Oscar Lanford (1940-2013)

Oscar Lanford III
Picture Source: IHES
by Oliver Knill, November 25, 2013


I learned the sad news that Oscar Lanford III has died in Switzerland on November 16, 2013. Oscar Lanford was
my PhD advisor from 1989 to 1993. (Thesis). It was a perfect match for me because I had been interested in dynamical systems, functional analysis and ergodic theory, the field in which Lanford worked. Having taken a dynamical systems course from him, I knew that Lanford was extraordinarily approachable and friendly and also shared a passion for computers in mathematics and experimental mathematics. I was once working for a week on my Atari for a picture on some chaotic system which Lanford could reproduce on the spot on his computer, of course not just by numerically iterating but analytically computing the stable manifolds and using this to produce a high quality figure. I still find it quite remarkable that he allowed me to work on a field on my own and give me complete freedom and still be strong and patient guidance.

I have taken two dynamical systems courses given by Lanford. It was custom in all lectures that proofs of all theorems would be presented in detail. It was not unusual for undergraduate courses to see detailed proofs, sometimes proved over several lectures and there was already a high standard in precision. But the proofs presented by Lanford in class often surpassed even the details in the notes. It was always possible to understand every detail of his lectures.
As an expert in quantum field theory, statistical mechanics and dynamical systems, Lanford was able to get top shot mathematicians like David Ruelle, Krzysztof Gawedzki, Joel Feldman and Roland Dobrushin to give semester-long "Nachdiplom Vorlesungen" (graduate courses), which was a wonderful treat for us graduate students.

Picture Source: Oberwohlfach


About the work: (I'm not an expert in most of these subjects and this is only an attempt to summarize the most important contributions). Below are about 30 sources in PDF form of Lanford's papers. It would be nice of course to have the completed collected work.
Lanford studied at the Wesleyan University and got his PhD under the advise of Arthur Wightman (1922-2013) who passed away this January Princeton page). After an assistant professorship and later professorship at the university of California in Berkley, Lanford was from 1882-1987 at the IHES in France and from 1987 on at ETH Zürich, where he emerited in 2005. Lanford was a Sloan Fellow from 1969-1971, received the 1986 United States National Academy of Sciences award in Applied Mathematics and Numerical Analysis and became in 2012 a fellow of the American Mathematical Society.

Ruelle discusses in his book [1] the role of computer assisted proofs and especially mentions Lanford's proof of the Feigenbaum conjectures which involved computer code which was 200 pages long. Ruelle mentions:

"Oscar Lanford is a very careful person and took pains to check that, when the code is fed into the computer, the computer does exactly what it is supposed to do. (...) But Lanford added some remarks that you may find rather disheartening. "I'm sure" he said "that there are some mistakes in the code I wrote. But I'm also sure that they can be fixed that the result is correct.

An episode from a year long dynamical systems course, which quite a few visitors of the Forschungsinstitute FIM and also faculty from the department visited: After Lanford proved a theorem in detail, one of the dynamical systems specialist spoke up and told: "But that is trivial". Lanford calmly replied: "No, I just proved it."

The most spectacular work is certainly Lanford's proof of the Feigenbaum conjectures: he proved that there is an analytic fixed point of the renormalization operator and that the linearization has one eigenvalue outside the unit circle and the rest inside. The corresponding stable manifold is sometimes called Lanford stable manifold. An account of Sullivan is in [2]. The computer assisted proof provoked discussions about the role of computers in mathematics and how one should deal with computer assisted proofs.

Sharon Carlisle from Cambridge wrote me: "His sister was one of my best friends in high school. (She always referred to him as "Ockkie"...). He was two years older, quiet and shy, of course. But we all knew he was brilliant. I have no doubt that our rural school outside of Albany, NY, had never seen the likes of him; his accomplished family didn't quite fit into our run-of-the mill academic scene. Interestingly, his father and mother, both Columbia scientists, raised their children on a Hereford farm, which I visited." About the father of Oscar Lanford Local copy.

