445-1 - Differential Geometry

Monday, Wednesday, Friday 1:00pm - 1:50pm, Lunt 101
Course website: www.math.northwestern.edu/~tosatti/cdg.html

Instructor:

Valentino Tosatti
Email: tosatti@math.northwestern.edu
Office: Lunt 225

Office hours:

Thursdays 1.00pm - 2.00pm
or by appointment

Course Description:

This course is an introduction to complex analytic techniques in algebraic geometry. Topics that will likely be covered include:

Prerequisites:

Familiarity with basic differential geometry and complex analysis.

Textbook:

We will roughly follow the textbook: Two other useful references are

Daily Schedule:

This is a tentative syllabus and it is likely to change as the course progresses.

Date Topics Covered Remarks
Sept. 21, 23, 25 Plurisubharmonic functions
Sept. 28, 30, Oct. 2 Closed positive currents, Lelong numbers
Oct. 5, 7, 9 Hörmander's L2 estimates for
Oct. 12, 14, 16 Friedrichs-Hörmander's density in the graph norm
Oct. 19, 21, 23 Ohsawa-Takegoshi extension theorem
Oct. 26, 28, 30 Demailly's regularization theorem for currents
Nov. 2, 4, 6 Multiplier ideal sheaves and Nadel vanishing theorem
Nov. 9, 11, 13 Invariance of plurigenera
Nov. 16, 18, 20 Openness conjecture, Volume of line bundles
Nov. 23, 25 Fujita's approximation theorem
Nov. 30, Dec. 2 Boucksom-Demailly-Păun-Peternell's characterization of uniruled manifolds