Regular lectures Summer semester 2012: MPI MIS

Please find more information about the lectures at the detail pages.

For rooms at the MPI MiS please note:
Use the entry doors Kreuzstr. 7a (rooms A3 01, A3 02) and Kreustr. 7c (room G3 10), both in the inner court yard, and go to the 3rd. floor.
To reach the Leibniz-Saal (E1 05, 1st. floor) and the Leon-Lichtenstein Room (E2 10, 2nd. floor) use the main entry Inselstr. 22.

Please remember: The doors will be opened 15 minutes before the lecture starts and closed after beginning of the lecture!


Apr 1, 2012	Nils Bertschinger Maschinelles Lernen: Theorie und Algorithmen KeywordsMonday, 15:15 - 16:45 h
Apr 1, 2012	Peter Hornung, Wolfgang Hackbusch, Emanuele Spadaro, László Székelyhidi IMPRS Ringvorlesung: Summer semester 2012 About this lectureDue to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field. Topics Peter Hornung: Weyl's isometric embedding theorem We give a (very slightly modified) version of Nirenberg's celebrated proof of the Weyl's problem about the realization of smooth convex metrics on the 2-sphere. Wolfgang Hackbusch: Discretisation of linear, instationary partial differential equationsThe lecture considers the instationary difference equations obtained by discretising partial differential equations. We focus to the three properties: consistency, convergence, and stability. The equivalence theorem states that convergence and stability are (almost) equivalent. Therefore, it is of interest to describe sufficient and/or necessary criteria for stability. Emanuele Spadaro: Variational methods for PDEs: existence of closed geodesics on spheresPartial differential equations can be often treated via variational methods. Some of these equations are, indeed, naturally associated to an energy and their solutions correspond to critical points of such an energy. In order to give a glimpse of these techniques, in this lecture we will review the min-max construction of a closed geodesic on a 2-dimensional sphere, as proved by Birkhoff in 1917. In particular, we will discuss the difference between finding minimizers and general stationary points of a functional and, time permitting, will put this result in perspective of recent developments. László Székelyhidi: An invitation to quasiconformal mapsQuasiconformal maps are a generalization of conformal maps and as such, evolved originally from complex function theory. Besides being fascinating objects in their own right, they have been an invaluable tool in many different fields, ranging from elliptic PDEs to Teichm\"uller theory, from nonlinear elasticity to low-dimensional topology. In the words of Juha Heinonen "they are flexible enough to be ubiquitous, yet they harbor enough analytic and geometric properties so as to be useful in a variety of contexts." In fact, the theory is much more real than complex analysis, using tools from geometric measure theory, singular integrals, PDE and the calculus of variations. In these lectures I will give a brief introduction to quasiconformal mappings from a primarily analytic point of view. Date and time infoWednesdays 13:30-15:00
Apr 1, 2012	Peter Hornung Partielle DGLn in Aktion: Isometrische Immersion von Flächen Date and time infoThursday, 13:15 - 14:45 h
Apr 1, 2012	Jürgen Jost Mathematical concepts of economic theory 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.Date and time infoFriday, 13:30 - 15:00 h
Apr 1, 2012	Georgy Kitavtsev, Stephan Luckhaus Seminar on Mathematics of Thin Liquid Films 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.
Apr 1, 2012	Felix Otto Selected topics in Applied Analysis Date and time infoTuesday, 9:00 - 11:00 h
Apr 1, 2012	Emanuele Spadaro Regularity and Singularity in obstacle problems 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.Date and time infoThursday, 11:00 - 12:30 h

Apr 1, 2012

Nils Bertschinger

Maschinelles Lernen: Theorie und Algorithmen

KeywordsMonday, 15:15 - 16:45 h

Apr 1, 2012

Peter Hornung, Wolfgang Hackbusch, Emanuele Spadaro, László Székelyhidi

IMPRS Ringvorlesung: Summer semester 2012

About this lectureDue to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field. Topics Peter Hornung: Weyl's isometric embedding theorem We give a (very slightly modified) version of Nirenberg's celebrated proof of the Weyl's problem about the realization of smooth convex metrics on the 2-sphere. Wolfgang Hackbusch: Discretisation of linear, instationary partial differential equationsThe lecture considers the instationary difference equations obtained by discretising partial differential equations. We focus to the three properties: consistency, convergence, and stability. The equivalence theorem states that convergence and stability are (almost) equivalent. Therefore, it is of interest to describe sufficient and/or necessary criteria for stability. Emanuele Spadaro: Variational methods for PDEs: existence of closed geodesics on spheresPartial differential equations can be often treated via variational methods. Some of these equations are, indeed, naturally associated to an energy and their solutions correspond to critical points of such an energy. In order to give a glimpse of these techniques, in this lecture we will review the min-max construction of a closed geodesic on a 2-dimensional sphere, as proved by Birkhoff in 1917. In particular, we will discuss the difference between finding minimizers and general stationary points of a functional and, time permitting, will put this result in perspective of recent developments. László Székelyhidi: An invitation to quasiconformal mapsQuasiconformal maps are a generalization of conformal maps and as such, evolved originally from complex function theory. Besides being fascinating objects in their own right, they have been an invaluable tool in many different fields, ranging from elliptic PDEs to Teichm\"uller theory, from nonlinear elasticity to low-dimensional topology. In the words of Juha Heinonen "they are flexible enough to be ubiquitous, yet they harbor enough analytic and geometric properties so as to be useful in a variety of contexts." In fact, the theory is much more real than complex analysis, using tools from geometric measure theory, singular integrals, PDE and the calculus of variations. In these lectures I will give a brief introduction to quasiconformal mappings from a primarily analytic point of view. Date and time infoWednesdays 13:30-15:00

Apr 1, 2012

Peter Hornung

Partielle DGLn in Aktion: Isometrische Immersion von Flächen

Date and time infoThursday, 13:15 - 14:45 h

Apr 1, 2012

Jürgen Jost

Mathematical concepts of economic theory

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.Date and time infoFriday, 13:30 - 15:00 h

Apr 1, 2012

Georgy Kitavtsev, Stephan Luckhaus

Seminar on Mathematics of Thin Liquid Films

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.

Apr 1, 2012

Felix Otto

Selected topics in Applied Analysis

Date and time infoTuesday, 9:00 - 11:00 h

Apr 1, 2012

Emanuele Spadaro

Regularity and Singularity in obstacle problems

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.Date and time infoThursday, 11:00 - 12:30 h

Regular lectures Summer semester 2012

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Administrative Contact

Katharina Matschke