Mathematics Junior Colloquium

Speaker: Srishti Singh (UTK)

Title: Chicken Nuggets, Numerical Semigroups, and Wilf's Conjecture

Abstract: Imagine that you want to buy a certain number of chicken nuggets and the store only offers boxes of 6, 9, and 20. Can you buy 10 nuggets? (no!) What about 18? (in two different ways!) All the amounts of nuggets you can buy form the numerical semigroup generated by 6, 9 and 20. Of course, you can have a numerical semigroup generated by any finite set of positive integers. These objects have some really nice combinatorial properties that can be used to study otherwise complicated algebraic problems, with applications ranging from integer programming and optimization to algebraic geometry and even music theory. In this talk, we will explore these numerical semigroups, see some of their applications, and discuss a long-standing open problem known as Wilf's Conjecture.