SFU Mathematics of Computation, Application and Data ("MOCAD") Seminar: Craig Fraser

Carl Jacobi worked in the 1830s at the University of Königsberg on what became known as Hamilton-Jacobi theory, and also on the theory of the second variation in the calculus of variations. The first was a subject in dynamical analysis, while the second was a subject in pure mathematics. Insofar as the calculus of variations was concerned, Jacobi’s contributions were seminal and highly original but presented in an incomplete and programmatic form. Together his writings stimulated active but independent traditions of research in both subjects. In the late 1850s and 1860s Alfred Clebsch and Adolph Mayer – mathematicians associated with the Königsberg school - established a new approach to the investigation of sufficient conditions in the calculus of variations by bringing methods from Hamilton-Jacobi theory to bear on the transformation of the second variation. In doing so they established the basis for research on the subject that was eventually codified in writings around 1900 of Camille Jordan, Gustav von Escherich and Oskar Bolza.