Here is a snapshot of some papers mentioned in mathscinet: (the Period doubling paper in higher dimensions (Physica 7D), the mean entropy paper (J. Math Phys) and the Functional Analysis lecture notes of the Summer school as well as Dynamical systems notes) were added. I started to add PDF sources to some of the papers:

  • Lanford, Oscar E., III Informal remarks on the orbit structure of discrete approximations to chaotic maps. Experiment. Math. 7 (1998), no. 4, 317-324. [PDF]
  • Lanford, O. E., III; Ruedin, L. Statistical mechanical methods and continued fractions. Papers honouring the 60th birthday of Klaus Hepp and of Walter Hunziker, Part I (Zürich, 1995). Helv. Phys. Acta 69 (1996), no. 5-6, 908-948. [PDF]
  • Baladi, Viviane; Jiang, Yun Ping; Lanford, Oscar E., III Transfer operators acting on Zygmund functions. Trans. Amer. Math. Soc. 348 (1996), no. 4, 1599-1615. [PDF]
  • Williams, R. F.; Karp, D.; Brown, D.; Lanford, O.; Holmes, P.; Thom, R.; Zeeman, E. C.; Peixoto, M. M.; et al.; Final panel. From Topology to Computation: Proceedings of the Smalefest (Berkeley, CA, 1990), 589-605, Springer, New York, 1993.
  • Lanford, Oscar E., III Computer assisted proofs. Computational methods in field theory (Schladming, 1992), 43-58, Lecture Notes in Phys., 409, Springer, Berlin, 1992.
  • Lanford, Oscar E., III; Robinson, Derek W. Fractional powers of generators of equicontinuous semigroups and fractional derivatives. J. Austral. Math. Soc. Ser. A 46 (1989), no. 3, 473-504.
  • Lanford, Oscar E., III Renormalization group methods for circle mappings. Nonlinear evolution and chaotic phenomena (Noto, 1987), 25-36, NATO Adv. Sci. Inst. Ser. B Phys., 176, Plenum, New York, 1988.
  • Lanford, Oscar E., III Computer-assisted proofs in analysis. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 1385-1394, Amer. Math. Soc., Providence, RI, 1987.
  • Lanford, Oscar E., III Renormalization group methods for critical circle mappings with general rotation number. VIIIth international congress on mathematical physics (Marseille, 1986), 532-536, World Sci. Publishing, Singapore, 1987.
  • Lanford, Oscar E., III An introduction to computers and numerical analysis. Phénomènes critiques, systèmes aléatoires, théories de jauge, Part I, II (Les Houches, 1984), 1-86, North-Holland, Amsterdam, 1986.
  • Lanford, Oscar E., III Lectures in Dynamical Systems, 1991-1992, revised in 1997, [PDF]
  • Lanford, Oscar E., III Renormalization group methods for circle mappings. Statistical mechanics and field theory: mathematical aspects (Groningen, 1985), 176-189, Lecture Notes in Phys., 257, Springer, Berlin, 1986.
  • Lanford, O. E. Strange attractors and turbulence. Hydrodynamic instabilities and the transition to turbulence, 7-26, Topics Appl. Phys., 45, Springer, Berlin, 1985.
  • Lanford, Oscar E., III A numerical study of the likelihood of phase locking. Phys. D 14 (1985), no. 3, 403-408. [PDF]
  • Lanford, Oscar E., III A shorter proof of the existence of the Feigenbaum fixed point. Comm. Math. Phys. 96 (1984), no. 4, 521-538. [PDF]
  • Gambaudo, Jean-Marc; Lanford, Oscar, III; Tresser, Charles Dynamique symbolique des rotations. (French) [Symbolic dynamics of rotations] C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), no. 16, 823-826.
  • Lanford, Oscar E., III Computer-assisted proofs in analysis. Mathematical physics, VII (Boulder, Colo., 1983). Phys. A 124 (1984), no. 1-3, 465-470. [PDF]
