Abstracts of Papers Presented at MathFest 2019 Cincinnati, OH July 31 – August 3, 2019 Published and Distributed by The Mathematical Association of America Contents Invited Addresses 1 Earle Raymond Hedrick Lecture Series by Laura DeMarco . 1 Complex Dynamics and Elliptic Curves Lecture 1: Thursday, August 1, 11:00–11:50 AM, Grand Ballroom A Lecture 2: Friday, August 2, 10:30–11:20 AM, Grand Ballroom A Lecture 3: Saturday, August 3, 10:00–10:50 AM, Grand Ballroom A . 1 AMS-MAA Joint Invited Address . 1 Learning in Games by Eva´ Tardos Thursday, August 1, 10:00–10:50 AM, Grand Ballroom A . 1 MAA Invited Address . 1 Uncertainty: The Mathematics of What we Don’t Know by Ami Radunskaya Thursday, August 1, 9:00–9:50 AM, Grand Ballroom A . 1 Solving Algebraic Equations by Irena Swanson Friday, August 2, 11:20AM–12:10 PM, Grand Ballroom A . 1 A Vision of Multivariable Calculus by Robert Ghrist Saturday, August 3, 11:00–11:50 AM, Grand Ballroom A . 2 MAA James R.C. Leitzel Lecture . 2 What’s at Stake in Rehumanizing Mathematics? by Rochelle Gutierrez´ Saturday, August 3, 9:00–9:50 AM, Grand Ballroom A . 2 AWM-MAA Etta Z. Falconer Lecture . 2 Dance of the Astonished Topologist ... or How I Left Squares and Hexes for Math by Tara Holm Friday, August 2, 1:30–2:20 PM, Grand Ballroom A . 2 MAA Chan Stanek Lecture for Students . 2 Secrets of Grad School Success by Mohamed Omar Thursday, August 1, 1:30–2:20 PM, Grand Ballroom A . 2 Pi Mu Epsilon J. Sutherland Frame Lecture . 3 Alice in Numberland — Adventures in Cryptography, Number Theory, and Life by Alice Silverberg Wednesday, July 31, 8:00–8:50 PM, Grand Ballroom A . 3 NAM David Harold Blackwell Lecture . 3 Dudeney’s No Three-In-Line Problem: Problem, Solutions, Conditions, Progress, and Conjectures by Johnny L. Houston Friday, August 2, 4:00–5:45 PM, Grand Ballroom A . 3 Martin Gardner Lecture . 3 Recreational Mathematics and Computer Science: Martin Gardner’s Influence on Research by Erik Demaine Saturday, August 3, 2:00–2:50 PM, Grand Ballroom A . 3 Alder Awards 4 Alder Award Session Friday, August 2, 2:30–3:50 PM, Grand Ballroom A . 4 How I Learned to Stop Worrying and Love the School by PJ Couch Friday, August 2, 2:30–2:50 PM, Grand Ballroom A . 4 The Undergraduate Mathematics Classroom as a Publishing House: A New Type of Learning Community by Pamela Harris Friday, August 2, 3:00–3:20 PM, Grand Ballroom A . 4 iii iv Contents Teaching with H by Alicia Prieto Friday, August 2, 3:30–3:50 PM, Grand Ballroom A . 4 Invited Paper Sessions 5 The Serious Side of Recreational Mathematics Friday, August 2, 1:30–3:50 PM, Room 200 . 5 Cryptography and the Mathematics Behind It Thursday, August 1, 1:30–3:50 PM, Room 205 . 6 The Mathematics of Uncertainty Friday, August 2, 10:10 AM–12:00 PM, Room 200 . 7 Equity and Justice in the Context of Inquiry Thursday, August 1, 1:50–4:20 PM, Room 200 . 8 Mathematical Diversity in Mathematical Biology Friday, August 2, 1:30–5:20 PM, Room 205 . 9 Commutative Algebra Saturday, August 3, 9:00–11:20 AM, Room 200 . 11 Contributed Paper Sessions 13 A Centennial Celebration of David Harold Blackwell Part A: Thursday, August 1, 1:30–3:30 PM, Room 232 . 13 Building Teaching Teams: Professional Development in Departments Part A: Saturday, August 3, 9:00–10:40 AM, Rooms 230 & 231 . 14 Diversity, Equity, and Inclusion in Mathematics Part A: Friday, August 2, 10:10 AM–12:10 PM, Rooms 260, 261 & 262 . 15 Part B: Friday, August 2, 1:30–4:30 PM, Rooms 260, 261 & 262 . 17 Part C: Saturday, August 3, 9:00–11:00 AM, Rooms 237 & 238 . 19 Encouraging Effective Teaching Innovation Part A: Thursday, August 1, 3:50–5:50 PM, Rooms 230 & 231 . 20 Part B: Friday, August 2, 10:10 AM–12:10 PM, Rooms 237 & 238 . 21 Part C: Friday, August 2, 1:30–4:30 PM, Rooms 237 & 238 . 22 Part D: Saturday, August 3, 10:30 AM–12:10 PM, Room 205 . 24 Part E: Saturday, August 3, 3:00–5:20 PM, Room 205 . 25 Enhance your teaching through best practices that align with the IP Guide Part A: Thursday, August 1, 9:00–10:40 AM, Rooms 260, 261 & 262 . 27 Part B: Saturday, August 3, 9:00–11:50 AM, Room 232 . 28 Ethics in the Mathematics Classroom Part A: Thursday, August 1, 1:30–4:10 PM, Rooms 260, 261 & 262 . 30 History of Mathematics in a Math Circle Part A: Thursday, August 1, 9:00–10:40 AM, Rooms 237 & 238 . 31 Part B: Thursday, August 1, 1:30–3:25 PM, Rooms 237 & 238 . 