# 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

#### Martin Stoll — Low-rank methods in optimization with PDEs

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

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

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.

#### Annette Vogt — Statistics between economy and mathematics in Berlin resp. Germany (1863-1946)

Statistics in Berlin (and Prussia) has been developed very successfully in the 19th century. The Royal Prussian Statistical Bureau (sic) was established in 1805, in 1862 the first statistical office of a town was opened - in Berlin. And in 1863 the 5th International Statistical Congress was held in Berlin (founded in 1853). From 1860 to 1882 the statistician Ernst Engel (1821-1896) was the director of the Royal Prussian Statistical Bureau, and here he introduced the first seminar on statistics, i.e. teaching and training courses in descriptive and state statistics. After his demission a special seminar was established at the Berlin University - the Economic-Statistical Seminar in 1886. Two famous statisticians became the first directors: August Meitzen (1822-1910) and Richard Boeckh (1824-1907), the other two directors were the economists Adolph (Adolf) Wagner (1835-1917) and Gustav von Schmoller (1838-1917). After 1907/1910 statistics became less important, although the famous Ladislaus von Bortkiewicz (1868-1931) taught at the Berlin University from 1901 until his death in 1931 and at the Berlin School of Economics (Berliner Handels-Hochschule) from 1906 until 1923.

First, I'll give an overview on the history of the Economic-Statistical Seminar at the Berlin University from the beginning. Second, I'll describe the development of the seminar in the 1920s and 1930s, including the close relations between the Philosophical Faculty of the Berlin University and the Berlin School of Economics (Berliner Handels-Hochschule) which was opened in 1906. Third, I'll give an overview on the situation until the 1950s, describing the deep break because of the Nazi's, and the reconstruction after 1946 when the Economics Faculty was opened at the Berlin University (from 1948 on Humboldt University).

The University was re-opened in January 1946, the School of Economics and the fields economics and statistics of the Law Faculty of the University were united and founded the new Faculty of Economics. In the tradition of August Meitzen and Richard Boeckh a statistician became the first dean of the Faculty: Bruno Gleitze (1903-1980), who left Berlin-East in December 1948 and moved to Berlin-West.

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

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.