Problems of deformation theory are often motivated by questions from physics. In my talk I will first consider deformation theory of an associative algebra. Then I will describe a problem of deformation quantization and formulate Kontsevich's
result which closes this problem with a positive answer. Finally, I will talk about the application of Kontsevich's quantization to the Kashiwara-Vergne conjecture.

Extending results of Van Der Vlugt,
I shall derive a new non-trivial upper bound for the dimension of trace
codes connected to algebraic-geometric codes. Furthermore, I will deduce
their true dimension if certain conditions are satisfied. Finally,
potential areas of improvement and other related results will be outlined.

We consider a polymer measure based on random walks which are based on sums of iid stable random variables.
A Gibbs measure is defined which models an attraction to the origin for these walks. A phase transition occurs as the the strength of the attraction to the origin occurs.
We examine various "thermodynamic" quantities and show they are all related to each other in a simple way and exhibit universality.