Event Type:

REU Colloquium

Date/Time:

Friday, July 8, 2016 - 10:00 to 11:00

Location:

Stag 161

Abstract:

A dessin d'enfant (French for a child's drawing) is a finite, bipartite graph embedded on a compact Riemann surface. There is a correspondence between isomorphism classes of compact Riemann surfaces and complex algebraic curves, i.e., the zeroes of an irreducible polynomial in two variables with complex coefficients. A theorem of the late 1970s classifies those Riemann surfaces for which their associated algebraic curve has coefficients in some number field: they must admit a ramified covering of the Riemann sphere with at most three branch values. These coverings will give a dessin on a surface by considering the preimage of the unit interval. This talk will introduce dessins and Riemann surfaces, give some examples, and conclude with some discussion of the driving force behind why we study these combinatorial objects.