| Peter B. Kronheimer | |
|---|---|
| Nationality | United Kingdom |
| Fields | Mathematics |
| Institutions | Harvard University |
| Alma mater | City of London School University of Oxford |
| Doctoral advisor | Michael Atiyah |
| Doctoral students | Ian Dowker Ciprian Manolescu Jacob Rasmussen Olga Plamenevskaya |
| Notable awards | Veblen Prize (2007) |
Peter Benedict Kronheimer is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology. He is presently William Casper Graustein Professor of Mathematics at Harvard University.
Kronheimer has frequently collaborated with Tomasz Mrowka of MIT. One of their first important results was a structure theorem for Donaldson's polynomial invariants and applications to minimal genus problems of embedded surfaces in 4-manifolds. After the arrival of Seiberg–Witten theory their work on embedded surfaces culminated in a proof of the Thom conjecture—which had been outstanding for several decades. Another of Kronheimer and Mrowka's results was a proof of the Property P conjecture for knots.
Kronheimer attended the City of London School. He completed his PhD at Oxford University under the direction of Michael Atiyah. He has had a long association with Merton College, the oldest of the constituent colleges of Oxford University, being an undergraduate, graduate, and full fellow of the college.
Besides his research articles, his writings include a book, with Simon Donaldson, on 4-manifolds, and a book with Mrowka on Seiberg–Witten–Floer homology, entitled "Monopoles and Three-Manifolds".
His PhD students have included Ian Dowker, Jacob Rasmussen, Ciprian Manolescu, and Olga Plamenevskaya.
On a lighter note, Kronheimer is known for having made small changes to a slightly obscure calligraphic font (Ralph Smith's formal font) for use in his mathematical papers, having been unable to find a generic font that was sufficiently to his taste.