An Explicit Polynomial Counterexample to Connes'Embedding Conjecture
We construct an explicit Hermitian polynomial $ f $ with integer coefficients, of degree $ 12 $ in $ 65 $ selfadjoint variables, whose normalized trace is at least $3/4$ on every tuple of selfadjoint matrix contractions, in every dimension, and equals $-1$ at a specified tuple of selfadjoint unitaries in a group von Ne...