Approximate cohomology
Recent developments in Analytic Number Theory May 01, 2017  May 05, 2017
Location: MSRI: Atrium
cohomology
Fourier analysis
inverse conjecture for Gowers norms
Gowers norm
homogeneous multilinear forms
Ziegler
Let V be an infinite vector space over a finite field k and let be an approximate homomorphism from V to End(V), i.e. the rank of f(x+y)f(x)f(y) is uniformly bounded by some constant r. We show that there is a homomorphism g such that fg is of rank uniformly bounded by R(r).
We introduce a notion of a approximate cohomology groups and interpret this result as a computation of H^1 in a special case. Our proof uses the inverse theorem for the Gowers norms over finite fields; and an independent proof of this result (and some natural generalizations of it) would lead to a new proof of the inverse theorem. Joint work with D. Kazhdan
Ziegler.Notes

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