Projective and Non-Abelian SET

Mathematicians love SET. On the surface, this classic game is a contest of pattern recognition, but it also presents an interesting way to visualize the geometry of a torus over a finite field. In this talk, we will discuss some of the mathematics connected to SET and then explore several new versions of the game, including one arising from projective geometry and one arising from non-abelian groups. In particular, we will see how these non-abelian variations on SET can give intuitive visualizations of abstract group structures.

Connections, Scrabble, Change Ringing, Square Dancing, and Finite Fields

Can re-scrambling the clues in a Connections puzzle help us solve it more quickly? Can we design re-scramblings of the sixteen words that will make each pair of words appear next to each other exactly once? Ideas from combinatorics, number theory, and abstract algebra can help us answer such questions. Along the way we'll encounter similar, simpler problems with connections to change ringing and square dancing. This is joint work with Alon Danai, Joshua Kou, Andy Latto, and Haran Mouli.

How Video Games Saved Math (for Me)

How did a self-described "not a math kid" end up becoming a professor of computer graphics, one of the most notoriously math-heavy subdisciplines of computer science? The answer: a love of animation and video games! In this talk, I'll journey back to my least-favorite math class ever (10th grade Algebra II) and show how the topics I found most mind-numbing at the time are actually at the heart of some of the most important (and elegant) algorithms for video game graphics.

Lucy and Lily, a game of geometry and number theory

In this talk I will explain a game I made which illustrates some basic algebraic number theory in a fun and colorful way. I call the game "Lucy and Lily", after my two daughters, because one can interpret the game as trying to herd two uncooperative children into bed simultaneously.  I will demonstrate the game and some of its surprising features, then discuss the math behind it.