Date: Thu., Jan. 29, 2026, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Drew Sills, Georgia Southern University
Title: Mathematically inspired musical scales
Abstract: We review some basics of "musical physics" from Pythagoras to modern times, and
then examine variations on these ideas whereby we can build nonstandard musical scales inspired by the elementary functions of mathematics. We then show how to build an infinite family of musical scales for which Wendy Carlos's alpha, beta, and gamma scales are special ca\
ses. Some of this work is ongoing and joint with
Robert Schneider, frontman for the indie rock band The Apples in Stereo, and Assistant Professor of Mathematics at Michigan Technological University.
slides
lecture
Date: Thu., Feb. 5, 2026, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker: Matthew C. Russell
Title: Mechanical proofs of partition identities through atomic relations
Abstract: Integer partition and q-series sum-to-product identities, such as the Rogers-Ramanujan identities, lie at the intersection of combinatorics, number theory, and the representation theory of affine Lie algebras. This talk will focus on the method of atomic relations, which has been developed by Shashank Kanade and the author in recent years as a way to prove these identities. In some cases, computer output from this method can guide human-constructed proofs, while in other cases, our proofs are totally computer-generated. Applications of this method to problems involving cylindric partitions and colored partitions will also be discussed.
Special Guest Lecture in Dr. Z.'s experimental math class, Thurs. Feb. 12, 2026, 12:10-1:10 pm
Speaker: Wadim Zudilin, Radboud University, Nijmegen, Netherlands
Title: Jesus Guillera (1955-2026)
slides
[ The people in the picture in slide 16 are, from left to right
1) Jesús Guillera Goyanes 2) Wadim Zudilin 3) Eva A. Gallardo Gutiérrez 4) Francisco Ruiz Blasco 5) Jesús Bastero Eleizalde 6) Javier Cilleruelo (1961-2017) 7) Juan Carlos Peral Alonso or Jose Luis Cuadra
8) Fernando Chamizo Lorente 9) Herbert Wilf
(Thanks to Guruzeta Guillera-Arroita) ]
Title: Counting Colored Tilings on Grids and Graphs
Abstract: In this talk we study a counting problem that originated on Mathematics Stack Exchange: How many ways can a rectangular grid be partitioned into a prescribed number of connected polyominoes when the pieces are colored, and any two pieces that share an edge must have different colors? We organize these numbers using bivariate generating functions, where one variable records the length of the grid and the other records the number of pieces. Using generating functions, we obtain explicit rational expressions in the first nontrivial cases of two and three r\ ows. We then recast the model in graph-theoretic terms by replacing grids with Cartesian products of a fixed graph and a path, and by counting properly colored partitions into connected blocks. This leads to analogous generating functions on graphs, including closed forms f\ or specific families (such as complete graphs), and to a computational framework for exploring further examples. This is joint work with Diego Villamizar (Xavier University of Louisiana
Date: Thu., Feb. 19, 2026, 5:00pm (Eastern Time)
Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]
Speaker:
Timothy Chow, Center for Communication Research, Princeton, NJ
Title: Game theory, Scrabble, and poisons
Abstract: We describe two unexpected applications of game theory to recreational mathematics. The first, which is joint work with Scrabble expert Nick Ballard, is a Scrabble position in which the best strategy is mixed (i.e., randomized). Although it is not theoretic\ ally surprising that such positions should exist, ours is the first provably correct explicit example, and even elite Scrabble players find it striking. The second concerns an old but little-known lateral-thinking "poison puzzle" by Michael Rabin, which turns out to have se\ veral alternative solutions to the intended solution. We are led to consider a two-player game with three distinct Nash equilibria, which is difficult to analyze theoretically and begs for experimental investigation
Speaker: Lucy Martinez, Rutgers University
Title: How many coin tosses would you need until you get n Heads or m Tails?
Abstract: How many coin tosses would it take until reaching for the first time either n Heads or m Tails?. Although this setup is related to the classical Problem of points, prior work by Fermat and Pascal focused on the probability of getting n Heads vs getting m Tails, rather than on the duration of the game. Using probabilistic techniques, togeth\ er with symbolic computation, we derive probability generating functions, closed-form expressions, and asymptotic formulas for moments of the stopping time to reach either n Heads or m Tails. In the symmetric case when n=m, we show that the expected duration with a fair coi\ n is a polynomial in p whose coefficients are Catalan numbers. Time permitting, we will also discuss the related problem of obtaining n Heads and m Tails. Joint work with Svante Janson and Doron Zeilberger