Tomasz Mrowka | |
|---|---|
 Mrowka atAarhus University, 2011 | |
| Born | (1961-09-08)September 8, 1961 (age 64) |
| Alma mater | |
| Known for | Kronheimer–Mrowka basic class |
| Awards |
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| Scientific career | |
| Fields | Mathematics |
| Institutions | MIT |
| Thesis | A local Mayer-Vietoris principle for Yang-Mills moduli spaces (1988) |
| Doctoral advisor | Clifford Taubes Robion Kirby |
| Doctoral students | Larry Guth Lenhard Ng Sherry Gong |
Tomasz Stanislaw Mrowka (born September 8, 1961) is an American mathematician specializing indifferential geometry andgauge theory. He is the Singer Professor of Mathematics and former head of theDepartment of Mathematics at theMassachusetts Institute of Technology.
Mrowka is the son of Polish mathematicianStanisław Mrówka [pl],[1] and is married to MIT mathematics professorGigliola Staffilani.[2]
A 1983 graduate of the Massachusetts Institute of Technology, he received the PhD from theUniversity of California, Berkeley in 1988 under the direction ofClifford Taubes andRobion Kirby. He joined the MIT mathematics faculty as professor in 1996, following faculty appointments atStanford University and at theCalifornia Institute of Technology (professor 1994–96).[3] At MIT, he was the Simons Professor of Mathematics from 2007–2010. Upon Isadore Singer's retirement in 2010 the name of the chair became the Singer Professor of Mathematics which Mrowka held until 2017. He was named head of the Department of Mathematics in 2014 and held that position for 3 years.[4]
A priorSloan fellow and Young Presidential Investigator, in 1994 he was aninvited speaker at theInternational Congress of Mathematicians (ICM) inZurich. In 2007, he received theOswald Veblen Prize in Geometry from theAMS jointly withPeter Kronheimer, "for their joint contributions to both three- and four-dimensionaltopology through the development of deep analytical techniques and applications."[5] He was named a Guggenheim Fellow in 2010, and in 2011 he received theDoob Prize withPeter B. Kronheimer for their bookMonopoles and Three-Manifolds (Cambridge University Press, 2007).[6][7] In 2018 he gave a plenary lecture at the ICM inRio de Janeiro, together with Peter Kronheimer. In 2023 he was awarded theLeroy P. Steele Prize for Seminal Contribution to Research (with Peter Kronheimer).[8]
He became a fellow of theAmerican Academy of Arts & Sciences in 2007,[9] and a member of theNational Academy of Sciences in 2015.[10]
Mrowka's work combines analysis, geometry, andtopology, specializing in the use ofpartial differential equations, such as theYang-Mills equations from particle physics to analyze low-dimensional mathematical objects.[4] Jointly withRobert Gompf, he discovered four-dimensional models of space-time topology.[11]
In joint work with Peter Kronheimer, Mrowka settled many long-standing conjectures, three of which earned them the 2007 Veblen Prize. The award citation mentions three papers that Mrowka and Kronheimer wrote together. The first paper in 1995 deals withDonaldson's polynomial invariants and introducedKronheimer–Mrowka basic class, which have been used to prove a variety of results about the topology and geometry of4-manifolds, and partly motivated Witten's introduction of theSeiberg–Witten invariants.[12] The second paper proves the so-calledThom conjecture and was one of the first deep applications of the then brand new Seiberg–Witten equations to four-dimensional topology.[13] In the third paper in 2004, Mrowka and Kronheimer used their earlier development ofSeiberg–Witten monopole Floer homology to prove theProperty P conjecture forknots.[14] The citation says: "The proof is a beautiful work of synthesis which draws upon advances made in the fields of gauge theory,symplectic andcontact geometry, andfoliations over the past 20 years."[5]
In further recent work with Kronheimer, Mrowka showed that a certain subtle combinatorially defined knot invariant introduced byMikhail Khovanov can detect “unknottedness.”[15]