  • Lanford, Oscar E., III Functional equations for circle homeomorphisms with golden ratio rotation number. J. Statist. Phys. 34 (1984), no. 1-2, 57-73. [PDF]
  • Lanford, Oscar E., III Introduction to the mathematical theory of dynamical systems. Chaotic behavior of deterministic systems (Les Houches, 1981), 3-51, North-Holland, Amsterdam, 1983.
  • Lanford, Oscar E., III A computer-assisted proof of the Feigenbaum conjectures. Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 427-434. [PDF]
  • Oscar E., III The strange attractor theory of turbulence. Annual review of fluid mechanics, Vol. 14, pp. 347-364, Annual Reviews, Palo Alto, Calif., 1982. [PDF]
  • Lanford, Oscar E., III Smooth transformations of intervals. Bourbaki Seminar, Vol. 1980/81, pp. 36-54, Lecture Notes in Math., 901, Springer, Berlin-New York, 1981.
  • Collet, P.; Eckmann, J.-P.; Lanford, O. E., III Universal properties of maps on an interval. Comm. Math. Phys. 76 (1980), no. 3, 211-254.[PDF]
  • Collet, P.; Eckmann, J.-P.; Lanford, O. E. Renormalization group analysis of some highly bifurcated families. Quantum fields-algebras, processes (Proc. Sympos., Univ. Bielefeld, Bielefeld, 1978), pp. 125-134, Springer, Vienna, 1980
  • Lanford, Oscar E., III Time dependent phenomena in statistical mechanics. Mathematical problems in theoretical physics (Proc. Internat. Conf. Math. Phys., Lausanne, 1979), pp. 103-118, Lecture Notes in Phys., 116, Springer, Berlin-New York, 1980.
  • Lanford, Oscar E., III Remarks on the accumulation of period-doubling bifurcations. Mathematical problems in theoretical physics (Proc. Internat. Conf. Math. Phys., Lausanne, 1979), pp. 340-342, Lecture Notes in Phys., 116, Springer, Berlin-New York, 1980. [PDF]
  • van Beijeren, H.; Lanford, O. E., III; Lebowitz, J. L.; Spohn, H. Equilibrium time correlation functions in the low-density limit. J. Statist. Phys. 22 (1980), no. 2, 237-257. [PDF]
  • Lanford, Oscar E., III An introduction to the Lorenz system. Papers from the Duke Turbulence Conference (Duke Univ., Durham, N.C., 1976), Paper No. 4, i+21 pp. Duke Univ. Math. Ser., Vol. III, Duke Univ., Durham, N.C., 1977.
  • Lanford, Oscar E., III Computer pictures of the Lorenz attractor. Turbulence Seminar (Univ. Calif., Berkeley, Calif., 1976/1977), pp. 113-116. Lecture Notes in Math., Vol. 615, Springer, Berlin, 1977.
  • Lanford, Oscar E., III; Lebowitz, Joel L.; Lieb, Elliott H. Time evolution of infinite anharmonic systems. J. Statist. Phys. 16 (1977), no. 6, 453-461. [PDF]
  • Lanford, Oscar E., III A derivation of the Boltzmann equation from classical mechanics. Probability (Proc. Sympos. Pure Math., Vol. XXXI, Univ. Illinois, Urbana, Ill., 1976), pp. 87-89. Amer. Math. Soc., Providence, R. I., 1977.
  • Lanford, Oscar E., III On a derivation of the Boltzmann equation. International Conference on Dynamical Systems in Mathematical Physics (Rennes, 1975), pp. 117-137. Asterisque, No. 40, Soc. Math. France, Paris, 1976.
  • Lanford, Oscar E., III Time evolution of large classical systems. Dynamical systems, theory and applications (Recontres, Battelle Res. Inst., Seattle, Wash., 1974), pp. 1-111. Lecture Notes in Phys., Vol. 38, Springer, Berlin, 1975.
