Peter Benedict Kronheimer (born 1963) is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology.
Kronheimer's early work was on gravitational instantons, in particular the classification of hyperkähler 4-manifolds with asymptotical locally Euclidean geometry (ALE spaces), leading to the papers "The construction of ALE spaces as hyper-Kähler quotients" and "A Torelli-type theorem for gravitational instantons."
Their collaboration began at the Mathematical Research Institute of Oberwolfach, and their first work developed analogues of Simon Donaldson's invariants for 4-manifolds with a distinguished surface.
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.
They developed an instanton Floer invariant for knots which was used in their proof that Khovanov homology detects the unknot.
[4] Kronheimer's PhD students have included Ian Dowker, Jacob Rasmussen, Ciprian Manolescu, Olga Plamenevskaya and Aliakbar Daemi.