  We give a pseudorandom generator that fools degree-$d$ polynomial threshold
functions over $n$-dimensional Gaussian space with seed length
$\mathrm{poly}(d)\cdot \log n$. All previous generators had a seed length with
at least a $2^d$ dependence on $d$.
  The key new ingredient is a Local Hyperconcentration Theorem, which shows
that every degree-$d$ Gaussian polynomial is hyperconcentrated almost
everywhere at scale $d^{-O(1)}$.
