Ezra Getzler | |
---|---|
Born | 9 February 1962 |
Alma mater | Harvard University |
Scientific career | |
Fields | Mathematical physics |
Institutions | Northwestern University |
Thesis | Degree Theory of Wiener Maps and Supersymmetric Quantum Mechanics (1986) |
Doctoral advisor | Arthur Michael Jaffe |
Website | https://sites.northwestern.edu/getzler/ |
Ezra Getzler (born 9 February 1962 in Melbourne) 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). In 1982 he moved to Harvard University with a Fulbright Scholarship; he received his PhD in 1986 under Arthur Jaffe, with a thesis entitled Degree theory for Wiener maps and supersymmetric quantum mechanics. [1]
From 1986 to 1989 he was a Junior Fellow at Harvard. [2] He then moved to the Massachusetts Institute of Technology, where he became assistant professor in 1989 and associate professor in 1993. In 1997 he became associate professor at Northwestern University 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 (1992), the 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. [3]
From 1991 to 1993 a Sloan Research Fellow. [4] In 2012 he became a fellow of the American Mathematical Society. [5]
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.
Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize in 2004.
Edward Witten is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of knots as Feynman integrals. He is considered the practical founder of M-theory.
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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 is equal to the topological index. It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
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