Chennai Mathematical Institute


3:30 pm, Seminar Hall
Analytic and tropical geometry

Dhruv Ranganthan
University of Cambridge.


Analysis and analytic geometry over non-archimedean fields has attracted substantial interest, beginning with work of Tate in the 1970s, and then work of Raynaud, Huber, and Berkovich. Of these, Berkovichs theory has particularly nice topological properties, and one can access much of its analytic geometry by using tropical methods. I will give a tropically minded introduction to Berkovich analytic geometry. In particular, I will explain how to get access to the underlying topological space, as well some of the analytic structure, using tropical and polyhedral methods. Time permitting, Ill explain how the theories of Huber and Raynaud fit into this picture.