Curves, Surfaces, and Mapping Class Groups


In this talk I will introduce you to the wonderful world of 2-dimensional topology! We will mainly focus on how we can use combinatorial constructions of curves (1-dimensional objects) on surfaces (2-dimensional objects) to answer questions about the group of symmetries of a surface, which we call the mapping class group. I intend for this talk to be accessible to folks with a wide variety of backgrounds including undergraduate and graduate students.