Seidel–Smith conjecture on symplectic Khovanov cohomology

Let $L\subset S^3$ be a link. The singly graded symplectic Khovanov cohomology is denoted by $Kh^k_{symp}(L)$, and the bigraded combinatorial Khovanov homology by $Kh^{i,j}(L)$. Seidel–Smith conjecture. For every integer $k$,

$$Kh^k_{symp}(L)\cong \bigoplus_{i-j=k}Kh^{i,j}(L).$$

This conjecture asserts that symplectic Khovanov cohomology recovers the Jones grading of Khovanov homology after collapsing the bigrading along $i-j=k$. It is true over any characteristic-zero field, by work of Abouzaid and Smith.