Heat kernel and Riesz transform on non-compact metric measure spaces

The project is devoted to evolution type equations such as heat or Schrodinger equations. It will develop new methods and techniques in the theory of partial differential equations and harmonic analysis. The proposed research will contribute to the area recognized as one of main areas of focus in harmonic analysis. The project is relevant to modeling of wide range of phenomena in the real world including fluid dynamics, thermodynamics or financial markets. Schrodinger equations are the foundation of quantum mechanics. Expected outcomes include solutions of number of significant open problems concerning the Riesz transform and heat kernels in a large range of geometric settings (Riemannian manifolds, Lie groups, discrete graphs, fractals).