The beautiful utility of any duality is that it allows for the surprisingly meaningful flow of ideas between two disparate areas. Indeed, through Homological Mirror Symmetry, symplectic considerations have yielded concrete results in the theory of derived categories of coherent sheaves on algebraic varieties.  These results are unexpected: the apparent flexibility of symplectic topology contrasts with the rigidity found in solutions of  polynomial equations. That difference has been resolved by the surprising abundance found in the group of autoequivalences of the derived category. One particularly successful example was the paper of Seidel and Thomas on spherical twists, which inspired many successors and enjoyed further expansions.

Over the past 25 years, many new, important, and intriguing notions have arisen in algebraic geometry, specifically when we focus on the study of derived categories. Within the context of HMS, the basic question is to understand their manifestation in  symplectic topology.  The goal of this workshop is to understand specific structures in the study of derived categories (Bridgeland Stability, Phantom Categories, Fourier-Mukai Partners, GIT Windows) and their mirror realization for Fukaya Categories.