Elliott H. Lieb | |
---|---|

Born | |

Nationality | American |

Alma mater | Massachusetts Institute of Technology University of Birmingham |

Known for | Araki–Lieb–Thirring inequality Temperley–Lieb algebra Lieb's square ice constant Lieb–Liniger model Strong Subadditivity of Quantum Entropy Lieb–Thirring inequality Brascamp–Lieb inequality Lieb–Oxford inequality AKLT model Lieb–Robinson bounds Lieb–Yngvason Entropy principle Choquard equation Wehrl entropy conjecture 1-D Hubbard model Lieb lattice ^{[1]} |

Awards | Heineman Prize for Mathematical Physics (1978) Max Planck medal Birkhoff Prize (1988) Boltzmann medal (1998) Rolf Schock Prizes in Mathematics (2001) Levi L. Conant Prize (2002) Henri Poincaré Prize (2003) |

Scientific career | |

Fields | Mathematics, Physics |

Institutions | Princeton University |

Doctoral advisor | Samuel Frederick Edwards Gerald Edward Brown |

**Elliott Hershel Lieb**^{[2]} (born July 31, 1932) is an American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis.

In particular, his scientific works pertain to: the quantum and classical many-body problem,^{[3]}^{[4]}^{[5]} atomic structure,^{[5]} the stability of matter,^{[5]} the theory of magnetism,^{[4]} and the Hubbard model.^{[4]}

Lieb is a prolific author in mathematics and physics with over 300 publications.^{[6]} He received his B.S. in physics from the Massachusetts Institute of Technology in 1953^{[7]} and his Ph.D. in mathematical physics from the University of Birmingham in England in 1956.^{[7]}^{[8]} Lieb was a Fulbright Fellow at Kyoto University, Japan (1956–1957),^{[7]} and worked as the Staff Theoretical Physicist for IBM from 1960 to 1963.^{[7]} In 1961–1962, Lieb was on leave as professor of applied mathematics at Fourah Bay College, the University of Sierra Leone.^{[7]}

He has been a professor at Princeton since 1975,^{[7]} following a leave from his professorship at MIT. Lieb has been awarded several prizes in mathematics and physics, including the 1978 Heineman Prize for Mathematical Physics of the American Physical Society and the American Institute of Physics (1978),^{[9]} the Max Planck Medal of the German Physical Society (1992),^{[10]} the Boltzmann medal of the International Union of Pure and Applied Physics (1998),^{[11]} the Schock Prize (2001),^{[12]} and the Henri Poincaré Prize of the International Association of Mathematical Physics (2003).^{[13]} Lieb is a member of the U.S. National Academy of Sciences^{[14]} and has twice served (1982–1984 and 1997–1999) as the President of the International Association of Mathematical Physics.^{[15]} Lieb was awarded the Austrian Decoration for Science and Art in 2002.^{[16]} In 2012 he became a fellow of the American Mathematical Society^{[17]} and in 2013 a Foreign Member of the Royal Society.^{[18]}

He is married to fellow Princeton professor Christiane Fellbaum.

## Publication list (partial)

- Lieb, Elliott H.; Seiringer, Robert. The stability of matter in quantum mechanics. Cambridge University Press, 2010 ISBN 978-0-521-19118-0
- Lieb, Elliott H.; Loss, Michael. Analysis. Graduate Studies in Mathematics, 14. American Mathematical Society, Providence, RI, 1997. xviii+278 pp. ISBN 0-8218-0632-7
- Lieb, Elliott H. The Stability of Matter: From Atoms to Stars. Selecta of Elliott H. Lieb. Edited by W. Thirring, with a preface by F. Dyson. Springer-Verlag, Berlin, 2005. xv+932 pp. ISBN 3-540-22212-X
- Lieb, Elliott H. Inequalities. Selecta of Elliott H. Lieb. Edited, with a preface and commentaries, by M. Loss and M. B. Ruskai. Springer-Verlag, Berlin, 2002. xi+711 pp. ISBN 3-540-43021-0
- Lieb, Elliott H. Statistical mechanics. Selecta of Elliott H. Lieb. Edited, with a preface and commentaries, by B. Nachtergaele, J. P. Solovej and J. Yngvason. Springer-Verlag, Berlin, 2004. x+505 pp. ISBN 3-540-22297-9
- Lieb, Elliott H. Condensed matter physics and exactly soluble models. Selecta of Elliott H. Lieb. Edited by B. Nachtergaele, J. P. Solovej and J. Yngvason. Springer-Verlag, Berlin, 2004. x+675 pp. ISBN 3-540-22298-7
- Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob. The mathematics of the Bose gas and its condensation. Oberwolfach Seminars, 34. Birkhäuser Verlag, Basel, 2005. viii+203 pp. ISBN 978-3-7643-7336-8; 3-7643-7336-9

## See also

- Adiabatic accessibility
- AKLT model
- Brascamp–Lieb inequality
- Entropy
- Lieb conjecture
- Lieb–Liniger Model
- Lieb–Oxford inequality
- Lieb–Robinson bounds
- Lieb–Thirring inequality
- Ice-type model
- Lieb's square ice constant
- Lieb's theorem
- Temperley–Lieb algebra
- Von Neumann entropy

## References

**^**Lieb, Elliott H. (6 March 1989). "Two theorems on the Hubbard model".*Physical Review Letters*.**62**(10): 1201–1204. doi:10.1103/PhysRevLett.62.1201.**^***Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture*.**^***Statistical mechanics : selecta of Elliott H. Lieb*. Springer. ISBN 3-540-22297-9.- ^
^{a}^{b}^{c}*Condensed matter physics and exactly soluble models : selecta of Elliott H. Lieb*. Springer. ISBN 3-540-22298-7. - ^
^{a}^{b}^{c}*The stability of matter : from atoms to stars : selecta of Elliott H. Lieb*(4th ed.). Springer. ISBN 3-540-22212-X. **^**"Publications of Elliott H. Lieb". Retrieved 5 January 2020.- ^
^{a}^{b}^{c}^{d}^{e}^{f}"Lieb, Elliott H."*American Institute of Physics*. Retrieved 5 January 2020. **^**"Elliott Lieb".*Mathematics Genealogy Project*. Retrieved 5 January 2020.**^**"1978 Dannie Heineman Prize for Mathematical Physics".*American Physical Society*. Retrieved 5 January 2020.**^**"Preisträgerinnen und Preisträger, Max Planck Medaille".*Deutsche Physikalische Gesellschaft*(in German). Retrieved 5 January 2020.**^**"The Boltzmann Award".*The Web Archive*. 20 February 2015. Archived from the original on 20 February 2015.**^**"Schock Prize 2001".*Kungl. Vetenskaps-Akademien*. Retrieved 5 January 2020.**^**"The Henri Poincaré Prize".*International Association of Mathematical Physics*. Retrieved 5 January 2020.**^**"Elliott Lieb".*U.S. National Academy of Sciences*. Retrieved 5 January 2020.**^**"About the IAMP - Past presidents".*International Association of Mathematical Physics*. Retrieved 5 January 2020.**^**"Reply to a parliamentary question" (pdf) (in German). p. 1517. Retrieved 19 November 2012.**^**List of Fellows of the American Mathematical Society, retrieved 2013-01-27.**^**"New Fellows 2013". Royal Society. Retrieved 30 July 2013.

## External links

- Faculty page at Princeton.