Fakultätskolloquium im Sommersemester 2017

Termin: Das Kolloquium findet in loser Folge mittwochs statt, mit jeweils zwei Vorträgen von 14:30 – 15:30 Uhr und von 16:00 – 17:00 Uhr im Hörsaal 3 (MI 00.06.011).
In der Pause ist für Getränke und Brez'n in der Magistrale gesorgt.

Ansprechpartner: Felix Krahmer, Robert König.

Vorträge im vergangenen Semester: Wintersemester 2016/17.

Vorträge im Sommersemester 2017

10.5.2017 um 14:30 Martin Stoll
(MPI Magdeburg)
Low-rank methods in optimization with PDEs
14.6.2017 ab 15:00 Festkolloquium zu Ehren von Jürgen Scheurle
im TUM Institute for Advanced Study
 
28.6.2017 um 14:30 Valentin Blomer
(Universität Göttingen)
Eigenfunktionen auf arithmetischen Mannigfaltigkeiten
28.6.2017 um 16:00 Frithjof Lutscher
(University of Ottawa)
Reaction-diffusion equations with discontinuous coefficients: Derivation, analysis and applications in spatial ecology
12.7.2017 um 14:30 Annette Vogt
(MPI Berlin)
12.7.2017 um 16:00 Michael Griebel
(Universität Bonn)
Sparse Grid Methods For Multi-Scale Viscoelastic Flows

Martin Stoll — Low-rank methods in optimization with PDEs

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Optimization subject to PDE constraints is crucial in many application ranging from image processing to the life sciences. Numerical analysis has contributed a great deal to allow for the efficient solution of these problems and our focus in this talk will be on the solution of the large scale linear systems that represent the first order optimality conditions or found are at the heart of a nonlinear optimization method.

We illustrate that these systems, while being of very large scale, usually contain a lot of mathematical structure. In particular, we focus on a low-rank methods that utilize the Kronecker product structure of the system matrices. These methods allow the solution of a time-dependent problem with the storage requirements of a small multiple of the steady problem. We then illustrate that this low-rank technique extends to problems in uncertainty quantification and allows the solution of otherwise intractable problems.

Valentin Blomer — Eigenfunktionen auf arithmetischen Mannigfaltigkeiten

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Es ist eine klassische Fragestellung, Eigenfunktionen des Laplace-Operators auf Riemannschen Mannigfaltigkeiten zu untersuchen. Vom zahlentheoretischen Standpunkt ist diese Frage vor allem interessant, wenn die Mannigfaltigkeit eine "arithmetische Struktur" besitzt, etwa in Form einer Hecke-Algebra. Ein typisches Beispiel hierfür ist die 2-Sphäre. Es werden analytische und diophantische Techniken vorgestellt, Eigenfunktionen in solchen Fällen zu untersuchen.

Frithjof Lutscher — Reaction-diffusion equations with discontinuous coefficients: Derivation, analysis and applications in spatial ecology

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Reaction-diffusion equations have been applied successfully to gain insights into problems in spatial ecology for many decades. As ecologists are increasingly interested in understanding population dynamics in heterogeneous landscapes, the coefficients in these equations should be spatially dependent. While a lot of abstract theory is known for the case of smooth coefficient functions, explicit calculations are virtually impossible, and therefore the application to ecology is limited.

In this talk, I present an approach by which coefficient functions are chosen to be piecewise constant, yet novel, discontinuous matching conditions at an interface arise. I present some results and illustrate several applications of this framework to ecological problems such as population persistence, species spread and spatial pattern formation.

Michael Griebel — Sparse Grid Methods For Multi-Scale Viscoelastic Flows

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In this presentation, we give an overview on generalized sparse grid methods for higher dimensional approximation. We focus on optimal numerical schemes based on sparse grids where the product between the spatial variables, the temporal variable, the stochastic variables and the modelling parameters of a parametrized PDE is collectively taken into account. To this end, we especially employ the adaptive combination technique.

We give examples from incompressible non-Newtonian fluid simulations involving multi-scale viscoelastic flows.
 

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