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Thursday, September 8, 2016

**Abstract:** In the late 80ties, Anderson gave a method for describing the Galois action on the singular homology of Fermat curves. In this talk, I will concentrate on Fermat curves of prime exponent p, and the singular homology will have mod p coefficients. I will describe how to explicitly determine the Galois action using Anderson’s work, and then proceed to compute some Galois cohomology groups, which naturally appear when studying certain obstructions to the existence of rational points. This is all joint work in progress with R. Davis, R. Pries, and K. Wickelgren.