Delve into the advanced mathematical concept of homological mirror symmetry for singularities in this one-hour lecture by Kyoung-Seog Lee from the University of Miami/IMSA. Explore the intricacies of graded matrix factorizations of invertible polynomials and examine various methods for their description. The talk may also cover stability conditions on the categories of graded matrix factorizations of weighted homogeneous polynomials, as developed by Takahashi, Kajiura-Saito-Takahashi, Toda, and Otani-Takahashi, time permitting. This lecture serves as a continuation of previous discussions on the topic, offering deeper insights into this complex area of mathematical research.