Felix Otto: Catalogue data in Autumn Semester 2020

Name Prof. Dr. Felix Otto
(Professor Max-Planck-Institut für Mathematik in den Naturwissenschaften - Leipzig)
Address
Forschungsinstitut für Mathematik
Rämistrasse 101
HG G 44.1 / Frau Waldburger
8092 Zürich
SWITZERLAND
DepartmentMathematics
RelationshipLecturer

NumberTitleECTSHoursLecturers
401-5001-70LStochastic Homogenization Information 0 credits1VF. Otto
AbstractNachdiplom lecture
Objective
ContentIn engineering applications, heterogeneous media are often described in
statistical terms. This partial knowledge is sufficient to determine the
effective, i.e. large-scale behavior. This effective behavior may be inferred
from the Representative Volume Element (RVE) method. I report on last decades
progress on the quantitative understanding of what is called stochastic
homogenization of linear elliptic partial differential equations with random
coefficient fields: optimal error estimates of the RVE method and the
homogenization error, and the leading-order characterization of fluctuations.
Methods connect to elliptic regularity theory, and in fact lead to a fresh look
upon this classical area, and to concentration of measure arguments.

In this course, I try to be both self-contained and efficient, by focussing on
simple situations. Some prior knowledge on linear elliptic equations and
functional analysis will be more helpful than advanced knowledge on probability
theory, beyond elementary concepts like expectation or variance.