Complex Geometry and Analysis

Complex geometry is a rich field of mathematics that lies at the intersection of three classical areas: complex analysis, algebraic geometry, and differential geometry. It focuses on geometric objects defined using complex numbers, and includes the study of complex manifolds and complex algebraic varieties, their associated holomorphic vector bundles and coherent sheaves, as well as other related topics. Some areas of special interest for our group are: analysis on singular varieties, Calabi–Yau manifolds, canonical metrics and stability conditions, Kähler metrics, multivariable residue theory, pluripotential theory, and toric geometry. We also explore connections to topics such as algebraic and arithmetic geometry, convex geometry, intersection theory, probability theory and statistical mechanics, as well as other aspects of theoretical physics.