Professor Stephen Milne
Department of Mathematics
The Ohio State University
100 Math Tower
231 W 18th Avenue
Columbus, OH 43210
Telephone: (614) 292-7049
- Ph.D. University of California, San Diego, 1976.
Thesis advisor: Professor Adriano M. Garsia
Thesis: Peano curves and smoothness of functions
- A.B. San Diego State University, 1972.
Current work involves algebraic combinatorics, classical analysis
(elliptic functions, continued fractions, and multiple basic
hypergeometric series), Lie algebras, analytic number theory,
and their relationships with one another. This research studies higher
dimensional analogs of classical special functions which are inspired
by certain aspects of mathematical physics and the unitary groups
U(n). Applications include topics in combinatorics
(summation theorems, symmetric functions identities, combinatorics of
the symmetric group and weighted inversion statistics), q-series,
additive number theory (constructing one-to-one correspondences between
different sets of partitions of n), analytic number
theory (sums of squares identities via elliptic functions, continued
fractions, and multiple basic hypergeometric series), Lie algebras
(generalizations of the Macdonald identities with extra free
applications to raising operators of row type for Macdonald
polynomials, and multivariable orthogonal polynomials.
- Currently supported by a two year National Security Agency Grant
2008 through January 2010. ``Analytic Number Theory and Multiple Basic
- Continuous support by N.S.F. or N.S.A. from 1976 through Fall,
2004. Then, 2006 - 2010. Previously awarded National Security Agency
June 1, 1988 - May 31, 1989; September 1, 1991 through February 28,
1994; June 1,
1993 through November 30, 1997; January 17, 1997 through July 31, 1999;
November 17, 1998 through November 16, 2000. These grants provided
Milne one month
Summer salary and also partially supported (during both Summer and/or
most of Milne's Ph.D. students during their thesis work. Continuous
support by N.S.F.
from 1976 through Spring, 1991.
Stephen Milne wins the 2007 Euler Medal
Stephen Milne was awarded the 2007 Euler
Medal for "a senior member of the ICA
[The Institute of
Combinatorics and its Applications] who is still active in research and
who has made substantial and important contributions to combinatorial
research during his research career". (March 16, 2008.
Award to be presented March 2009 at the Fortieth Southeastern
International Conference on Combinatorics, Graph Theory, and Computing,
Florida Atlantic University, Boca Raton, Florida.) Departmental
``Science News'' article by Ivars Peterson on Milne's sums of
- A very recent article by Ivars Peterson in Science News
featured Milne's sums of squares work in (PNAS online
reprint) and (Kluwer
online abstract) and consequences it has had
in the subsequent investigations of Don Zagier and Ken Ono. (The
reference is: [Ivars Peterson, Surprisingly Square:~Mathematicians
fresh look at expressing numbers as the sums of squares, Science
News, June 16,
2001; Vol. 159, No. 24, p. 382--383].) This long-established (since
publication has reported on important developments in all areas of
mathematics) for many years. For references and sources used in this
article see the
following Science News URL:~ (online
sources). For a text only version of the article, see the URL:~ (text of SN article).
Recent AMS Invited Hour Address on Milne's sums of squares and tau
- (March 14-16, 2003), AMS meeting in Baton Rouge, LA at LSU.
Invited hour address: ``A new look at sums of
squares, Jacobi elliptic functions, and Ramanujan's tau function.''
Note that this is Milne's second AMS Invited Hour Address. The first
was in 1984.
Featured Math Review MR1906722 (2003m:11060) December 2003 of
Milne's sums of
squares paper in RAMA 6.1:
1997 FPSAC Paper by Milne on his sums of squares work
PDF Scan of FPSAC'97 (1997) Paper by Milne on his sums of
squares work. (See Theorem 2.7 on page 411 for the main identities of
Milne's proof of the Kac-Wakimoto conjectures for triangular numbers.)
exact reference is: Stephen C. Milne, ``New infinite families of exact
sums of squares formulas, Jacobi elliptic functions, and Ramanujan's
function'', pp. 403 - 417 of Formal Power Series and Algebraic
Combinatorics, 9th Conference, July 14 - July 18, 1997,
Wien, Conference Proceedings -- Volume 3 of 3. (eds.: P. Kirschenhofer,
C. Krattenthaler, D. Krob, and H. Prodinger), FPSAC'97 (1997).