Many materials and media in nature and engineering feature random heterogeneities on a microscopic scale, yet often behave like a homogeneous material on large scales. On a mathematical level, this corresponds to the observation that solutions to PDEs with random coefficient fields can often be approximated by solutions to an effective PDE with constant coefficients on large scales. This effect is known as homogenization and has been the subject of intensive mathematical research in the last decades.
In recent years, the quantitative theory of stochastic homogenization has seen a series of breakthroughs, resulting in the derivation of optimal estimates on homogenization rates. The goal of this course will be to provide an introduction to the theory of stochastic homogenization, including
-Homogenization error estimates for linear and nonlinear PDEs
-The concepts of correctors and two-scale expansions
-Spectral gap inequalities
-Regularity properties of elliptic operators with random coefficient field
-The structure of fluctuations in stochastic homogenization
Target group: PhD students and young postdocs in mathematics, especially analysis.
Prerequisites: Background in Mathematical Analysis
Basic knowledge of PDEs (Sobolev spaces, elliptic equations)
Evaluation: Regular Assignments.
Teaching format: Lectures.
ECTS: 3 Year: 2021
Track segment(s):
MAT-ANA Mathematics - Analysis
MAT-PROB Mathematics - Probability
Teacher(s):
Nicolas Clozeau Julian Fischer
Teaching assistant(s):
Alice Marveggio
If you want to enroll to this course, please click: REGISTER
- Teacher: Nicolas Clozeau
- Teacher: Julian Fischer
- Teaching Assistant: Alice Marveggio