We will introduce the notion of an operad, which generalize the properties coming from associative algebras or Lie algebras. While the definition of an operad to somewhat complex everything will be done through example so we can get familiar with operads and their vast array of applications. If time permits we will give some applications to deformation theory of associative algebras.

In this talk we introduce a notion of stochastic viscosity solution

for a class of fully nonlinear SPDEs and the corresponding Path-dependent

PDEs (PPDEs). The definition is based on our new accompanying work

on the pathwise stochastic Taylor expansion, using a variation of the path-

derivatives initiated by Dupire. As a consequence this new definition of the

viscosity solution is directly in the pathwise sense, without having to invoke

the stochastic characteristics for the localization. The issues of consistency,

stability, comparison principles, and ultimately the well-posedness of the

stochastic viscosity solutions will be discussed under this new framework.

This is a joint work with Rainer Buckdahn and Jianfeng Zhang.