# John-von-Neumann lecture - Wintersemester 2014/15

**Local minimization, variational evolution and Gamma-convergence**

**Prof. Andrea Braides**

**The course will begin after January 7, 2015.**Exact times and locations tba.

**Content:**The course's objective is the description of energy-driven systems in the presence of (many) local minima. We will recall the notion of Gamma-convergence, which has been introduced to study global minimum problems for sequences of energies, and briefly analyze some basic examples. We will then exhibit examples that show how this notion may fail to capture the behaviour of local minima, and discuss additional conditions that allow to deduce the convergence of local minimum problems. We will then treat evolution problem described by the concept of minimizing movement, which has been introduced to study gradient-flow type dynamics. We will discuss stability properties also of this notion.

**Prerequisites (recommended):**Students are supposed to have a Bachelor degree in Mathematics, Physics or Computer Science. Some basic notions of topology are needed, and some knowledge of functional analysis (such as weak convergence) may be helpful, even though not necessary.

**Intended Learning Outcomes:**After successful completion of the module, students are able to analyse physical phenomena that can be modeled through the introduction of sequences of energies with many local minima. Students are able to apply the competences won in the module both to static and dynamic optimization problems.