6 problems

Kahn–Komlós–Szemerédi conjecture.

The paper constructs cells between structures whose components are bi-invertible morphisms. Higher category structure conjecture. Continuing this construction should generate a hig…

Non-singularity conjecture for random regular graphs. The adjacency matrices of random $d$-regular directed and undirected graphs on $n$ vertices are non-singular with probability…

Conjecture on the main singularity obstruction. The main reason for singularity of a matrix with independent and identically distributed Rademacher entries is the existence of two…

Let $M$ be a uniform random element of the set of $n\times n$ zero-one matrices with every row and column sum equal to $d$. Polynomial singularity conjecture. There are absolute co…

Dense singularity conjecture. There are constants $C,c>0$ depending only on $\pe_0$ such that