booklet - CUMC - Canadian Mathematical Society

SPELLING BEE: HOW DO YOU ADD A WORD?POLLY YUWhen does a sequence of integers contain a double arithmetic progression - a subsequencewhose terms and their positions both form arithmetic sequences? This questionis one of the motivations for the study of infinite words, spelled with numbers ratherthan with letters, and in particular, the study of additive complexity of an infinite word,which is one way of measuring how "complicated" the word is. This talk will motivatewords as another approach to double arithmetic progressions, and investigate wordsusing their visual representations.CONTRACTIVE SUBGROUPS OF THE GROUP ALGEBRA CGRANDY YEEWe give a brief introduction to the homomorphism problem in abstract harmonicanalysis, discussing the works of Cohen and Greenleaf on the characterization of contractivehomomorphisms in the Abelian and non-Abelian cases. Stokke provided analternate factorization which all contractive homomorphism must have. As a corollary,one obtains a version of this factorization for contractive homomorphisms of the groupalgebras CG and CH. Our work looks to provide a purely algebraic proof of the factorizationtheorem in this special case. We will examine the characterization of norm oneidempotents and the contractive subgroups of CG.Required Background: Group TheoryCONSTRUCTION OF NATURAL NUMBERS TO REAL NUMBERS USING SET THEORYRAYMOND VANMy discussion will be concerning the following:The construction of natural numbers and it’s evolution towards the reals. I will beusing a more set theoretic route to construct the naturals, integers and rationals. Thereare some different routes to get to the reals but mine will be concerning dedekind cuts.Throughout each number system, I will be introducing how to define addition.Required Background: set operations, equivalence classes, recursion42