Jessica Striker, NDSU professor of mathematics, spoke recently on campus at a Women in Research luncheon work funded by a grant of $384,623 from the National Science Foundation (NSF) to conduct research in a branch of math called algebraic combinatorics. The award supports research from Striker and her team across three projects.

Algebraic combinatorics involves determining patterns and relationships in shapes and structures that exist in spaces with more than two dimensions.

In the first project, the researchers are exploring how systems change and evolve over time. They are looking at how different actions impact the paths of objects and have uncovered a connection between two mathematical ideas: promotion on P-strict labelings and rowmotion on B-bounded P-partitions. This implications of this connection are important because it will help expand our understanding of how we count and arrange objects in complex situations and with a wide variety of objects.

In the second project, Striker is addressing a longstanding challenge involving alternating sign matrices, which are mathematical structures with similarities to the square ice model in physics. She is attempting to establish links between these structures and another mathematical concept known as totally symmetric self-complementary plane partitions.

The third project involves making special tools, called sl4-web bases, for four-row rectangular diagrams. These tools will help researchers understand how elements can be arranged, especially in diagrams with four rows. Quantum link theories and cluster algebras (which help explain complex geometric and algebraic structures) will be able to utilize these tools.

The grant also supports the development of SageMath open-source software. SageMath is a powerful tool for mathematical computation and visualization, and Striker will make the code related to her research available and train others in SageMath coding for combinatorics research. These contributions will enhance SageMath's capabilities in algebraic combinatorics and related fields.

Striker's grant prioritizes broader impacts and aims to foster mentorship, diversity, and outreach in mathematics and supports efforts to increase the representation of women and North Dakotans in mathematics. While Striker is currently engaged in K-12 student outreach and has already developed materials and visited classrooms to inspire the next generation of mathematicians, the grant will further enable these efforts. It will also include the establishment of a Math Exploration Camp for high school students and a book of combinatorics activities.

"Dr. Striker's project showcases the way excellent research and outreach can be intertwined successfully, and is a noteworthy example of the type of value our NDSU researchers provide to the state," said Colleen Fitzgerald, NDSU vice president for research and creative activity. "By sharing and promoting her unique accomplishments in mathematics, she's serving as a role model for women and youth in our state and truly living out NDSU's land grant mission."

Striker's research is supported by the National Science Foundation, award 2247089