Tomasz S. Mrowka
Massachusetts Institute of Technology
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2015)
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Biosketch
Tom Mrowka is a mathematician recognized for his work analysis and geometry and their applications to low dimensional topology. Known for the resolution of a series of long standing conjectures due to among others Bing, Milnor, and Thom, regarding the topology of knots, and manifolds of dimension three and four. Much of his work is joint with Peter Kronheimer. Together they developed tools which give deep insight into low dimensional topology using the differential equations of high energy physics, like the Yang-Mills and Siebert-Witten equations. Born in State College Pennsylvania in 1961 and spent time there, Kalamazoo, and Buffalo as a child. He received his SB from MIT in 1983 and his PhD from UC Berkeley under the direction of Clifford Taubes in 1988. He spent a year at the Mathematical Sciences Research Institute in Berkeley. After 2 years as Szego Assistant Professor at Stanford University, he moved to Caltech receiving tenure in 1992. He moved to MIT in 1996 and has been the department head since 2014. He is the winner of the 2007 Veblen Prize and 2011 Doob Prize both jointly with Peter Kronheimer. He was a Sloan Foundation Fellow, a Radcliffe Fellow and is a member of American Academy of Arts and Sciences, class of 2007 and the National Academy of Sciences, class of 2015.
Research Interests
Mrowka's interests are focused on the topological implications of the differential equations of high energy physics
in particular the Yang-Mills equations and the Seiberg-Witten equations. These equations are can be use to reveal very subtle properties of low dimensional manifolds. In 1992, with Gompf, he showed that there were four dimensional manifolds far more complicated than ones known previously. With Kronheimer, he gave new insights into the structure of Donaldson’s invariants and together they developed many tools for the study of three and four dimensional manifolds. They used these tools to resolve a long standing conjecture of Thom on the complexity of surfaces in four-dimensional manifolds, a conjecture of Bing on possible counter examples to the Poincare conjecture and more recently they showed that a popular knot invariant, Khovanov Homology was able to distinguish the unknot.
