The annual Mathematics Department Summer Research Poster Symposium took place on Oct. 17 with a wide range of presentations, including studies on “Knot Polynomials,” “Trisections of 4-Manifolds via Covering Spaces” and “Optimizing an Agent-Based Model for Cardiac Cell Signaling.”

Students showcased the culmination of their intensive research, working alongside faculty members to explore various pure math and applied math studies.

“I’m super impressed,” said Saba Gerami, an assistant professor in math. “I am really proud of how their research turned out. The students exceeded my expectations every step of the way.”

With studies primarily supported by the Frost Summer Undergraduate Research Program, students received funding to conduct research alongside faculty members to explore topics of interest in depth.

Some students will present their results at conferences and cite their studies in Ph.D. program applications, among other possibilities for sharing their work with others.

“Now that I’m applying for a Ph.D., it’s great because I can show that I have research experience,” said Tri Tran, an international student from Vietnam, who’s in his last year of the Mathematics Department’s blended bachelor’s and master’s degree program. “Over the past two years, we have had papers that are published or in pre-print. Studying math feels very rewarding to me. I like solving puzzles.”

Working with faculty advisor Terrin Warren, Tran and fellow student researcher Matthew Stark said their team’s study titled “Trisections of 4-Manifolds via Covering Spaces” focused on work they summarized as follows: “There are lots of interesting objects in 4- and 5-dimensions but they are extremely hard to visualize. However, there are tools such as Heegaard splittings and trisections that allow us to ‘see’ higher-dimensional objects by building them up from lower-dimension ‘handles.’ There has been research on these objects but analyzing them is quite hard given their nature. We restrict our attention to a subclass of these objects called spun 4-manifolds and studied their trisections. The result is a generalized description of a finite-sheeted covering space of any spun 4-manifold. Moreover, we apply the universal property to trisection cubes to show the existence and uniqueness of any finite-sheeted cover of a 4-manifold admitting a trisection. Future works include finding a unifying result of our two main theorems to classify and describe all finite-sheeted covers of a spun 4-manifold.”

Paco Jones, a third-year math major from Seattle, said that his applied math study related to heart cell signaling, a continuation of ongoing research which could one day hopefully lead to a better understanding of heart function and health, has been educational and captured his interest.

“From a high level, my biggest interests are math, data science and computer science,” Jones said. “This project combined those things. I don’t have a specific career goal that I'm really targeting yet, but I’d like to pursue work that kind of combines all of my interests.”

The two-hour symposium included the following team poster presentations:

Computation of Legendrian Contact Homology

• Students: Elijah Guptill, James Rea
• Faculty advisor: Austin Christian

Targeting Conceptions of Derivative: Introducing Derivatives in Calculus with Inquiry

• Students: Chris Liu, Morgan Raak, Hannah Freund
• Faculty Advisor: Saba Gerami

Knot Polynomials

• Students: Kyler Andolina, Vanessa Garcia Sanchez
• Faculty Advisor: Anton Kaul

Optimizing an Agent-Based Model for Cardiac Cell Signaling

• Students: Eve O’Neill, Paco Jones
• Faculty Advisor: Alexander Ruys de Perez

Trisections of 4-Manifolds via Covering Spaces

• Students: Matthew Stark, Tri Tran
• Faculty Advisor: Terrin Warren

Magic Positivity and Ehrhart Theory

• Student: Chance Crigler
• Faculty Advisor: Dana Paquin

50,000 Spectra and Counting: A Python Pipeline for Hubble Data

• Students: Maya Seagraves, Rachael Beaton, Meredith Durbin, Vanessa Rivera
• Faculty advisor: Dana Paquin

Optimizing Calculus Textbook Use Outside of the Classroom

• Students: Natalie Hawk, Maurice Kennedy, Taiga Sobajima
• Faculty Advisor: Danielle Champney

Representation Theory via the lens of Categories

• Student: Mark Muzquiz
• Faculty Advisor: Rob Easton

Counting Representations Arising from Group Actions with n Orbits

• Student: Elli Sumera
• Faculty Advisor: Jeffrey Liese

Topological Data Analysis Techniques in Genetic Stock Identification of Chinook Salmon

• Alison Watson (and team)
• Research Experiences for Undergraduates at UW Bothell