Session 2B — Lectures by Fellows/Associates

Umesh Waghmare, JNCASR, Bengaluru

Two stories of PDE arising from differential geometry and physics View Presentation

My research focuses on PDE arising from geometry (and connected vaguely to physics). I shall describe some of my results in the context of two such PDE - the gravitating vortex equation and the vortex Monge-Ampere equation. Along with collaborators, I proved that these equations have solutions if and only if some easy-to-check algebra-geometric conditions are met. These equations are actually special cases of more complicated equations, namely, the Kahler-Yang-Mills equations and the vector bundle Monge-Ampere equation. If time permits, I hope to convey why one must care about these more general equations too.