Jim Stasheff

James Dillon Stasheff (born January 15, 1936, New York City)[1] is an American mathematician, a professor emeritus of mathematics at the University of North Carolina at Chapel Hill.

[3] Stasheff then began his graduate studies at Princeton University; his notes for a 1957 course by John Milnor on characteristic classes first appeared in mimeographed form and later in 1974 in revised form book with Stasheff as a co-author.

Two years later in 1961, with a pregnant wife, needing an Oxford degree to get reimbursed for his return trip to the US, and yet still feeling attached to Princeton, he split his thesis into two parts (one topological, the other algebraic) and earned two doctorates, a D.Phil.

Stasheff's research contributions include the study of associativity in loop spaces and the construction of the associahedron (also called the Stasheff polytope), ideas leading to the theory of operads; homotopy theoretic approaches to Hilbert's fifth problem on the characterization of Lie groups; and the study of Poisson algebras in mathematical physics.

In the 1980s he turned to the application of characteristic classes and other topological and algebraic concepts in mathematical physics, first in the algebraic structure of anomalies in quantum field theory, where he worked with among others, Tom Kephart and Paolo Cotta-Ramusino.