4 problems

Linear-programming improvement conjecture. Linear programming methods could be used to improve the constants in Theorem.

Non-convex extension conjecture. Similar results should hold when $K$ is not convex.

Möller's bound conjecture. A version of the bound in Corollary should hold for every centrally symmetric subvariety $X\subset S^n$, even when the measure $\mu$ is not centrally sym…

Let $d$ be the dimension of the underlying Brownian motion, let $D$ be the dimension of the cubature integrand's output, and consider constructing cubature on Wiener space using ra…