Georgia Institute of Technology College of Sciences

Surfaces are some of the most basic examples of spaces. Although topologists have studied surfaces for a long time, they continue to fascinate. I'll give an overview of the study of surfaces over the past 150 years by highlighting work of seven mathematicians. We'll discuss the classification of surfaces, and we'll also discuss mapping class groups, which are collections of symmetries of surfaces. I'll also give the flavor of four of my own research projects about surfaces, one for each of four broad mathematical areas: group theory, geometry, topology, and dynamics.