Kamuela Yong, *University of Hawai’i - West O’ahu*

*Please note, the session from 2pm-4pm on Friday December 9th will be a closed
session.*

Traditional Indigenous marriage rules have been studied extensively since the mid-1800s. Despite this, they have historically been cast aside as having very little utility. Here, I will walk through some of the interesting mathematics of the Gamilaraay system and show that, instead, they are in fact a very clever construction. Indeed, the Gamilaraay system dynamically trades off kin avoidance – to minimise incidence of recessive diseases – against pairwise cooperation, as understood through Hamilton’s rule.

I’ve been introduced to the concepts of ethnomathematics, decolonization and Indigenization throughout my career as a mathematics educator and researcher. I will share the ways in which these concepts shape research and teaching conversations that I now have.

A pangram is an expression which contains all letters of the alphabet in the expression’s language. An autogram is an expression which describes itself (correctly) by (for example) describing how many copies of each letter appear in the expression. The first pangrammatic autogram found in English was the result of an 18-month long project in the 1980’s resulting is the sentence, “Only the fool would take trouble to verify that his sentence was composed of ten a’s, three b’s, four c’s, four d’s, forty-six e’s, sixteen f’s, four g’s, thirteen h’s, fifteen i’s, two k’s, nine l’s, four m’s, twenty-five n’s, twenty-four o’s, five p’s, sixteen r’s, forty-one s’s, thirty-seven t’s, ten u’s, eight v’s, eight w’s, four x’s, eleven y’s, twenty-seven commas, twenty-three apostrophes, seven hyphens and, last but not least, a single !” In this presentation, Edward Doolittle, Associate Professor of Mathematics at First Nations University of Canada, will describe his effort to “translate” such sentences into the Plains Cree language. Joint work with Arok Wolvengrey, Professor of Linguistics at First Nations University.

The use of infinitesimal methods (nonstandard analysis) in calculus can simplify computations, including the determination of convergence or divergence of a series. The level comparison test for series with nonnegative terms is an example. Featuring a computation that is similar in difficulty to the test for divergence, this test hinges on whether the reciprocal of the “omegath” term of the series lies in the “convergence zone” or in the “divergence zone.” In this talk the test is described, justified, and demonstrated. (The level comparison test is introduced in the textbook Calculus Set Free: Infinitesimals to the Rescue, Oxford University Press, 2022.)

Tribal colleges and universities have and continue to seek out connections between the local heritage and culture and the mainstream education content. In math, calls for culture to be more integrated into the classroom have been met with epistemological challenges as well as a dearth of math and local culture resources. This research project addresses both of these challenges. This presentation will specifically share on the collaborative development, evaluation, and confirmation of an epistemological framework for curriculum development at Sitting Bull College. Following an Indigenous Research Methodology, a group of tribal college math instructors, Lakota language immersion teachers, and fluent elders gathered to discuss D/Lakota math connections. Specific examples from these recorded discussions will be shared. The framework and the results demonstrate that math fluency and Dakota/Lakota language fluency can grow together.

In this talk I will introduce you to the wonderful world of 2-dimensional topology! We will mainly focus on how we can use combinatorial constructions of curves (1-dimensional objects) on surfaces (2-dimensional objects) to answer questions about the group of symmetries of a surface, which we call the mapping class group. I intend for this talk to be accessible to folks with a wide variety of backgrounds including undergraduate and graduate students.

The Steklov eigenvalue problem has been one of the central topics in spectral geometry over the last decade. In particular, a lot of research has been focused on the asymptotic distribution of Steklov eigenvalues. In this talk, we investigate asymptotics for Steklov eigenvalues on surfaces with a boundary that is only smooth to finite order. In particular, we obtain remainder estimates in Weyl’s law with a rate of decay depending on the order of smoothness.

Given a graph, we define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Using the theory of geometric tropicalization, we characterize when the tropical compactification of the compact moduli space agrees with the theory of geometric tropicalization. In this talk, I will give a gentle introduction to the moduli spaces of graphically stable curves and their tropical counterparts, and briefly describe that such a tropicalization occurs only when the graph is complete multipartite.

In 1987, physicists Bak, Tang, and Wiesenfeld created an idealized version of a sandpile in which grains of sand are piled on the vertices of a (combinatorial) graph and are subjected to certain avalanching rules. In the last three decades, there has been a broad effort in the statistical physics community to understand the dynamics of this model, which has a natural underlying algebraic structure. The sandpile monoid and the sandpile group encode the short and long-term dynamics of the system. Disguised under different names, these algebraic structures have been widely studied in diverse contexts including algebraic combinatorics, arithmetic geometry, and algebraic geometry.

In this talk we give an introduction to the sandpile model and the algebraic structures attached to it. We provide a broad overview of the theory and discuss some of the more celebrated results. We end the talk with a discussion about an ongoing project that showcases some of the unresolved fundamental questions accessible to undergraduates.

In this joint talk, we’ll discuss some pedagogical methods we have developed and used in Applied Precalculus, a course for pre-Business majors at TCU to prepare them for Applied Calculus. The population of students who take this course frequently provides certain challenges to the instructor, so we implemented a new course structure in several sections of the course a few years ago, and it has been evolving ever since. In this new course structure, the course is flipped, with exposure to material happening outside of class, and the course is also somewhat individually-paced, incorporating mastery-based grading in a series of module quizzes. We will discuss our motivation for this course structure, details on its implementation, how it has evolved over time, and what challenges still remain.

This presentation will share our work, through the Aboriginal and Torres Strait Islander Mathematics Alliance (ATSIMA), in teaching mathematics in connection to the culture of our Communities. I will give an overview of my personal journey in mathematics and how this led to the development of ATSIMA. I will introduce the Goompi Model, which is built on the premises that mathematics is an intrinsic part of culture and can guide the development of connected, culturally responsive pedagogies in mathematics. I will then share some stories from the classroom to show what is possible from this approach and have an open dialogue across the gathering to share ideas.

Indigenous cultures have been using mathematics in their lives for generations. In this talk, we present methods of using place-based examples in a trigonometry classroom using Native Hawaiian culture. Through these examples, we hope to increase student participation in the classroom from both Indigenous and non-Indigenous students as well as spread awareness of various cultures.