Here are some suggestions for topics for your paper. It’s not required to pick one of these; you can certainly pick something else if you like.
Partitions, the pentagonal number theorem, and Macdonald’s identities.
Expander graphs and their applications.
“On the notion of generating function,” by Doubillet, Rota, and Stanley.
Umbral calculus
Matrix models and random tensors
“Classical Hurwitz Numbers and Related Combinatorics”, by Dubrovin, Yang, and Zagier.
Asymptotics, a lecture by Don Zagier.