UBC Math Department Colloquium: Mathav Murugan

Harnack inequalities have proved to be a powerful tool in PDE (regularity estimates), geometry (geometric flows) and probability (heat kernel estimates). In the early 1990s Grigor'yan and Saloff-Coste gave a characterisation of the parabolic Harnack inequality (PHI). This characterisation implies that PHI is stable under perturbations (quasi-isometries). In this talk, I will provide an introduction to Harnack inequalities and discuss the stability of elliptic Harnack inequality.

This is joint work with Martin Barlow.