Biography: Dr. Pamela E. Harris is a Mexican-American mathematician and serves as Associate Professor of Mathematics at the University of Wisconsin-Milwaukee. She received her BS from Marquette University and MS and Ph.D. in mathematics from the University of Wisconsin-Milwaukee. Dr. Pamela E. Harris’s research is in algebraic combinatorics and she is the author of over 70 peer-reviewed research articles in internationally recognized journals. She is a Fellow of the American Mathematical Society and of the Association for Women in Mathematics. Dr. Harris is also an award-winning mathematical educator, receiving the 2022 MAA’s Haimo Award for Excellence in Mathematical Education, the 2020 MAA Northeast Section Award for Distinguished Teaching, the 2019 MAA Alder Award for Distinguished Teaching by a Beginning Mathematics Faculty Member, and the 2019 Council on Undergraduate Research Mathematics and Computer Sciences Division Early Career Faculty Mentor Award. She is the President and co-founder of Lathisms: Latinxs and Hispanics in the Mathematical Sciences, cohosts the podcast Mathematically Uncensored, and is a coauthor of the books Asked And Answered: Dialogues On Advocating For Students of Color in Mathematics, Practices, and Policies: Advocating for Students of Color in Mathematics and Read and Rectify: Advocacy Stories from Student of Color in Mathematics.

Additional information can be found here.

Topics include:

Finding needles in haystacks: Boolean intervals in the weak order of $\mathfrak{S}_n$
Finding and enumerating Boolean intervals in W(Sn)W(\mathfrak{S}_n)W(Sn​), the weak order of the symmetric group Sn\mathfrak{S}_nSn​, 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(Sn)W(\mathfrak{S}_n)W(Sn​). We show that for any π∈Sn\pi \in \mathfrak{S}_nπ∈Sn​, the number of Boolean intervals in W(SnW(\mathfrak{S}_nW(Sn​ with minimal element π\piπ is a product of Fibonacci numbers. This is joint work with Jennifer Elder, Jan Kretschmann, and J. Carlos Martínez Mori.

Multiplex juggling sequences and Kostant’s partition function
Multiplex juggling sequences are generalizations of juggling sequences (describing throws of balls at discrete heights) that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. Kostant’s partition function is a vector function that counts the number of ways one can express a vector as a nonnegative integer linear combination of a fixed set of vectors. What do these two families of combinatorial objects have in common? Attend this talk to find out!

How to choose your own mathematical adventures
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 nor 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…?”