Arthur Jacob Parzygnat

Arthur Jacob ParzygnatQuantum Field Theorist

Mathematician Arthur Jacob Parzygnat (Macaulay Honors College at Queens College, 2010), now exploring topological quantum field theory at the CUNY Graduate Center, is one of five CUNY students to win 2011 awards under the National Science Foundation Graduate Research Fellowship Program. It is geared to assuring the vitality and diversity of America’s scientific and engineering workforce.

Parzygnat, who describes himself as a mathematical physicist, received a $30,000 NSF grant payable over three years. He said his interest is in understanding quantum field theory (a description of our universe which occurs at the intersection of quantum mechanics and relativity) from a mathematically rigorous point of view.

Rather than working with Feynman path integrals, which physicists use extensively for computations, mathematicians look at the underlying structure of particle interactions. These seem to be best described by one-dimensional graphs, but analysis hasn’t been developed for such objects. Therefore, most modern research involves a two- or higher-dimensional “tubed” version of these objects. Seeking a new pathway, Parzygnat will utilize topology, algebra and category theory to again consider one-dimensional versions.

If this sounds abstruse, it is. Are there practical payoffs? Perhaps, but the applications of many areas of mathematics have taken years to become evident.

Parzygnat veered into mathematics as a freshman thanks to the Macaulay Honors College, when he got advice on what math course to take from a Macaulay junior, Joseph Hirsch, who now also is working toward his Ph.D. in math at the Graduate Center (Parzygnat’s doctorate will be in physics, possibly in 2015). “He advised me to take an honors abstract algebra course. I didn’t know what I was getting myself into. It was too advanced for me, and I didn’t do phenomenal, but I learned I wanted to go into math. I wanted a real challenge and I knew I’d be in good company,” Parzygnat said.