Milnor number–modality conjecture for isolated singularities in positive characteristic

Let $K$ be a field of characteristic $p>0$, and let $f_k\in K\{x_1,\ldots,x_n\}$ be a sequence of isolated singularities whose Milnor numbers tend to infinity as $k\to\infty$. The Milnor number–modality conjecture. The right modality of $f_k$ tends to infinity as $k\to\infty$. This conjecture proposes that, in positive characteristic, isolated singularities with unbounded Milnor number cannot have bounded right modality; it extends the finiteness phenomenon for right simple singularities.