Undergraduate Student Seminar (Pi Mu Epsilon talk)- Title: Conway-Coxeter Friezes and SL_k-Tilings

Title: Conway-Coxeter Friezes and SL_k-Tilings
Speaker:  Zachery Peterson, College of William and Mary
Date and time: Friday, April 17, 4:30-5:30
Place: Duques 152
 
Abstract:
Friezes were first introduced and studied in the case k=2 by Conway and Coxeter in the 1970s. They proved various results about periodicity and symmetry of friezes and, in particular, that there is a bijection between SL_2-friezes over positive integers, often called Conway-Coxeter friezes, and triangulations of polygons. Later, the discovery of cluster algebras in the 2000s created a newfound interest in friezes, as cluster algebras of type A are closely tied to triangulations of polygons. Moreover, additive categorification of cluster algebras yields another important relation between friezes and representation theory of quivers. Subsequent connections were also discovered between frieze patterns and Farey graphs, cross-ratios, and continued fractions.  We will discuss the original results of Conway and Coxeter and attempt to contextualize the modern work which extends their results.

Short bio:
Dr. Zachery Peterson received a BS in Mathematics from the George Washington University in 2018 and a Ph.D. from the University of Kentucky in 2024.  His focus is on algebraic combinatorics, with specific interests in cluster algebras and their relationship to friezes and flow polytopes.  He currently works at the College of William and Mary as a visiting assistant teaching professor in the mathematics department teaching classes of all levels from precalculus to abstract algebra as well as advising undergraduates.  In his free time, he enjoys playing board games and taking long walks through many of Virginia's beautiful parks.

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This talk is open to everyone.  Mathematics majors and minors are especially encouraged to attend.