Kontsevich's original conjecture dealt solely with Calabi-Yau varieties. Later, it was realized that to incorporate Fano varieties into the statement one needed something a bit more general than varieties: the objects called Landau--Ginzburg models in physics. At its roughest a Landau--Ginzburg model  is a (complex) variety $X$ equipped with a regular function $w: X \to \mathbb{C}$. Landau--Ginzburg models provide theories where the interesting behavior localizes to the singular locus of $w$. As such, they are well-known in a number of mathematical fields. This workshop is meant to gather experts in a broad range of areas around the theme of Landau-Ginzburg models -- all of which are touched by HMS. Specific problems of interest are are the study of Fan--Jarvis--Ruan--Witten Theory and Homological Projective Duality through matrix factorizations in Algebraic Geometry and their dual realization in Fukaya Categories.