He is known for his innovative work in a number of fields, such as prehomogeneous vector spaces and Bernstein-Sato polynomials; and particularly for his hyperfunction theory. This initially appeared as an extension of the ideas of distribution theory; it was soon connected to the local cohomology theory of Grothendieck, for which it was an independent origin, and to expression in terms of sheaf theory. It led further to the theory of microfunctions, interest in microlocal aspects of linear PDE and Fourier theory such as wave fronts, and ultimately to the current developments in D-module theory. Part of that is the modern theory of holonomic systems: PDEs over-determined to the point of having finite-dimensional spaces of solutions.
He also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension. In number theory he is known for the Sato-Tate conjecture on L-functions.
He received the Schock Prize in 1997, and the Wolf Prize in 2003.