Joel Feldman

Pure and Applied Mathematics

Quantum physics mathematician: constructed a number of quantum field theories

After a research fellowship at Harvard and a two-year instructership at MIT, Feldman came to UBC as an Assistant Professor in 1977. By 1987, he was Full Professor.

Feldman's field crosses the line between physics and mathematics. He specializes in the mathematics behind quantum physics, particularly for systems with essentially infinitely many particles. Such systems exhibit fascinating and mysterious behaviour, like superconductivity. But the mathematical models used to try and understand them are notoriously complex and difficult to work with.

Feldman and his collaborators developed machinery capable of controlling many-fermion models at low temperature and used it to

  • rigorously construct the first model of an interacting Fermi liquid at temperature zero Calvin.
  • show that, at least in principle, the expansions that are widely used to compute, approximately, properties of these models really do determine the properties.
  • show that almost all eigenvalues (atomic spectral lines, for example, are eigenvalues) of almost all periodic Schrödinger operators (used in modeling crystals) remain almost stationary even under large perturbations of the potential. But they also found exceptional eigenvalues that move a lot.
  • In a completely different subject, Feldman and his collaborators generalized a study of two dimensional surfaces, initiated by Georg Bernhard Reimann in about 1850, to include many surfaces of infinite genus. A donut is a surface of genus one. A surface of genus five is like a donut but has five holes. They then applied the conclusions of this study to show that all solutions of the Kadomcev-Petviashvilli equation (which arises in the study of shallow water waves) that start off periodic in space, evolve almost periodically in time.

     

    Feldman has co-written or edited several research monographs and collections of research papers, edits the CRM Series in Mathematical Physics, and has served on the editorial boards of many academic journals including the Canadian Journal of Mathematics. He has been invited to speak about his work in a dozen different countries. In 1996, he received the John L. Synge award, the top research prize in the mathematical sciences in Canada, awarded infrequently, and only for the third time by the Royal Society of Canada.

    Sources: On-line resume, The Pacific Institute for the Mathematical Sciences Annual Report, 1997-1998, Dr. Feldman's webpage, Joel Feldman, personal communication. Photo: Dr. Feldman's webpage.

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