  • Lanford, Oscar E., III; Lebowitz, Joel L. Time evolution and ergodic properties of harmonic systems. Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974), pp. 144-177. Lecture Notes in Phys., Vol. 38, Springer, Berlin, 1975.
  • Lanford, Oscar E., III Time evolution of infinite classical systems. Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 2, pp. 377-381. Canad. Math. Congress, Montreal, Que., 1975. [PDF]
  • Goldstein, Sheldon; Lanford, Oscar E., III; Lebowitz, Joel L. Ergodic properties of simple model system with collisions. J. Mathematical Phys. 14 (1973), 1228-1230. [PDF]
  • Lanford, Oscar E., III Selected Topics in Functional Analysis, University de Grenoble Summer School, Statistical Mechanics and Quantum field theory, Ed. C. De Witt and R. Stora, Gordon, Breach Science Publishers, 1971 [PDF]
  • P. Colella and O. E. Lanford III, Appendix: Sample field behavior for the free Markov random field [PDF]
  • Lanford, Oscar E., III Time-evolution of infinite classical systems. Mathematical aspects of statistical mechanics (Proc. Sympos. Appl. Math., New York, 1971), pp. 65-75. SIAM-AMS Proceedings, Vol. V, Amer. Math. Soc., Providence, R. I., 1972.
  • Lanford, O. E., III.; Robinson, Derek W. Approach to equilibrium of free quantum systems. Comm. Math. Phys. 24 1972 193-210. [PDF].
  • Lanford, O. E., III. The KMS states of a quantum spin system. 1970 Systèmes à un Nombre Infini de Degrés de Liberté (Actes du Colloque, Gif-sur-Yvette, 1969) pp. 146-154 Éditions Centre Nat. Recherche Sci., Paris
  • Gallavotti, G.; Lanford, O. E., III; Lebowitz, Joel L. Thermodynamic limit of time-dependent correlation functions for one-dimensional systems. J. Mathematical Phys. 11 1970 2898-2905. [PDF]
  • Bowen, R.; Lanford, O. E., III. Zeta functions of restrictions of the shift transformation. 1970 Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) pp. 43-49 Amer. Math. Soc., Providence, R.I.
  • Lanford, O. E., III; Robinson, Derek W. Mean Entropy of States in Quantum-Statistical Mechanics, J. Math. Phys, 9, No 8, July 1968, page 1120-1125 [PDF]
  • Lanford, O.E, III and RObinson D.W. Statistical mechanics of quantum spin systems III, 1968, Cern Library [PDF]
  • Lanford, O. E., III; Ruelle, D. Observables at infinity and states with short range correlations in statistical mechanics. Comm. Math. Phys. 13 1969 194-215. [PDF].
  • Jaffe, Arthur M.; Lanford, Oscar E., III.; Wightman, Arthur S. A general class of cut-off model field theories. Comm. Math. Phys. 15 1969 47-68. [PDF]
  • Lanford, O. E., III The classical mechanics of one-dimensional systems of infinitely many particles. II. Kinetic theory. Comm. Math. Phys. 11 1968/1969 257-292. [PDF]
  • Lanford, Oscar E., III.; Robinson, Derek W. Statistical mechanics of quantum spin systems. III. Comm. Math. Phys. 9 1968 327-338. [PDF].
  • Lanford, O. E., III. The classical mechanics of one-dimensional systems of infinitely many particles. I. An existence theorem. Comm. Math. Phys. 9 1968 176-191. [PDF]
  • Lanford, O.; Ruelle, D. Integral representations of invariant states on B# algebras. J. Mathematical Phys. 8 1967 1460-1463. [PDF]
  • Lanford, Oscar E., III A note on a paper of Ginsburg. Duke Math. J. 30 1963 113-116. [PDF]
  • Green, T. A.; Lanford, O. E., III. Rigorous derivation of the phase shift formula for the Hilbert space scattering operator of a single particle. J. Mathematical Phys. 1 1960 139-148. [PDF]


Oliver Knill, Last edit: December 27, 2013