Some applications of almost mathematics

Sophie Morel, Harvard University
Fine Hall 314

I will try to explain how, by inserting the word "almost" in appropriate places in a commutative algebra textbook and using the fact that $\mathbb{Q}_p$ an $\mathbb{F}_p((t))$ have the same residue field, Faltings gave a new proof of a result of Fontaine and Wintenberger relating the absolute Galois groups of these two fields. I will also talk about the generalizations of these type of results to higher dimensions.