Valery Alexeev, Hülya Argüz, Pierrick Bousseau, David Gay and Mike Usher. Mirror symmetry is a phenomenon inspired by string theory in physics. It is in the intersection of algebraic and symplectic geometry. Particularly, it predicts that moduli spaces of certain types of algebraic varieties, called Calabi–Yau varieties, are related to the symplectic geometry of a mirror Calabi–Yau variety. A central question in this field is understanding mirror symmetry in mathematical terms, and two major tools are the SYZ and homological mirror symmetry conjectures. The symplectic and topological side of these conjectures has been studied by Gay and Usher. In addition, our RTG group studies quantum generalization of mirror symmetry to understand moduli spaces of non-commutative algebraic varieties, mirror symmetry for cluster varieties which play an important role in representation theory, combinatorics, higher Teichmüller theory, and mathematical physics, andcompactifications of moduli spaces of log Calabi-Yau surfaces.
