2 problems

Generic central slice conjecture. The upper bound on the number of vertices of a $k$-dimensional slice of $C_d$ can be attained by a generic central $k$-dimensional slice for every…

Isoperimetric conjecture on the three-dimensional cube. For every $\bar v\in(0,1)$, at least one of the following sets or its complement is an isoperimetric minimizer in…