Analysis II
Contact Information
- Course Timing: Tuesday & Thursday 10-11:30.
- Email: swarnava@math.tifr.res.in
- Discussion: If you want to discuss some aspects of this course or the material discussed, please feel free to stop by during office hours or sent me an email and set-up an appointment. I will have dedicated office hours every Tuesday and Thursday right after class.
Course Description
This is the second analysis course for all first year mathematics students entering the Ph.D or Int-Ph.D. program in TIFR. This course along with Analysis I will be part of the interview which is conducted at the end of the first year of the program. Please refer to the syllabus for the recommended books and study materials.
Homework
Topics for presentation
- Prime Number theorem (assigned)
- Riemann Hilbert Correspondence (assigned)
- Hartogs Extension Theorem (assigned)
- Picard Fuchs equations and Gauss Manin connection (assigned)
- Hypergeometric functions and their differential equations (assigned)
- Fuchsian Groups, Selberg Lemma and its application to construct Riemann surfaces (assinged)
- Constant terms in powers of a Laurent polynomial- by J.J. Duistermaat and Wilberd van der Kallen.
- Subharmonic functions and the Dirichlet problem (assigned)
- Boundary behaviour of conformal maps
- Poincare metric and Picard's big theorem
- Theta functions on the complex tori