Bio: Denise Rangel Tracy is an Assistant Professor of Mathematics at Francis Marion University in Florence, South Carolina. Her mathematical interests include commutative and homological algebra and making abstract ideas accessible through outreach and play. She earned her bachelor’s and master’s degrees from the University of North Carolina at Greensboro and her PhD from the University of Texas at Arlington.

She is actively involved with the MAA, where she serves as the MAA Southeastern Section State Director for South Carolina and on the Executive Committee of the SIGMAA on Recreational Mathematics. She is also involved with the AWM, serving on the Project Management Committee for the EvenQuads project, as well as the Social Media Committee and the JMM Planning Committee. Across her teaching, service, and outreach, she is especially interested in mentoring students and building welcoming mathematical communities.

Outside of her professional work, she enjoys spending time with her husband and two children.

Additional information can be found here.

Topics Include:

Syzygy shenanigans, when will it end? 
We’ll explore chains of relations hidden inside matrices where each relation spawns another as we wonder just how long this can go?

This interactive talk invites participants to bring a laptop or tablet as we build ideas together. We will introduce polynomial rings and develop the notion of free resolutions using the familiar language of linear algebra and matrix theory, as such matrix multiplication and kernels (null spaces). As a group, we will form and test conjectures about the maximum possible length of free resolutions over different polynomial rings, culminating in Hilbert’s Syzygy Theorem.

EvenQuads: the game, the mathematics, and the honorees
EvenQuads is a double-sided card deck created to celebrate the 50th anniversary of the AWM. The deck is built around a mathematically rich structure that gives rise to a wide range of games and support exploration of a variety of mathematical concepts. One side of each card features a profile of a woman mathematician who has made significant contributions to the field, while the other side displays symbols in varying colors and quantities that encode the underlying mathematics of the deck.

This talk can be structured in multiple ways depending on audience and goals. It may combine historical context and biographical narratives to highlight the lives and impact of women mathematicians. Additionally, the focus may be placed on the mathematics of the deck itself, spanning discrete mathematics, combinatorics, probability, algebra, and finite geometry. In either case, the talk introduces the design of the deck and basic game play, with opportunities for audience interaction throughout.