Riemann Surfaces (SoSe 2022)
Course objective:
Riemann Surfaces appeared in mathematics in the nineteenth century by the necessity of finding natural domains of definition of complex-valued functions such as log or the square-root. Nowadays they are an object that sits in the middle terrain between geometry, algebra and analysis. The idea of the course is to give an elementary introduction to the subject. See definitions and examples, then move to divisors, differentials and hopefully (if time allows) end the course with the Riemann-Roch theorem. Our main reference will be Rick Miranda's book "Algebraic Curves and Riemann Surfaces". There will be weekly homework exercises and a final oral exam.
Literature:
There are many books on the subject. For most of the course we will follow:
Miranda, R., Algebraic curves and Riemann surfaces. American Mathematical Society
R. Cavalieri and E. Miles, Riemann surfaces and algebraic curves. Cambridge University Press.
O. Forster, Lectures on Riemann Surfaces. Springer GTM 81. Avaliable online in the digital collection of the university library.
We meet on:
Tuesdays: 14 -- 16 Uhr (room E2 304)
Thursdays: 14 -- 16 Uhr (room C4 216)
Fridays (Exercise session): 11 -- 13 Uhr (room E2 304)
Announcements:
--> Friday 6th of May Übung is changed to Monday 9th from 11 to 13 in room D1 312.
--> Friday 13th of May Übung is changed to Monday 16th from 11 to 13 in room Q2 101.
--> Friday 20th of May Übung is changed to Monday 23th from 11 to 13 in room Q2 101.
Homework: