What Really Counts: The Joy of Enumeration

At a first glance, counting seems like a skill relegated to elementary school, and yet it forms an entire active area of research-level mathematics.  Rather than counting by listing “one, two, three,…” research in counting answers questions of “how many?” by making clever use of structure.  What do I count?  And why and how?  I will share some of my favorite counting problems and the surprising connections they have with other subjects.