Oberseminar "Numerische Mathematik, Optimierung und dynamische Systeme"
Oberseminar
,
Nummer im Vorlesungsverzeichnis: 10525
SWS: 2
Dozenten
Mario
Bebendorf,
Kurt
Chudej,
Lars
Grüne,
Anton
Schiela
Allgemeines
gemeinsames Oberseminar der Lehrstühle für Angewandte Mathematik und Ingenieurmathematik
Vortragsankündigungen für das Oberseminar
Im Rahmen unseres gemeinsamen Oberseminars
finden folgende Vorträge statt:
Am
Montag, dem
17. Juli 2017, um 16:15 Uhr im
S 80,
Gebäude NW II, spricht
über das Thema
"The Social Cost of Carbon Dioxide – Mitigating Global Warming Whilst Avoiding Economic
Collapse"

Abstract:
Many governments and international finance organizations use a carbon price in costbenefit analyses, emissions trading
schemes, quantification of energy subsidies, and modelling the impact of climate change on financial assets. The most
commonly used value in this context is the social cost of carbon dioxide (SCCO2). Users of the social cost of carbon dioxide
include the US, UK, German, and other governments, as well as organizations such as the World Bank, the International
Monetary Fund, and Citigroup. Consequently, the social cost of carbon dioxide is a key factor driving worldwide investment
decisions worth many trillions of dollars.
The social cost of carbon dioxide is derived using integrated assessment models that combine simplified models of the
climate and the economy. One of three dominant models used in the calculation of the social cost of carbon dioxide is the
Dynamic Integrated model of Climate and the Economy, or DICE. DICE contains approximately 70 parameters as well as
several "exogenous" driving signals such as population growth and a measure of technological progress. Given the quantity of
finance tied up in a figure derived from this simple highly parameterized model, understanding uncertainty in the model and
capturing its effects on the social cost of carbon dioxide is of paramount importance. Indeed, in late January this year the US
National Academies of Sciences, Engineering, and Medicine released a report calling for discussion on "the various types of
uncertainty in the overall SCCO2 estimation approach" and addressing "how different models used in SCCO2 estimation
capture uncertainty."
This talk, which focuses on the DICE model, essentially consists of two parts. In Part One, I will describe the social cost of
carbon dioxide and the DICE model at a highlevel, and will present some interesting preliminary results relating to uncertainty
and the impact of realistic constraints on emissions mitigation efforts. Part one will be accessible to a broad audience and will
not require any specific technical background knowledge. In Part Two, I will provide a more detailed description of the DICE
model, describe precisely how the social cost of carbon dioxide is calculated, and indicate ongoing developments aimed at
improving estimates of the social cost of carbon dioxide.
Am
Montag, dem
10. Juli 2017, um 16:15 Uhr im
S 80,
Gebäude NW II, spricht
über das Thema
"(Nonsmooth) Control Lyapunov Functions"

Abstract:
Control Lyapunov functions (CLFs) and the design of feedback controllers from CLFs has faded from
the spotlight over recent years even though their full potential has not been explored yet. To reactivate
research on CLFs we review existing results on (nonsmooth) CLFs in the context of stability and
stabilization of nonlinear dynamical systems. Moreover, we highlight open problems and results on
CLFs for destabilization. The talk concludes with ideas on Complete CLFs, which combine the
concepts of stability and instability, and with the numerical construction of nonsmooth CLFs. The
results presented in the talk are illustrated and motivated on the examples of a nonholonomic
integrator and Artstein’s circles.
Am
Montag, dem
3. Juli 2017,
um 16:15 Uhr im
S 80,
Gebäude NW II, spricht
im Rahmen des Oberseminars und des „
Forschungszentrums für Modellierung und Simulation (MODUS)”
über das Thema
"Mathematical aspects of biological fitness landscapes"

Abstract:
Biological evolution can be conceptualized as a search process in the space of gene sequences
guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each
genotype. The relationship between genotype and fitness is generally complex, as it is mediated by
the multidimensional organismic phenotype that interacts with the environment and thereby
determines reproductive success. Two modeling strategies have been devised to deal with this
situation. One is to shortcut the intermediate phenotypic level by assigning fitness directly to
genotypes. This leads to probabilistic models that define ensembles of random functions on Hamming
spaces or (in the standard case of binary sequences) on the hypercube. An alternative and biologically
more realistic approach is provided by Fisher's geometric model (FGM), which describes the
phenotype as a vector in an ndimensional Euclidean trait space with a unique fitness optimum.
Genetic mutations are encoded as random phenotypic displacements, and complexity arises from the
difficulty of optimizing a smooth function by a finite number of random vectors. After a historical
introduction and an overview of the current understanding of real fitness landscapes that is available
from empirical studies, I will survey quantitative measures of fitness landscape complexity and present
the results of a recent analytical study of the fitness landscape generated by FGM.
Am
Freitag, dem
2. Juni 2017,
um 13:00 Uhr im
S 80,
Gebäude NW II, spricht
über das Thema
"Computational methods for Lyapunov functions and estimation of basins of attraction"

Abstract:
We discuss several different numerical methods for the computation of Lyapunov functions and the corresponding estimation of
basins of attraction for nonlinear systems in different settings. We discuss how some of these methods can be combined and/or
adapted to compute approximations to complete Lyapunov functions, which are Lyapunov functions defined on the whole statespace
and subdivide it into two disjunct sets with very different dynamical properties. Namely the chainrecurrent part and the gradientlike
part, where solutions pass through.
Am
Montag, dem
29. Mai 2017, um 16:15 Uhr im
S 80,
Gebäude NW II, spricht
über das Thema
"“Feedback stabilization of the FokkerPlanck equation"

Abstract:
The probability distribution function of a dragged Brownian particle can be characterized by the
FokkerPlanck equation. By means of an optical tweezer, interaction with the particle is possible and
leads to a bilinear control system. It is known that the uncontrolled system converges to the stationary
distribution. However, depending on the parameters of the system, this convergence can be
inadequately slow. Projectionbased decoupling of the FokkerPlanck equation allows to design
certain feedback control laws that locally increase the rate of convergence to the stationary
distribution. Different strategies based on a projected Riccati equation and approximations of the
HamiltonJacobiBellman equation are discussed.
This is joint work with Karl Kunisch and Laurent Pfeiffer (University of Graz).
Am
Montag, dem
22. Mai 2017, um
16:15 Uhr im
S 80,
Gebäude NW II, spricht
über das Thema
"Weaklynormal basis vector fields in RKHS with an application
to shape Newton methods"

Abstract:
In this talk I discuss the approximation of normal vector fields defined on the boundary of a domain in
the plane. For this purpose we introduce socalled weakly normal basis functions with the help of
reproducing kernels. These normal functions enjoy several nice properties and are tailored to shape
optimisation problems. This is joint work with Alberto Paganini.
Einladende:
Prof. Dr. Mario Bebendorf Prof. Dr. Kurt Chudej Prof. Dr. Lars Grüne Prof. Dr. Anton Schiela