Thomas C. Spencer (born December 24, 1946) is an American

mathematical physicist Mathematical physics refers to the development of 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 developmen ...

, known in particular for important contributions to

constructive quantum field theory In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise mathematical structures. This demonstration requires new mathematics, in a sense analogous t ...

, statistical mechanics, and

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result ...

of random operators. He is an emeritus faculty member at the

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

.IAS website
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Career

Spencer earned his doctorate in 1972 from

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then- Secretary of the Treasury Albert Gallatin. In 1832, ...

with a dissertation titled ''Perturbation of the Po2 Quantum Field Hamiltonian'' written under the direction of

James Glimm James Gilbert Glimm (born March 24, 1934) is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applie ...

. Since 1986, he has been a faculty member in the School of Mathematics at the

Research

* Together with

and

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 caree ...

he invented the

cluster expansion In statistical mechanics, the cluster expansion (also called the high temperature expansion or hopping expansion) is a power series expansion of the partition function of a statistical field theory around a model that is a union of non-intera ...

approach to quantum field theory that is widely used in constructive field theory. * Together with

Jürg Fröhlich Jürg Martin Fröhlich (born 4 July 1946 in Schaffhausen) is a Swiss mathematician and theoretical physicist. He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmet ...

and

Barry Simon Barry Martin Simon (born 16 April 1946) is an American mathematical physicist and was the IBM professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonr ...

, he invented the approach of the

infrared bound Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of Light, visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from ...

, which has now become a classical tool to derive phase transitions in various models of statistical mechanics. * Together with

, he devised a 'multi-scale analysis' to provide, for the first time, mathematical proofs of: the Kosterlitz–Thouless transition, the phase transition in the one-dimensional ferromagnetic Ising model with interactions

J_\sim , x-y, ^

and

Anderson localization In condensed matter physics, Anderson localization (also known as strong localization) is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to su ...

in arbitrary

dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...

. * Together with

David Brydges David Chandos Brydges (born 1 July 1949 in Chester, UK) is a mathematical physicist. Brydges received in 1976 his Ph.D. from the University of Michigan with thesis advisor Paul Federbush and thesis '' A Linear Lower Bound for Generalized Yukawa Mo ...

, he proved that the

scaling limit In mathematical physics and mathematics, the continuum limit or scaling limit of a lattice model refers to its behaviour in the limit as the lattice spacing goes to zero. It is often useful to use lattice models to approximate real-world process ...

of the

self-avoiding walk In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (S ...

greater or equal than 5 is

Gaussian Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...

, with

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of number ...

growing linearly in time. To achieve this result, they invented the technique of the lace expansion that since then has had wide application in probability on graphs.

Awards and honors

Spencer is a member of the

United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nat ...

, and the recipient of the

Dannie Heineman Prize for Mathematical Physics Dannie Heineman Prize for Mathematical Physics is an award given each year since 1959 jointly by the American Physical Society and American Institute of Physics. It is established by the Heineman Foundation in honour of Dannie Heineman. As of 2 ...

(joint with

, "''For their joint work in providing rigorous mathematical solutions to some outstanding problems in statistical mechanics and field theory.''").1991 Dannie Heineman Prize for Mathematical Physics Recipient
American Physical Society. Accessed June 24, 2011

References

1946 births Living people Mathematical physicists Members of the United States National Academy of Sciences Institute for Advanced Study faculty New York University alumni University of California, Berkeley alumni {{US-mathematician-stub