# Regular Lectures - Summer semester 2012

## Mathematical concepts of economic theory: Jürgen Jost

**Date:**Friday, 13:30 - 15:00 h**Location**: MPI MiS, room A01**First lecture:**April, 27th**Last lecture:**June, 8th**Description:**In this course, I shall describe mathematical concepts from topology, dynamical systems, and stochastic processes that are useful and important for modelling economic processes, with a view towards a dynamically conception of economics.

The course is intended both for students of mathematics and related fields that want to learn the aforementioned mathematical theories, and for people interested in economic theory.

## Selected topics in Applied Analysis: Felix Otto

**Date:**Tuesday, 9:00 - 11:00 h- in case the lecture cannot take place due to travel etc.:
- Thursday, 9:00 - 11:00 h

**Location:**MPI MiS, room A01**First lecture:**April, 10th

## Maschinelles Lernen: Theorie und Algorithmen: Nils Bertschinger

**Date:**Monday, 15:15 - 16:45 h**Location:**MPI MiS, room A02**First lecture:**April, 16th

## Partielle DGLn in Aktion: Isometrische Immersion von Flächen: Peter Hornung

**Date:**Thursday, 13:15 - 14:45 h**Location:**University, SG 3-11 (Seminargebaeude)**First lecture:**April, 12th

## Seminar on Mathematics of Thin Liquid Films: Georgy Kitavtsev, Stephan Luckhaus

**Date:**Tuesday, 13:30 - 15:00 h**Location:**MPI MiS, room A01**Description**: Originating in the works of Laplace, Young, Neumann and Reynolds the mathematical theory of liquid films have newly attracted mathematicians in the last two decades during which the theoretical justification for the lubrication approximation was suggested and developed. Describing the evolution of liquid micro and nanoscopic films raises many mathematical challenges. These include modeling issues such as finding appropriate simplied descriptions of the systems that are physically correct, and analytically and numerically tractable. Furthermore partial differential equations describing thin liquid films are (due to their nonlinearity, higher order, and the degenerate nature of the diffusion terms) notoriously difficult to analytically understand and simulate numerically. Mathematics ranging from functional analysis, variational methods, asymptotic analysis to modeling and numerics is essential to gain insights about thin liquid films and will be considered in this seminar.

There will be weekly presentations on selected papers. The seminar is addressed to graduate students planning a deep in the area of applied analysis or numerics, Ph.D. students and everybody who is just interested in. Feel very welcome to participate.**Selected topics:**- Lubrication approximation for liquid films. The role of geometry and physical effects (e.g. Marangoni, gravity, evaporation and slippage).
- Special classes of solutions: bifurcations of stationary solutions; traveling waves; self-similar solutions.
- Existence of entropy solutions and their regularity. Example of non-uniqueness.
- Analysis of the moving boundary value problems.
- Numerical schemes for lubrication equations and their convergence properties.
- Analysis of finite time rupture.
- Analysis of coarsening dynamics of droplets: reduced ODE models and coarsening rates.

## Regularity and Singularity in obstacle problems: Emanuele Spadaro

**Date:**Thursday, 11:00 - 12:30 h**Location:**MPI MiS, room A01**First lecture:**April, 12th**Description:**In this course we present a geometric approach to the study of the regularity and the singularity of the free boundary in the classical obstacle problem.

This approach is due to F. Lin and is based on the use of several techniques in geometric measure theory, such as the monotonicity formula for Almgren's frequency function, Federer's dimension reduction and Almgren's stratification theorem.

The aim of the course is to give an account of these techniques in perspective of the proof of Caffarelli's main result for the obstacle problem.