Professor Stephen Milne

Department of Mathematics
The Ohio State University
Math Building 318
231 W 18th Avenue
Columbus, OH 43210
Telephone: (614) 292-6615

Personal Data


Research Interests

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 parameters), applications to raising operators of row type for Macdonald polynomials, and multivariable orthogonal polynomials.

Current Teaching Information


Professional Honors


Other Scientific Activities

Research Grants

Stephen Milne named a Fellow of the American Mathematical Society

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 announcementICA Letter.

``Science News'' article by Ivars Peterson on Milne's sums of squares work:

Recent AMS Invited Hour Address on Milne's sums of squares and tau function work:

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.) The exact reference is: Stephen C. Milne, ``New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function'', pp. 403 - 417 of Formal Power Series and Algebraic Combinatorics, 9th Conference, July 14 - July 18, 1997, Universität Wien, Conference Proceedings -- Volume 3 of 3. (eds.: P. Kirschenhofer, C. Krattenthaler, D. Krob, and H. Prodinger), FPSAC'97 (1997).

Ph.D. Students