# Continuous time Principal-Agent problem and optimal planning

We consider a general formulation of the Principal-Agent problem with a continuous payment and a lump-sum payment at termination, and possibly in a random horizon setting.

# A new method for the best subset selection problem

In this talk we consider the following sparse approximation or best subset selection problem:

# Learning the Koopman Operator for Dynamic Data

Recent work in the study of dynamic systems has focused on data-driven decomposition techniques that approximate the action of the Koopman operator on observable functions of the underlying phenomena.

# The Tale of Two Tails

Abtract

We discuss formation of patterns due to Fisher-KPP reaction appended with fast or slow diffusions

$u_{t} = \left [ D(u) u_{x} \right ]_{x} + u(1 - u)$

where

$D(u) = \left \{\begin{array}{cl} u, & \text{slow diffusion} \\ 1, & \text{Standard Fisher-KPP}\\ \frac{1}{u}, & \text{fast (logarithmic)} \end{array} \right .$