In-Person and Online Talk - Canceled

A unicellular map on a genus g surface S_g is a graph embedded S_g such that S_g-G is a single disk. The study of unicellular maps was initiated by W. Tutte, who was interesting in counting these objects. 

In this talk, we will introduce a topological operation called surgery, which turns a unicellular map into another. The surgery operation on unicellular maps is reminiscent to Milnor surgery on manifolds. Then, we will address natural questions such as connectedness and diameter of graphs on unicellular maps associated to surgeries. We will see how answering these questions amount to study subgroups of the mapping class group, and also understand the so-called card shuffling problem in combinatorics