The General Theory of Homogenization: A Personalized Introduction (Lecture Notes of the Unione Matematica Italiana)

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Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of FranxE7;ois Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the authorx2019;s H-measures, variants by Patrick GxE9;rard, and others yet to be discovered.