Summer Graduate School

This Summer Graduate School will introduce students to the modern theory of the  inhomogeneous Cauchy-Riemann equation, the fundamental partial differential equation of Complex Analysis. This theory uses powerful tools of partial differential equations, differential geometry and functional analysis to obtain a refined understanding of holomorphic functions on complex manifolds. Besides students planning to work in complex analysis, this course will be valuable to those planning to study partial differential equations, complex differential and algebraic geometry, and operator theory. The exposition will be self-contained and the prerequisites will be kept at a minimum

Suggested prerequisites:

Students will be expected to have had graduate-level courses in complex and real analysis. A typical first or second year graduate course at the level of Rudin’s Real and Complex Analysis, for example, would be sufficient. Exposure to some basic functional analysis or PDE would be desirable, but not assumed. The basic results from those areas needed to understand subsequent material in the summer school will be developed in the course

Bibliography (PDF)

Projects

Lecture Notes
Day 1 - McNeal & Chakrabarti
Day 2 - McNeal & Chakrabarti
Day 3 - McNeal & Chakrabarti
Day 4 - McNeal & Chakrabarti
Day 5 - McNeal & Chakrabarti
Day 6 - Chakrabarti
Day 7 - Chakrabarti
Day 8 - Chakrabarti

Supplement Lectures
Lecture 1
Lecture 2

Homework
Day 1
Day 2
Day 3
Day 4
Day 5 - no homework
Day 6
Day 7 - no homework
Day 8 - no homework

Excercises
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8

Schedule for Final Projects