Ezra Getzler (born 9 February 1962) is an Australian mathematician and mathematical physicist.
Getzler studied from 1979 to 1982 at the Australian National University in Canberra (bachelor's degree with honours in 1982) and then at Harvard University, where he received his PhD in 1986 under Arthur Jaffe with thesis Degree theory for Wiener maps and supersymmetric quantum mechanics. From 1986 to 1989 he was a Junior Fellow at Harvard. In 1989 he became an assistant professor and in 1993 an associate professor at Massachusetts Institute of Technology. In 1997 he became an associate professor and in 1999 a professor at Northwestern University, where he now works. He was a guest professor at several universities, including the Max-Planck-Institut für Mathematik in Bonn (1996), l'École Normale Supérieure (1992), l'Institut Henri Poincaré (2007), the University of Nice Sophia Antipolis, the Imperial College London (2007/8), and the University of Paris VI. In 2002 and in 2003/4 he was at the Institute for Advanced Study.
Getzler is known for his new proof (1983) of the Atiyah–Singer index theorem using supersymmetry, based upon ideas of Luis Álvarez-Gaumé and Edward Witten in mathematical physics. In addition to mathematical physics, he works on algebraic geometry, category theory, and algebraic topology.
- with Nicole Berline, Michèle Vergne, Heat Kernels and Dirac Operators, Springer Verlag, Grundlehren der Mathematischen Wissenschaften, 1992.
- Pseudodifferential operators on supermanifolds and the Atiyah–Singer index theorem, Communications in Mathematical Physics, Vol. 92, 1983, p. 163, Online
- A short proof of the Atiyah–Singer index theorem, Topology 25 (1987), 111–117.
- The local Atiyah–Singer index theorem, in Konrad Osterwalder, Raymond Stora (eds.): Critical phenomena, random systems, gauge theories (Les Houches Lectures 1984), North-Holland, Amsterdam-New York, 1986, pp. 967–974.
- Editor with Mikhail Kapranov: Higher category theory, Workshop Northwestern University 1997, American Mathematical Society 1998.