CSUN Algebra, Number Theory, and Discrete Mathematics Seminar

Children’s drawings, flat refinements, and geometric construction of number fields with controlled ramification

Majid Hadian
California Institute of Technology

Wednesday    25 March 2015    3:00 pm–4:00 pm
Live Oak Hall 1325

In this lecture I will explain some applications of dessins (or children’s drawings). First, I define the notion of flat refinement of a dessin and show how this functorial notion enables one to assign to a given dessin infinite families of canonically defined dessins. From these geometric objects, one constructs infinite towers of number fields with controlled ramification in the sense that the set of ramified primes is stable. Then I will turn to applications which are more computational in nature and demonstrate how dessins are an effective tool for making explicit calculations that may have been difficult or impossible otherwise.