Analysis & PDE

Analysis and PDE are a major strength of Stanford’s Department of Mathematics, with strong connections to geometry and applied mathematics (since PDE describe fundamental aspects of these fields). 

The fields of interest represented among the senior faculty include elliptic and parabolic PDE, especially in connection with Riemannian geometry; propagation phenomena such as waves and scattering theory, including Lorentzian geometry; microlocal analysis, which gives a phase space approach to PDE; geometric measure theory; and stochastic PDE and wave propagation in random media as well as PDE of applied mathematics.