Quote:
Originally posted by MetaMan
i never said spelling, i spell shit wrong all the time also.
i called u a parrot because you use the same words.
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pardon me, is this better now?
The naive translation of the Metaman theorem from K3 surfaces to Calabi-Yau threefolds does not work, and counterexamples to it are helpful for understanding what the correct statement should be. In the first part of my talk I shall attempt to explain how the question of finding counterexamples to Metaman is related to equivalences of derived categories. Then, I'll atempt to construct such a counterexample using the Ogg-Shafarevich theory for elliptic threefolds. The equivalence of derived categories I construct is best explained through the use of the Jacobian fibration and twisted sheaves. If time will allow I shall attempt to explain why singularities appear and their relationship to the stable singularities in Mirror Symmetry, as well as how this relates to questions from algebra, like derived equivalences for Azumaya algebras and tilting modules.