Tomasz S. Mrowka, the Singer Professor of Mathematics, has been named interim head of the Department of Mathematics, effective immediately. Mrowka takes over the role from Michael Sipser, the Barton L. Weller Professor of Mathematics. On June 5, Sipser was named dean of the School of Science, after serving since last December as interim dean, and since 2004 as head of the Department of Mathematics.
Mrowka brings substantial experience as a researcher, educator, and administrator to his new role as interim department head. He received his SB in mathematics from MIT in 1983, and his PhD from the University of California at Berkeley in 1988, under the direction of Clifford Taubes and Robin Kirby. He taught at Stanford University, Caltech, and Harvard University before coming to MIT in 1996. He served as chair of the department's Graduate Student Committee from 1999 to 2002, and has chaired its Pure Mathematics Committee since 2004, with a one year pause in 2009-10.
Mrowka’s work mixes analysis, geometry, and topology, specializing in the use of partial differential equations, such as the Yang-Mills equations from particle physics, to analyze low-dimensional mathematical objects. Among his results is the joint discovery, with Robert Gompf of the University of Texas at Austin, of surprising four-dimensional models of space-time topology, going far beyond the expected examples envisaged by Kunihiko Kodaira and others.
In joint work with Peter Kronheimer of Harvard, Mrowka has settled longstanding conjectures posed by John Milnor, on the complexity of knots in three space, and by Rene Thom, on surfaces in four space. Mrowka and Kronheimer also revealed a deep structure underlying the Donaldson invariants of four-dimensional manifolds, which was an avatar of the Seiberg-Witten invariants. In further recent work with Kronheimer, Mrowka used these tools to show that a certain subtle combinatorially defined knot invariant introduced by Mikhail Khovanov can detect “knottedness.”
Mrowka’s joint work with Kronheimer has been honored by the American Mathematical Society with the 2007 Oswald Veblen Prize in Geometry and the 2010 Joseph L. Doob Prize for their monograph, "Monopoles and Three-Manifolds" (Cambridge University Press, 2007). Mrowka was elected a fellow of the American Academy of Arts and Sciences in 2007, and was named a Guggenheim fellow in 2010 and a fellow of the Radcliffe Institute for Advanced Studies in 2013.