MAT 339. Geometric Analysis - Autumn 2025 - Vamsi Pingali

The texts we will be referring to are as follows :
1. Do Carmo, Riemannian Geometry.
2. Griffiths and Harris, Principles of Algebraic Geometry.
3. S. Donaldson, Lecture Notes for TCC Course "Geometric Analysis" .
4. J. Kazdan, Applications of Partial Differential Equations To Problems in Geometry.
5. L. Nicolaescu, Lectures on the Geometry of Manifolds .
6. T. Aubin, Some nonlinear problems in geometry.
7. C. Evans, Partial differential equations.
8. Gilbarg and Trudinger, Elliptic partial differential equations of the second order.
9. G. Szekelyhidi, Extremal Kahler metrics.
10. R.O. Wells, Differential Analysis on Complex Manifolds.
11. Kodaira, Complex Manifolds and Deformation of Complex Structures.

The course description (along with pre-requisites) can be found on this webpage.

Instructor : Vamsi Pritham Pingali, vamsipingali@iisc.ac.in.

Office : N23 in the mathematics building.

Classroom and timings : Tuesday and Thursday from 3:30-5:00 in LH-4 (but first class on Aug 5 to be a pre-recorded lecture on MS Teams: Teams link to join).

The Grading policy : 25% for Homeworks, Midterm-25%, and 50% for either a Final or a project presentation (to be decided later).



Exams :

The Midterm shall be held on Sept 23 (Tues) from 3:30-5 in LH-4. The syllabus is everything up to and including the lecture on Hodge theorem and applications

Ethics: Read the information on the IISc student ethics page. In short, cheating is a silly thing. Don't do it. As for homeworks, write them up on your own. You are allowed to discuss them amongst yourselves but please write the solutions on your own. That said I must hasten to add that you learn mathematics best when you solve the problems entirely by yourself.

Here is the tentative schedule. (It is subject to changes and hence visiting this webpage regularly is one of the best ideas in the history of best ideas.)