Mathematics Assistant Professor David Penneys’ new, five-year, $420,000 National Science Foundation Early Career Development (CAREER) Award funds work on "Representing and Classifying Enriched Quantum Symmetry." Symmetry plays an important role in mathematics and science. In recent decades, quantum mathematical objects have emerged, whose symmetries form a group-like structure called a "tensor category,” which has a collection of objects with a binary fusion operation.

“The award will advance my work,” Penneys says, “by providing funding for travel for myself and my collaborators. Even in today's modern world, some of the best ideas come from in-person collaboration. Nothing can match being able to share a chalkboard in the same room.”

According to Penneys, one of the challenges for mathematicians is to find the correct mathematical language to accurately describe nature, such as the mathematical notion of a group describing symmetry. Fusion categories describe quantum symmetry, and they provide the mathematical language to describe topological phases of matter. In turn, topological phases of matter may be potentially useful in developing a topological quantum computer.

The award will allow Penneys to fund two graduate students to attend a 2017 Mathematical Sciences Research Institute Graduate Summer School, where they will take mini-courses from experts in the field. In addition, the award will support Penneys’ time to mentor undergraduate research during two summers of the five-year grant.

“Meanwhile, the grant’s outreach component allows me to hold summer schools for graduate students, postdocs and early-career faculty focused on quantum symmetries, which will help build and strengthen our developing research community," Pennys says. “I am also partnering with Ohio State's STEAM Factory to enhance general scientific and mathematical literacy in the community.”