Linear PDE with Constant Coefficients

  • Marc Härkönen (Georgia Institute of Technology, Atlanta)
E1 05 (Leibniz-Saal)


In an undergraduate differential equations course we learn to solve a homogeneous linear ordinary differential equation with constant coefficients by finding roots of the characteristic polynomial. Thus the problem of solving an ODE is reduced to factoring a univariate polynomial. A generalization of this was found in the 1960s for systems of linear PDE. The Fundamental Theorem by Ehrenpreis and Palamodov asserts that solutions to a PDE system can be represented by a finite sum of integrals over some algebraic variety. This representation can be used describe a primary decomposition of an ideal or module. This talk presents the main historical results, along with recent algorithms.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar