The Lumen Scholar is connecting her interests in dance and math by studying the danceability of a knot.
With a dancer mother and a math teacher father, it seems like the perfect fit for Lila Snodgrass 鈥26 to study dance and math at 黑料不打烊. But her desire for research as a Lumen Scholar comes from a deep passion for both subjects.
鈥淒ance has always been part of who I am; I鈥檝e been dancing my whole life,鈥 said Snodgrass, who is from Pittsburgh, Pennsylvania. 鈥淚鈥檝e always liked math out of all of the subjects, and my senior Calculus teacher opened my eyes to how math can be more than just the numbers.鈥
More than the numbers
Seeing her passion, a faculty member recommended Snodgrass to Nancy Scherich, assistant professor of mathematics, who also happens to be a dancer.
鈥淵ou might think that math and dance are totally different. How would you combine those? But there’s actually quite a large sub-community in mathematics of people who dance,鈥 said Scherich.
The pair have been working on research in the field of topology, specifically knot theory, a subfield of mathematics dedicated to the study of knots.
鈥淲e are all familiar with the mathematical field of geometry as the study of shapes. We can geometrically think of shapes as being made of rigid, unbendable wire. This perspective is limiting because if a circle is made of rope, it can bend and fold and will not be a geometric circle anymore, but it is still a perfectly good loop. This is how the mathematical field of topology thinks of shapes in a different way than geometry- shapes are bendable and flexible,鈥 said Scherich.
According to Scherich, as a dancer travels the stage over time, their path traces out a knotted curve. If multiple dancers are on stage, and it is assumed that each dancer ends in the starting position of another dancer, the total paths danced by all dancers form a large knot. The danceability of a knot is the minimum number of dancers required to create the knot.
Connecting the dance
Mathematicians use tools called 鈥渋nvariants鈥 to distinguish knots, so Snodgrass, along with her research collaborators, have developed a new knot invariant called the 鈥渄anceability index鈥 and are comparing it to other invariants.
鈥淲e鈥檙e connecting this one idea of the dancer鈥檚 paths on the floor with these other ideas which are more connected to the greater idea of knot theory,鈥 Snodgrass says.
But applying for the Lumen Prize wasn鈥檛 initially on Snodgrass鈥 radar. The Lumen Prize is 黑料不打烊鈥檚 premier undergraduate research award that includes a $20,000 scholarship to support and celebrate their academic achievements and research proposals.
It wasn鈥檛 until her modern dance professor, Keshia Wall Gee, assistant professor of dance, encouraged the class to apply, she brought it to Scherich and was eventually awarded the honor.
From theory to the stage
Lumen Scholars work closely with their mentors during their final two years to pursue and complete their projects. Efforts traditionally include coursework, study abroad, research both on and off campus, internships locally and overseas, program development, and creative productions and performances.
In August 2024, Snodgrass, Sol Addison 鈥25 and Scherich presented this research at two conferences, and their research article on the subject has been accepted for publication in a peer-reviewed journal. They also demonstrating the danceability of twisted virtual knots.
鈥淚鈥檓 really excited to be able to connect these two things that feel so me, but so different worlds,鈥 said Snodgrass. 鈥淚t’s crazy that this is possible and that I’m given the opportunity to do this and be able to present it for other people.鈥
For her senior year, Snodgrass is hoping to create a movement study and eventually a full-length performance demonstrating her research.
鈥淚t鈥檚 illustrating these mathematical ideas that I鈥檝e been researching for the past year through movement with live dances and hopefully projections to show audiences this deep math research in a more accessible way,鈥 said Snodgrass.
