ICTS

Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions between mathematics and theoretical physics, especially string theory, channels through complex analytic geometry. Some of the high points of research in this topic are: Yau’s proof of Calabi’s conjecture, Donaldson- Uhlenbeck-Yau’s theorem that polystable vector bundles are precisely the solutions of the Hermitian-Einstein equation, Demailly’s work of Kobayashi hyperbolicity.