Abstract: Tutte started the enumerative theory of planar maps in the 1960s, in an attempt to shed light on the Four Colour Problem. Since then the theory has grown considerably, extending to graphs on surfaces and to graph minors, and it has connections with statistical physics and algebra. In the talk we will survey recent results in the area, showing how complex analysis analysis and probability enter into the picture. The talk will be kept at a non-technical level, emphasizing the main ideas and developments.

This talk will be accessible to graduate students.