Tyson Klingner, University of Washington

CMU B006

*Classically, algebraic geometry was the study of varieties over the field of complex numbers. While contemporary algebraic geometers now consider schemes and varieties over arbitrary fields, there is a wealth of knowledge still to be obtained over the field of complex numbers. Moreover, over the field of complex numbers, one has access to smooth differential geometry and can use gauge theory objects to understand more about algebraic geometry. In this talk, we will present an introductory overview of complex algebraic geometry focussing on holomorphic line bundles and their relationship to divisors. If time permits, we will show the construction of the Jacobian variety and show how one may construct the variety with only differential geometric information, highlighting the connection to differential geometry.*