Peter B. Kronheimer

Peter Benedict Kronheimer (* 1963 in London ) is a British mathematician who deals with differential geometry and three - and four-dimensional topology.

Biography

Kronheimer visited the City of London School and studied at Merton College, Oxford University, where in 1984 he took his bachelor's degree and received his doctorate at Michael Atiyah 1986 (ALE Gravitational instanton ). After that, he was at Balliol College, Oxford, and two years at the Institute for Advanced Study, before returning as a tutor and Fellow at Merton College, Oxford. In 1995, he moved to Harvard University, where he is a professor of mathematics at the time William Caspar gray stone.

Kronheimer worked, often with Tomasz Mrowka from the Massachusetts Institute of Technology (MIT), about the topology of 4 -manifolds in connection to the seminal work of Simon Donaldson, with the Kronheimer also wrote a book. Together Kronheimer and Mrowka proved a structure theorem for the Donaldson invariants. In 1994, he proved (using the Seiberg -Witten theory ) with Mrowka the Thom conjecture that algebraic curves among the smooth embedded in the complex projective plane associated curves are awarded the same homology class in which they have minimal gender ( gender, a topological invariant is again defined in the algebraic curves by their degree ). In 2003, he and Mrowka proved the " Property P conjecture " of knot theory with the help of various methods of ( differential ) topology of 3- dimensional manifolds ( results on taut foliations by David Gabai, relative to the contact structures ), a theorem on symplectic fillings of Contact manifolds of Eliashberg, the Nichtverschwindungssatz of Clifford Taubes on symplectic 4 -manifolds, results of PMN Feehan and TG Leness to Witten 's conjecture about Donaldson and Seiberg -Witten invariants, Verklebungssätzen for Donald Soni variants using instanton Floer homology, as well as the set of Floer on exact triangles in instanton Floer homology. The Property P conjecture states that by Dehn surgery (with parameters p, q, where q is not equal to zero ) along a non-trivial knot in generated 3-manifold has a non-trivial fundamental group.

Kronheimer was inducted into the Royal Society in 1997.

Among his doctoral students include Ian Dowker, Jacob Rasmussen, Ciprian Manolescu.

He is married and has two sons.

Prizes and awards

  • Whitehead Prize
  • Oswald Veblen Prize ( with Mrowka 2007)
  • Oberwolfach Prize 1991
  • Joseph L. Doob Prize 2011 with Mrowka ( for her book monopole and 3- manifolds )
  • In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( Embedded surfaces in 4- manifolds ).

Writings

  • Donaldson: The geometry of four - manifolds, Oxford University Press 1990, 1997
  • With Mrowka: " Embedded surfaces and the structure of Donaldson 's polynomial invariants, " Journal of Differential Geometry, Bd.41, 1995, S.573 -734;
  • With Mrowka, " Witten 's conjecture and property P, " Geometry and Topology, Bd.8, 2004, S -295 - 310.
  • Tomasz Mrowka " monopole and 3- manifolds ", Cambridge University Press 2007
Edward Witten Andreas Floer Oswald Veblen Prize in Geometry John Morgan (mathematician) Name Authority File
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