Valery Alexeev, Hülya Argüz and Pierrick Bousseau. Algebraic geometry is the study of algebraic varieties, which are spaces defined by polynomial equations in several variables. The moduli spaces parametrizing families of algebraic varieties are of central importance in algebraic geometry, and have major applications in topology, number theory and mathematical physics. Our group has developed and studies compactifications of stable varieties (KSBA), including moduli of K3 surfaces. Moreover, complex algebraic geometry provides a rich source of examples for geometric topology; smooth algebraic surfaces are 4-manifolds and links of isolated surface singularities are 3-manifolds. Theorems in the algebraic setting lead to important motivating conjectures in the topological context.
