241220 Introduction to the (invisibility) cloaking (V) (SoSe 2015)

This is a lecture by Prof. Boukricha from Tunis within the framework of
Bielefeld University's guest lectureship programme. The lecture will be
held in English and will focus on the following topic:

Since ages, the electromagnetic invisibility has had a big interest in
the fantasy literature and research. However, just in 2006,
simultaneously John Pendry and Ulf Leonhard proposed similar concepts to
achieve perfect invisibility. The principal idea behind their works was
to consider the transformation of optics or conformal mapping inspired
by general relativity. These transformations lead to design the material
parameters to deviate the light around some region.

The theoretical assumptions of perfect invisibility were possible by
applying materials with defined effective permittivity and permeability.
Such materials are commonly known as metamaterials- manmade materials-
which allow obtaining properties that are not found in nature.

Robert V. Kohn, Daniel Ouofrei, Michael S. Vogelius, Michael I.
Weinstein and others have introduced in 2008 the following definition
for the cloaking:

Definition: We say a region of space is cloaked for a particular class of
measurements if its contents - and even the existence of the cloak – are
invisible using such measurements.

To my knowledge, most research on cloaking has used several branches of
mathematics except probabilistic approaches (Stochastic Analysis).

The purpose of this course is to address this important concept of
cloaking by methods of stochastic analysis and potential theory.