Abstract: Hodge number duality is one of the most fundamental phenomena in 2d mirror symmetry. This is a 90-degree rotational symmetry of Hodge diamonds within a mirror pair of compact Calabi-Yau Kahler manifolds. A natural question arises: how does one refine this when dropping the compactness assumption? In 2019, Harder-Katzarkov-Przyjalkowski proposed an answer to this question, called the mirror P=W conjecture. This conjecture reveals that the weight filtration on one side corresponds to the perverse filtration of the affinization map on the other side. In this talk, I will introduce the mirror P=W conjecture and describe a combinatorial version of the perverse (=flag) filtration that appears in this context.