32 Inquiry-Based Learning and Teaching Part A: Thursday, August 1, 9:00–10:40 AM, Rooms 230 & 231 . 34 Part B: Thursday, August 1, 1:30–3:30 PM, Rooms 230 & 231 . 35 Part C: Friday, August 2, 10:10 AM–12:10 PM, Rooms 230 & 231 . 36 Part D: Friday, August 2, 1:30–2:50 PM, Rooms 230 & 231 . 37 Math + X: Mathematics Courses, Curriculum, and Projects Serving Professional Disciplines Part A: Thursday, August 1, 9:00–10:15 AM, Room 232 . 38 Part B: Saturday, August 3, 9:00–11:20 AM, Rooms 260, 261 & 262 . 39 Mathematics and Sports Part A: Saturday, August 3, 9:00–11:55 AM, Room 206 . 41 Mathematics and the Life Sciences: Initiatives, Programs, Curricula Part A: Thursday, August 1, 9:00–10:40 AM, Rooms 207 & 208 . 43 Part B: Thursday, August 1, 1:30–2:30 PM, Rooms 207 & 208 . 44 My Favorite Number Theory Proof Part A: Saturday, August 3, 9:00–11:20 AM, Rooms 207 & 208 . 45 Contents v Plug and Play Data Science Lessons Part A: Thursday, August 1, 9:00–10:40 AM, Room 233 . 46 Part B: Thursday, August 1, 1:30–4:10 PM, Room 233 . 47 Professional Development in Mathematics: Looking Back, Looking Forward, on the occasion of the 25th anniversary of MAA Project NExT Part A: Friday, August 2, 10:10 AM–12:10 PM, Junior Ballroom D . 49 Part B: Friday, August 2, 1:30–3:10 PM, Junior Ballroom D . 50 Recreational Mathematics: Puzzles, Card Tricks, Games, Gambling and Sports Part A: Thursday, August 1, 9:00–10:40 AM, Room 206 . 52 Part B: Thursday, August 1, 1:30–4:30 PM, Room 206 . 53 Part C: Saturday, August 3, 9:00–11:40 AM, Room 233 . 54 Showcase of Modeling to Motivate Differential Equations Part A: Friday, August 2, 10:10 AM–12:10 PM, Room 233 . 56 Part B: Friday, August 2, 1:30–4:10 PM, Room 233 . 57 Teaching Mathematics Through Games Part A: Friday, August 2, 10:10 AM–12:10 PM, Room 206 . 59 Part B: Friday, August 2, 1:30–3:30 PM, Room 206 . 60 Understanding Mathematics Through its History Part A: Friday, August 2, 10:10 AM–12:10 PM, Rooms 207 & 208 . 61 Part B: Friday, August 2, 1:30–4:30 PM, Rooms 207 & 208 . 63 General Contributed Poster Sessions 65 General Contributed Poster Session I Thursday, August 1, 10:00–10:45 AM, Grand Ballroom B . 65 General Contributed Poster Session II Thursday, August 1, 3:00–3:45 PM, Grand Ballroom B . 72 General Contributed Poster Session III Friday, August 2, 1:30–2:15 PM, Grand Ballroom B . 78 Graduate Student Session 85 Great Talks for a General Audience Saturday, August 3, 9:00 AM–1:00 PM, Junior Ballroom D . 85 PosterFest 2019 88 PosterFest 2019: Early Career Scholarship Friday, August 2, 3:00–4:30 PM, Grand Ballroom B . 88 Index of Speakers 93 Invited Addresses 1 Invited Addresses Earle Raymond Hedrick Lecture Series Laura DeMarco Northwestern University Complex Dynamics and Elliptic Curves Lecture 1: Thursday, August 1, 11:00–11:50 AM, Grand Ballroom A Lecture 2: Friday, August 2, 10:30–11:20 AM, Grand Ballroom A Lecture 3: Saturday, August 3, 10:00–10:50 AM, Grand Ballroom A In a series of three talks, I will present connections between recent research in dynamical systems and the classical theory of elliptic curves and rational points. On the dynamical side – specifically in the study of iteration of rational functions (Julia sets, bifurcations, the Mandelbrot set) – the first connections were observed about 100 years ago. On the arithmetic side, it was probably the 1960s when dynamical ideas were first used as tools to understand the arithmetic geometry of elliptic curves and higher-dimensional varieties. My goal is to provide an overview of how these relationships developed and where they have brought us today. The three lectures will be independent. AMS-MAA Joint Invited Address Thursday, August 1, 10:00–10:50 AM, Grand Ballroom A Eva´ Tardos Cornell University Learning in Games Selfish behavior can often lead to suboptimal outcome for all participants, a phenomenon illustrated by many classical examples in game theory. Over the last decade we have studied Nash equilibria of games, and developed good understanding how to quantify the impact of strategic user behavior on overall performance in many games (including traffic routing as well as online auctions). In this talk we will focus on games where players use a form of learning that helps them adapt to the environment. We ask if the quantitative guarantees obtained for Nash equilibria extend to such out of equilibrium game play, or even more broadly, when the game or the population of players.