Science Student Spotlight: Joe Boninger

As an undergraduate, Joe Boninger double majored in mathematics and computer science at Swarthmore College. He received his B.A. in 2016, and then spent a year working as a software engineer, followed by a year at an education nonprofit, before joining the math department at the Graduate Center in 2018. Joe will be defending his dissertation in spring 2022, under the direction of Professor Ilya Kofman. Afterward, he has accepted a three-year NSF Postdoctoral Fellowship at Boston College.

Joe studies mathematical knots like the ones pictured here: http://katlas.org/wiki/The_Rolfsen_Knot_Table. Intuitively, knots are a lot like tangled-up loops of string in the real world. Mathematically speaking, knots are embeddings of the circle into the three-sphere, considered up to ambient isotopy. Joe’s research focuses on quantum invariants of knots, powerful tools whose definitions are motivated by quantum physics, and which can be used to examine knots and distinguish them from each other. The most famous quantum invariant is the Jones polynomial.

Joe is interested in fundamental questions about the Jones polynomial: how can we make sense of the polynomial from a three-dimensional point of view? What can it tell us about the topology of a knot’s complement? In Joe’s research, he has presented a new, matrix construction of the Jones polynomial, and he has shown that the Jones polynomial and related invariants can encode information about the hyperbolic geometry of knots in the thickened torus. Joe has been invited to speak about his work at three AMS Sectional meetings.

 

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