Title: An introduction to continuous model theory

Abstract: The first order logic of metric structures is a new and rapidly developing field of mathematical logic. I'll give a basic introduction to this subject which helps to give a "peek under the hood" for the techniques motivating the colloquium talk.

Short Bio: Professor Thomas Sinclair is from Purdue University and works on Von Neumann Algebras, Model Theory of Metric Structures, Operator Systems and Ergodic Theory.

Title: Metric lattices

Abstract: A lattice is a partially ordered set so that each pair of elements has a least upper bound and greatest lower bound. I'll describe a class of lattices which admit natural compatible metric structures and give an attempt at what it means to construct continuous limits of sequences of finite metric lattices.

Speaker: Colleen Mitchell, Department of Mathematics

Title: Fibonacci and related numbers in determinants

Abstract: There are many references to matrices or determinants that have Fibonacci numbers as elements. In this talk, we show several determinants expressing the Fibonacci and related polynomials. This method is well-applicable to other numbers or polynomials too. In addition, these results, based on the form of the Hessenberg matrix, allow for many applications such as inverse formulas, explicit expressions, and continued fraction...

Title: Finding needles in haystacks: Boolean intervals in the weak order of $\mathfrak{S}_n$

Abstract: Finding and enumerating Boolean intervals in $W(\mathfrak{S}_n)$, the weak order of symmetric group $\mathfrak{S}_n$, can feel like trying to find needles in a haystack. However, through a surprising connection to the outcome map of parking functions we provide a complete characterization and enumeration for Boolean intervals in $W(\mathfrak{S}_n)$. We show that

for any $\pi\in\mathfrak{S}_n$...

Title: Fibonacci and related numbers in determinants

Abstract: There are many references to matrices or determinants that have Fibonacci numbers as elements. In this talk, we show several determinants expressing the Fibonacci and related polynomials. This method is well-applicable to other numbers or polynomials too. In addition, these results, based on the form of the Hessenberg matrix, allow for many applications such as inverse formulas, explicit expressions, and continued fraction...

Title: Number theory