We will introduce the theory of weak positivity which was developed by Fujita, Kawamata, Viehweg, Campana and others. We will discuss some applications to birational geometry.

Tikhonov regularization is commonly applied to the solution of linear discrete ill-posed problems. In many applications the desired solution is known to be nonnegative. It is then natural to require that the approximate solution determined by Tikhonov regularization is also nonnegative. The present ...

Abstract: TBA

In this talk, we will present some recent developments on using Physics-informed neural networks (PINNs) to quantify uncertainty propagation in a unified framework forward, inverse and mixed stochastic problems based on scattered measurements. We will also present generative models for data-driven un...