Frobenius problem over number fields (Lenny Fukshansky, CMC)

The classical Frobenius problem asks for the largest integer not representable as a non-negative integer linear combination of a relatively prime integer n-tuple. This problem and its various generalizations have been studied extensively in combinatorics, number theory, algebra, theoretical computer science and probability theory. In this talk, we will consider a reformulation of this problem in the context of number fields, which leads to some arithmetic questions about semigroups of algebraic integers and height functions. This is joint work with CMC student Edward Shi.