Course Descriptions

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

Siqi Fu

Subtitle:

Functions of Several Complex Variables: Selected Topics

Description:

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.

Text:

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

Prerequisites:

Complex Variables I

Contacts

Departmental Chair
Michael Saks