One part of Serre's conjectures was proved some time ago by Ribet and Edixhoven, and this was used as part of the proof of Fermat's Last Theorem. I have found on the web that the recent proof of some cases of Serre's conjecture is currently being explained by Edixhoven in two talks "On Serre's conjecture in level one [Khare, Wintenberger, Dieulefait]", at: www.math.leidenuniv.nl/~gabor/geom_sem.html,
and by Ribet in: "The modularity of some mod p Galois representations":
"I will sketch the main ideas of recent preprints of Khare-Wintenberger and Dieulefait that allow one to establish certain cases of Serre's conjectures", at:
http://www.cms.math.ca/Events/summer05/abs/Plenm.h tml
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One part of Serre's conjectures was proved some time ago by Ribet and Edixhoven, and this was used as part of the proof of Fermat's Last Theorem. I have found on the web that the recent proof of some cases of Serre's conjecture is currently being explained by Edixhoven in two talks "On Serre's conjecture in level one [Khare, Wintenberger, Dieulefait]", at: www.math.leidenuniv.nl/~gabor/geom_sem.html, and by Ribet in: "The modularity of some mod p Galois representations": "I will sketch the main ideas of recent preprints of Khare-Wintenberger and Dieulefait that allow one to establish certain cases of Serre's conjectures", at: http://www.cms.math.ca/Events/summer05/abs/Plenm.h tml