Explore the intricate connections between quiver mutations, Poisson X-cluster varieties, and Calabi-Yau categories in this advanced mathematics lecture. Delve into the combinatorics of quiver mutations and their role in constructing n-dimensional Poisson X-cluster varieties. Examine how the representation theory of quivers with potentials leads to the formation of 3-dimensional Calabi-Yau categories. Discover the correspondence between Donaldson-Thomas invariants and rational curve counts in normal crossings compactifications, relating to log Gromov-Witten invariants. Gain insights into ongoing research in homological mirror symmetry, presented by Hülya Argüz from the University of Georgia in collaboration with Pierrick Bousseau.