PHYSICAL MATHEMATICS SEMINAR
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139
TOPIC: MOBIUS SERIES INVERSION REDISCOVERED
SPEAKER: DR. MARTIN Z. BAZANT
Department of Physics
Harvard University
ABSTRACT:
After more than a century confined to pure mathematics, the Mobius
Inversion Formula of number theory and combinatorics is now finding
applications in science. In this talk the rich nineteenth century
literature on Mobius inversion is reviewed, including seminal
contributions by A. F. Mobius (1832), P. L. Chebychev (1851), E. Cesaro
(1885) and others. Some surprising historical facts are revealed. The
juxtaposition of venerable knowledge in mathematics with recent insights
from physics leads naturally to (i) a generalized ``Mobius Series
Inversion Formula'' containing all the previous cases and (ii) methods to
overcome various limitations of the old theory for physical applications.
No knowledge of number theory is assumed. The key ideas will be introduced
via the original papers of Mobius, Chebychev and Cesaro. Applications will
be taken from statistical and solid state physics.
DATE: TUESDAY, FEBRUARY 17, 1998
TIME: 2:30 P.M.
LOCATION: Building 2, Room 338
Refreshments will be served at 3:30 p.m. in Building 2, Room 349.