The theory of Riemann surfaces began (as one might expect) with Riemann wondering about the correct framework in which to study multivalued functions. Riemann realised he needed to consider 2-dimensional `domains' with some inscribed `geometry'; what we would now call Riemann surfaces and then of course the functions on these. As with complex analysis a number of remarkable theorems were then discovered with such beautiful examples as the Uniformization Theorem, Riemann-Roch Theorem and Riemann's Existence Theorem. This led naturally to wondering whether the analogues of these statements held for higher dimensional complex manifolds after which the theory was largely overhauled with the introduction of the language of sheaves, cohomology and the Serre Duality Theorem taking the place of the analytic tools previously developed with regards to harmonic functions and integrals.

If any of this has piqued your interest come along to MS.05 at the slightly unusual time of 7:00 to hear Callan McGill expound on this! After which, we will also have the opportunity to hear a bit about Algebraic K Theory from Joe Tait! Thereafter we will analytically continue ourselves to the pub!