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 is not biholomorphic to , 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:

more events to attend in summer

epilogue