(Singularitäten differenzierbarer Abbildungen)
WS23/24, Mi 12-14, M103
The Seminar is concerned with the study of the local behavior
of real-valued smooth functions of several variables and
the classification problem
for the types of singularities that can arise at the critial points.
We will develop methods to study these singularities through the properties of their Taylor polynomials and investigate
their genericity and stability properties.
Moreover, we will introduce the fundamental notion of (universal) unfolding
that involves smooth functions with additional
parameters and examine the dependence of the critical sets on the parameters.
(in the mathematical sense used in the theory) occurs when the critical set changes its form suddenly
a small pertubation of the parameters. Catastrophe Theory, introduced by René Thom, develops a fascinating viewpoint on
the qualitative understanding of singularities of smooth functions with many applications in other scientific fields.
See the Informal Overview for
The topic of the Seminar forms a natural continuation of the lecture courses in Analysis but will also make significant use of
methods from the lecture courses in (Linear) Algebra. The Seminar should be of interest to students at any level interested in
Analysis or (Differential) Geometry and Topology or Mathematical Physics.
The Seminar talks will be held in German or English. The written reports can be submitted in German or English.
Please contact me by e-mail if you are planning to attend the seminar.
: See here
Recommended Reading for the Seminar
Th. Bröcker, ''Differentiable Germs and Catastrophes''
D.P.L. Castrigiano, S.A. Hayes, ''Catastrophe Theory''
Y.-C. Lu, ''Singularity theory and an Introduction to Catastrophe Theory''
T. Poston, I. Stewart, "Catastrophe Theory and Its Applications".
Also see here
for material from a related seminar which
might be useful.
Analysis I-II/Lineare Algebra I-II/(some) Algebra