Ezra Getzler (born 9 February 1962 in

Melbourne Melbourne ( , ; Boonwurrung language, Boonwurrung/ or ) is the List of Australian capital cities, capital and List of cities in Australia by population, most populous city of the States and territories of Australia, Australian state of Victori ...

) is an Australian mathematician and mathematical physicist.

Education and career

Getzler studied from 1979 to 1982 at the

Australian National University The Australian National University (ANU) is a public university, public research university and member of the Group of Eight (Australian universities), Group of Eight, located in Canberra, the capital of Australia. Its main campus in Acton, A ...

Canberra Canberra ( ; ) is the capital city of Australia. Founded following the Federation of Australia, federation of the colonies of Australia as the seat of government for the new nation, it is Australia's list of cities in Australia, largest in ...

(bachelor's degree with honours in 1982). In 1982 he moved to

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

with a

Fulbright Scholarship The Fulbright Program, including the Fulbright–Hays Program, is one of several United States cultural exchange programs with the goal of improving intercultural relations, cultural diplomacy, and intercultural competence between the people ...

; he received his PhD in 1986 under

Arthur Jaffe Arthur Michael Jaffe (; born December 22, 1937) is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science. Education and career ...

, with a thesis entitled ''Degree theory for Wiener maps and supersymmetric quantum mechanics''. From 1986 to 1989 he was a

Junior Fellow The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intellect ...

at Harvard. He then moved to the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

, where he became assistant professor in 1989 and associate professor in 1993. In 1997 he became associate professor at

Northwestern University Northwestern University (NU) is a Private university, private research university in Evanston, Illinois, United States. Established in 1851 to serve the historic Northwest Territory, it is the oldest University charter, chartered university in ...

and since 1999 he is full professor. He was a guest professor at several universities, including the Max-Planck-Institut für Mathematik in Bonn (1996), the

École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

(1992), the

Institut Henri Poincaré The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrondi ...

(2007), the

University of Nice Sophia Antipolis A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...

, the

Imperial College London Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Al ...

(2007/8), and the

University of Paris VI Pierre and Marie Curie University ( , UPMC), also known as Paris VI, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, ...

. In 2002 and in 2003/4 he was at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. From 1991 to 1993 a Sloan Research Fellow. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-03-20.

Research

Getzler is known for his new proof (1983) of the

Atiyah–Singer index theorem In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space ...

using

supersymmetry Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...

, based upon ideas of

Luis Álvarez-Gaumé Luis Álvarez-Gaumé (born 1955) is a Spanish theoretical physicist who works on string theory and quantum gravity. Luis Álvarez-Gaumé obtained his PhD in 1981 from Stony Brook University and worked from 1981 to 1984 at Harvard University as a ...

and

Edward Witten Edward Witten (born August 26, 1951) is an American theoretical physics, theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics. He is a professor emeritus in the sc ...

in mathematical physics. In addition to

mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

, he works on

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

category theory Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...

, and

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

Works

* 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 ''Communications in Mathematical Physics'' is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, sta ...

, Vol. 92, 1983, p. 163
Online
* ''A short proof of the Atiyah–Singer index theorem'',

Topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

25 (1987), 111–117. * ''The local Atiyah–Singer index theorem'', in Konrad Osterwalder,

Raymond Stora Raymond Félix Stora (18 September 1930 – 20 July 2015) was a French theoretical physicist. He was a researcher at Service de Physique Théorique at CEA Saclay, then a research director at the French National Centre for Scientific Research ...

(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.

References

External links

*
Homepage at Northwestern University
{{DEFAULTSORT:Getzler, Ezra Australian physicists 1962 births 20th-century Australian mathematicians 21st-century Australian mathematicians Mathematical physicists Topologists Australian National University alumni Harvard University alumni Massachusetts Institute of Technology faculty Northwestern University faculty Institute for Advanced Study visiting scholars Fellows of the American Mathematical Society Living people Sloan Research Fellows