Tomasz Mrowka is the Singer Professor of Mathematics at the Massachusetts Institute of Technology. He studies the Yang-Mills equations and other partial differential equations of high-energy physics and is particularly interested in their applications to the study of low-dimensional topology. Recently he and Peter Kronheimer, of Harvard University, using these tools, showed that a certain subtle combinatorially defined knot invariant introduced by Mikhail Khovanov can detect “knottedness.”
Mrowka’s recent work centers mainly on using the simplest non-abelian gauge theory and its applications to knot theory. This provides a bridge from the toolbox of workers in three-manifold topology to that of workers in representation theory. In his work with Kronheimer, he intends to extend the range of this bridge to a wider class of representation theory–inspired invariants by considering more general gauge theories.
Mrowka and Kronheimer jointly won the 2007 Oswald Veblen Prize in Geometry and the 2011 Joseph L. Doob Prize for their monograph Monopoles and Three-Manifolds (Cambridge University Press, 2007); both prizes are awarded by the American Mathematical Society. He is a former Sloan Research Fellow and Guggenheim Fellow and has received an NSF Young Investigator Award. Mrowka is a fellow of the American Academy of Arts & Sciences and earned his PhD from the University of California, Berkeley.