What are some fields where physics is leading mathematics? [closed]

I know developments in physics and mathematics often nourish each other, and at different points in history, physics and math have taken turns leading each other. An example of a physicist "inventing" the required mathematics is Newton and his calculus. At other times, the mathematics have been discovered as a curiosity, and the physicists come along to show where it is used in nature.

My question is: In the current state of affairs, in which fields does the physics lead mathematics?

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Make-a-list, no? –  dmckee Dec 1 '12 at 3:16
In my defense, it would sure be an interesting list. :) (Actually, I didn't realize it was a long list) –  Joebevo Dec 1 '12 at 3:22
The opposite question: physics.stackexchange.com/q/4849/2451 –  Qmechanic Dec 1 '12 at 15:35