Course Descriptions

16:640:523 - Functions of Several Complex Variables I

Siqi Fu


Functions of Several Complex Variables: Selected Topics


The main themes of this topic-course are \(L^2\)-estimates of the \(\bar{\partial}\)-operator, spectral theory of the complex Laplacians, and their applications to problems in algebraic geometry. Topics include: H\"{o}rmander's \(L^2\)-estimates of the \(\bar{\partial}\)-operator; spectral discreteness of the \(\bar\partial\)-Neumann Laplacian; Holomorphic Morse inequality; vanishing theorems; and relevant recent developments.


Complex analytic and algebraic geometry, by J.-P. Demailly, available online at Demailly's website.


Complex Variables I

Schedule of Sections: