Shelstad has been a key player in the development of the theory of endoscopy which is part of Langlands program. She co-conjectured the fundamental lemma with Robert Langlands in 1984. After over 20 years, this conjecture was solved by Ngô Bảo Châu in 2009, thus opening up a wealth of consequences.

In 1999, Shelstad developed a theory of twisted endoscopy with Robert Kottwitz. In 2008–9 she completed work on tempered endoscopy.

In 2012 she became a fellow of the American Mathematical Society.^[1]

• Shelstad, D. Characters and inner forms of a quasi-split group over ${\displaystyle \mathbb {R} }$ . Compositio Mathematica, 39 (1979), no. 1, 11–45.
• Langlands, R.; Shelstad, D. On principal values on p-adic manifolds. Lie group representations, II (College Park, Md., 1982/1983), 250–279, Lecture Notes in Math., 1041, Springer, Berlin, 1984.
• Kottwitz, R. and D. Shelstad Foundations of Twisted Endoscopy, Asterisque, vol. 255, 1999
• Shelstad, D. On geometric transfer in real twisted endoscopy. Annals of Mathematics 176 (2012), no. 3, 1919-1985.

• Diana Shelstad at the Mathematics Genealogy Project
• August 2008 talk, Banff International Research Station (iTunes)
• http://publications.ias.edu/rpl/series.php?series=51
• https://sites.rutgers.edu/diana-shelstad