Caltech

This talk will review recent progress in understanding the effective

behavior of free boundaries in heterogeneous media.  Though motivated

by the pinning of martensitic phase boundaries, we shall explain

connections to other problems.  This talk is based on joint work with

Patrick Dondl.

This talk will give a survey of results in continuous-time

contract theory, and discuss open problems and plans for further

research on this topic.

The general question is how a ``principal" (a company, investors ...)

should design a payoff for compensating an ``agent" (an executive, a

portfolio manager, ...) in order to induce the best possible

performance.

The following frameworks are standard in contract theory:

(i) the principal and the agent have same, full information;

(ii) the principal cannot monitor agent's actions

(iii) the principal does not know agent's type We will discuss all

three of these problems.

The mathematical tools used are those of stochastic control theory,

stochastic maximum principle and Forward Backward Stochastic

Differential Equations.