Daniel Spector, Technion

**Title:** On fractional PDE in several dimensions

Stemming from recent work on nonlocal gradients, I became interested in fractional gradients, integral functionals of the fractional gradient, and fractional partial differential equations. In this talk, I will introduce the fractional gradient and make the case that it is an object of intrinsic interest. To support this case, I will state a number of known results for Sobolev functions and their extension to the fractional setting, as well as connect fractional derivatives to the ubiquitous fractional Laplacian. Applications to the fractional calculus of variations and fractional partial differential equations will be discussed. This talk is based on joint work with Tien-Tsan Shieh of National Chiao Tung University, Taiwan.