Soon after they were asked to develop a dance work based on the mathematical theory of differential cohomology, choreographers Kyla Barkin and Aaron Selisson found themselves sitting in a lecture at trying to understand the theory.
Jim Simons, the mathematician and hedge fund billionaire who helped establish the at Stony Brook, told Barkin, 36, and Selisson, 30, they would need at least four years of school to fully understand the theory. But the two dancers left the lecture with a clearer picture in their minds.
"Elements became more than dry definintions," Selisson said. "They possessed characteristics and interacted with each other in very specific ways. ... All of the sudden a world that was full of characters, each with their own personalities, emerged where once there was a theory we had heard of that was called differential cohomology."
After about two months of rehearsing about 25 to 30 hours a week, the Barkin/Selisson Project gave its world premiere performance of "Differential Cohomology" Monday Night at the , accompanied by music from composers Gregor Huebner, Rubin Kodheli and Fung Chern Hwei, performed by New York City-based Sirius String Quartet.
The performance was commissioned by the Simons Center Workshop on Differential Cohomology and Twisted K-Theory, funded by The Simons Foundation and The Stony Brook Foundation, and supported in part by the Fields Artist-in-Residence Program at FAR Space in New York City. Trombonist Ray Anderson also performed at the premiere.
The work opened with a pair of dancers moving closely within a hexagon of light cast from above, which remained a consistent image throughout the performance, as a key component of the theory of differential cohomology is the structure of a hexagon. As many as ten dancers moving within a larger hexagon, in harmony or in opposition at various points in the choreography, filled the stage in an artistic representation of concepts such as "heavy," "light," "linear," "geometric," and "fluid."
It differs from the choreographers' typical work, described by Barkin as "visceral and emotionally driven," which was illustrated by the lively performance of "And So On...," a duet between Barkin and Selisson, and the more complex quartet "Sequitur or Non," which preceded "Differential Cohomology."
"While creating the piece we felt that the interpretation of the theory needed to be clear to the mathematicians, but the piece, as a whole, needed to appeal to the senses and the masses as well as following the rules of the theory," Barkin said. "We had to find a way to execute a very specific task while still fulfilling our own artistic needs."
Many in the audience, which consisted of regular Staller Center guests and dance enthusiasts along with students, scientists and mathematicians, felt a connection to the performances even if unfamiliar with the theory of differential cohomology. Guests complimented the dancers' clarity of movement and depth of expression.
"There was such variety between the music and the dancing," said Bruce Futcher, a microbiologist from Stony Brook. "It was interesting and stimulating."
Lei Bowman of Huntington was impressed by the level of detail in the choreography.
"It definitely exceeded my expectations. I couldn't move my eyes from [Barkin] for a minute," said Lei Bowman of Huntington. "The emotion was just perfect. I liked the design of the dance."
John Morgan, director of the Simons Center, called "Differential Cohomology" fun to watch.
"The fundamental choreography seemed to capture the essence of the main diagram of differential cohomology," he said.