin | @Tim: Thanks. Sounds a lot like the number theory <-> curves over F_q <-> Riemann surfaces <-> physics "dictionary" which is explained here arxiv.org/abs/0906.2747 | |
| Jan 14, 2010 at 20:54 | comment | added | José Figueroa-O'Farrill | @Pete: you're completely right, of course. I took "mod p" not literally as finite field, but as arithmetic in general. This is what happens when write a post in a rush before going on a trip :( | |
| Jan 14, 2010 at 14:01 | comment | added | Tim Perutz | @Kevin: A-B use Morse theory to compute cohomology of the space of flat connections mod gauge, which by N-S is the moduli space of stable bundles, whose Betti numbers (for general rank) had been found by Harder-Narasimhan by char p methods (Weil conjectures). (BTW, the gauge theory proof of N-S itself is Donaldson's rather than Atiyah-Bott's.) | |
| Jan 14, 2010 at 6:55 | comment | added | Pete L. Clark | Forgive me in advance if this is an impertinent comment (I know literally nothing about string theory), but you do realize that the $p$-adics have characteristic $0$, right? Can you reduce string theory modulo an ideal?? | |
| Jan 14, 2010 at 6:00 | comment | added | Kevin H. Lin | In re your second paragraph: Where does arithmetic come in? I don't see any arithmetic in Atiyah-Bott nor in Narasimhan-Seshadri. | |
| Jan 14, 2010 at 5:31 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |