Jim Stasheff

James Dillon Stasheff (born January 15, 1936, New York City) is an American mathematician, a professor emeritus of mathematics at the University of North Carolina at Chapel Hill. He works in algebraic topology and algebra as well as their applications to physics.

Biography Stasheff did his undergraduate studies in mathematics at the University of Michigan, graduating in 1956.

From 1961 to 1962, Stasheff was a C.L.E. Moore instructor at the Massachusetts Institute of Technology. Then in 1962 joined the faculty of University of Notre Dame as an assistant professor; he was promoted to full professor there in 1968. He visited Princeton University from 1968 to 1969 and then stayed there the next year as a Sloan Fellow. Then in 1970 he moved to Temple University, where he held a position until 1978. In 1976, he joined the UNC faculty. He has been married since 1959 and has two children.

Research The three-dimensional Stasheff polytope. Its vertices represent the possible parenthesizations of a five-element sequence, and its edges represent applications of the associative property to these parenthesizations. 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 1960s he wrote fundamental papers on higher homotopy theory and homotopy algebras. He introduced , Stasheff algebras and Stasheff polytopes.

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. He referred to the research field as cohomological physics.

Awards and honors In 2012 he became a fellow of the American Mathematical Society.

Selected publications