Tristan Rivière: Catalogue data in Autumn Semester 2017 |
Name | Prof. Dr. Tristan Rivière |
Field | Mathematik |
Address | Professur für Mathematik ETH Zürich, HG G 48.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
Telephone | +41 44 632 06 71 |
tristan.riviere@math.ethz.ch | |
URL | http://www.math.ethz.ch/~triviere |
Department | Mathematics |
Relationship | Full Professor |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-4589-63L | Calculus of Variations and Conformal Invariance | 6 credits | 3V | T. Rivière | |
Abstract | In this course we will present the classical theory as well as more recent developments of the calculus of variation of surfaces. We will expose method mixing functional analysis and differential geometry in order to produce and describe global and local minimizers or saddle points to two dimensional Lagrangians. | ||||
Objective | |||||
Content | In the first part of the class we shall consider the area functional whose critical points are minimal surfaces and study the so called Plateau problem. Introduced originally by Lagrange in the 18th century. Then we will move to the systematic study of 2-dimensional conformally invariant Lagrangians and explain how they are all related to a generalized Plateau problem of prescribed mean curvature surfaces into submanifolds. In the last part of the class we will present a theory merging minimal surface theory and conformal invariance. This theory has been introduced in the early 20th century by Wilhelm Blaschke and is presently a very active field of research in geometric analysis due in particular to numerous applications in many fields of sciences such as general relativity, elasticity theory, cell biology etc. | ||||
Prerequisites / Notice | Requirements: Fundamental knowledge in functional analysis, Fourier analysis and differential geometry (FAI and DGI) | ||||
401-5350-00L | Analysis Seminar | 0 credits | 1K | M. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Ilmanen, T. Kappeler, T. Rivière, D. A. Salamon | |
Abstract | Research colloquium | ||||
Objective |