Categorification without Categories - On the book that I will probably never finish... — Arik Wilbert ⟨wilbert@southalabama.edu⟩

In this talk, I will tell you about a book I am trying to write. The book is supposed to contain fancy pictures of mathematical knots. To create a knot, take a piece of string or rope, tie a knot in it, and then glue the ends together. So far, I have had a hard time deciding what knots I would like to feature in my book. I will introduce you to the Jones polynomial and explain how it has been a helpful tool in making decisions. However, at this point, I still do not know how to finish the book. In graduate school, I learned about a mathematical field called "categorification". Categorification is an active area of research, and I will survey some of its results and applications. Maybe categorification is exactly what I need to finish my book?

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