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Mrowka receives Veblen geometry prize

Tomasz Mrowka
Tomasz Mrowka

Professor of mathematics Tomasz Mrowka received the 2007 Oswald Veblen Prize in Geometry, one of the highest honors in the field of geometry, on Jan. 6.

Mrowka shares the award with Harvard University professor Peter Kronheimer. The American Mathematics Society honored the pair "for their joint contributions to both three- and four-dimensional topology through the development of deep analytical techniques and applications."

Mrowka received the award, which is given every three years, at the annual meeting of the American Mathematics Society in New Orleans.

Mrowka said of winning the award: "The list of past Veblen prize winners contains many of my mathematical heroes and teachers. To be included in this list is a singular honor."

The award citation specifically mentions three papers Mrowka and Kronheimer wrote together in the past 13 years. One of the papers deals with Donaldson's polynomial invariants, which have been used to prove a variety of results about the topology and geometry and four-manifolds.

That paper, published in 1995, "gives a conceptual framework and an organizing principle for some of the disparate observations and calculations of Donaldson invariants that had been made earlier … and it has been the point of departure and the motivating example for important further developments, most spectacularly for Witten's introduction of the so-called Seiberg-Witten invariants," according to the award citation.

The second paper proves the so-called "Thom conjecture" and was one of the first deep applications of the then brand new Seiberg-Witten equations to four-dimensional topology.

In a third paper published in 2004, Mrowka and Kronheimer used their earlier development of Seiberg-Witten monopole Floer homology to prove the Property P conjecture for knots. "The proof is a beautiful work of synthesis which draws upon advances made in the fields of gauge theory, symplectic and contact geometry, and foliations over the past 20 years," reads the citation.

Mrowka joined the MIT faculty in 1996. He served as chair of the Graduate Student Committee from 1999 to 2002 and has chaired the Pure Mathematics Committee since 2004. He is also on the editorial boards of several mathematics journals.

He received the S.B. in mathematics from MIT in 1983 and the Ph.D. from the University of California at Berkeley in 1988. He taught at Stanford, Caltech and Harvard before coming to MIT.

In 1993 he received an Alfred P. Sloan Research Fellowship and a National Young Investigator Award.

A version of this article appeared in MIT Tech Talk on February 7, 2007 (download PDF).

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