For the Mathematics Graduate Student Seminar at Dartmouth, I would regularly present on fun mathematics topics. 
Title: How to Pick the Pope, or a Pizza -- The Mathematics of Democracy Abstract: Groups need to make decisions, and there are a wide variety of ways this can be done, each maximizing different notions of fairness. Social Choice Theory provides a mathematical framework to investigate these possibilities rigorously. Infamous for its many impossibility results, this topic reveals some fundamental limits to democracy. Beyond this, we'll discuss potential resolutions to these problems, as well as their real world implications. Come and see how mathematics, and voting, can make the world a better place! Slides 
Title: Why (almost) all puzzles are really just mazes, and how to solve them Abstract: Puzzles come in many shapes and forms, but one approach can solve an astounding number of them. By representing each state of the puzzle as a point in an abstract space, with connections when one can transition between states with a valid move, one can often find solutions easily. This talk explains this connection in detail, with several fun examples and puzzles for participants to interact with! If time allows, we’ll also discuss an amazing result known as the “Sprague-Grundy Theorem” that uses this technique to solve a broad class of games. If you like puzzles, or get frustrated when you can’t solve them, this talk is for you! Slides 
Title: Latin squares and beyond, what’s wrong with six? How an incorrect proof of a 200-year-old conjecture was fixed after over fifty years. Abstract: A Latin square is an n by n array of cells filled with the number in S = {1, 2, …, n} such that every row and column contains each of these numbers exactly once. An Euler square is a pair of “orthogonal” Latin squares, which are superimposed to yield every pair of S^2 exactly once. It was long conjectured that Euler squares couldn’t exist when n = 4k+2 for some natural number k, and there was even a proof of this after a few centuries. However, in 1959, mathematicians discovered not only a flaw in this proof, but that there are actually Euler squares for ALL n of this form, except 2 and 6! If you want to learn about the stained glass artwork in the middle of the first floor in Kemeny Hall, or just a neat way to make magic squares of any size, you’re sure to enjoy this talk! Slides 
Title: Math Art Abstract: George Hart once said that "Math is the most abstract art," and indeed few people see the creativity and beauty in it that many mathematicians do. By combining mathematical ideas with traditional media like sculpture and music, the broader public can appreciate this artistic side of math. In this talk, we'll explore the uncountable ways art has been infused with math, from using DeBrujin's theorem to count the patterns in traditional Japanese braiding, to edible polyhedra and much more! Slides 
Title: Probability Paradoxes Abstract: Along with other graduate students David Freeman, Alina Glaubitz, and Jinman Park, I developed material for and instructed the Exploring Mathematics Summer camp for middle and high school children in Summer 2022. One week was on paradoxical results in probability. Slides 