Summer 2025 seminar course on Riemann surfaces (and beyond)

A seminar on Riemann surfaces by Prof Kapil Hari is organized at IISER Mohali during the summer of 2025. Details follow.

(Possible) pre-requisites:

• Open mapping theorem in complex analysis
• Definition of Riemann surfaces and understanding that one smooth 2-manifold may have multiple Riemann surface structures (such as $\mathbb{C}$ is not biholomorphic to $D$, different complex tori, etc)
• History of Jacobi and Abelian integrals

notes §

The notes for the topics discussed will be kept here: https://dub.sh/riemann

plan §

• June to July: Essentially some topics from chapters 4 to 15 from Narasimhan - Compact Riemann Surfaces
  • sheaves
  • (Etale space) definition of Riemann surface of a global holomorphic function (in Ahlfors)
  • Riemann surfaces of algebraic functions
  • Riemann-Roch theorem
  • The Jacobian of a Riemann surface and Abel’s theorem
  • Torelli theorem - Wikipedia
• August to November: The previous plan was to follow Ramanan’s global analysis but we shall consider the interests of the participants.

references §

Possible references for topics in Riemann surfaces:

• https://www.mat.univie.ac.at/~armin/lect/advanced_complex_analysis.pdf

(Narasimhan may be too daunting)

More at: inculcation-riemann-surfaces

more events to attend in summer §

• Summer School on Rigidity of Discrete Groups, June 30 – July 4, 2025 at IISER Mohali

epilogue §

• A message from Kapil Hari, the Dean academics: https://iisermmag.wordpress.com/2012/08/23/message-from-the-dean-academics/