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Oct 3, 2013 at 16:09 comment added Vesselin Dimitrov To this example we may add Laumon's proof of Weil's conjecture on weights in $\ell$-adic cohomology (Transformation de Fourier constantes d'equation fonctionnelles et conjecture de Weil), which in a way takes Witten's original idea [which inspired Demailly's work] closer to Grothendieck style algebraic geometry. This is probably a separate answer in itself, though. Deligne's algebro-geometric counterpart to the Fourier transform plays a crucial role in the proof, and is worthy of mentioning by itself.
Oct 3, 2013 at 15:35 history answered Koushik CC BY-SA 3.0