Dissections of Lattice Polygons into Lattice Triangles of Integer Area -
A lattice polygon is a polygon in the plane whose vertices have integer coordinates.  The area of such a polygon is either an integer or a half-integer.  It is a fact that every lattice polygon can be cut into lattice triangles of area 1/2.

On the other hand, not every lattice polygon of integer area can be cut into lattice triangles of area 1.  (For example, consider the unit square.)  In this talk we will address the general question of which lattice polygons of integer area can be dissected into lattice triangles of area 1. As a warm up, try cutting a 3x5 rectangle into lattice triangles of area 1. 

Answering this general question involves a delightful blend of number theory, combinatorics, and topology.