Majid Hadian : Children's drawings, flat refinements, and geometric construction of number fields with controlled ramification

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

March 17, 2015, 11 a.m.

In

SEO 427

Abstract

In this lecture I will explain two applications of dessins (or children's drawings). The first application demonstrates how dessins are an effective tool for making explicit calculations that may have been difficult or impossible otherwise. A second application is more theoretical in nature. The notion of flat refinement of a dessin is introduced. This functorial notion enables one to assign to a given dessin infinite families of canonically defined dessins. From these geometric towers one constructs infinite towers of number fields with controlled ramification in the sense that the set of ramified primes is stable (This lecture represents joint work with Ali Kamalinejad and Mehrdad Shahshahani).