Pamela E. Harris

University of Wisconsin, Milwaukee

How to Choose Your Own Mathematical Adventures

Public lecture

Thursday, November 2, 2023

6:00 p.m.

Haldeman 041

Abstract: What is mathematical research? How does a mathematician find problems to work on? How does one build mathematical collaborations? In this talk, I will share my journey to research mathematics, what it entails, how I have developed new research ideas, and how I have found my place within the mathematical community. Mathematical topics of discussion will include lattice point visibility, parking functions, and a connection between vector partition functions and juggling. No prior mathematical background on these topics is expected or assumed, as we will introduce all of the needed concepts from first principles. All that is needed is the willingness to wonder and ask the question: “what happens if...?”

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

Colloquium

Thursday, November 2, 2023

3:15 p.m.

Kemeny 007

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 $\pi\in W(\mathfrak{S}_n)$, the number of Boolean intervals in $W(\mathfrak{S}_n)$ with minimal element $\pi$ is a product of Fibonacci numbers. This is joint work with Jennifer Elder, Jan Kretschmann, and J. Carlos Martínez Mori.