Thu, 19 Feb 2015

12:00 - 13:00
L6

Linear inviscid damping for monotone shear flows.

Christian Zillinger
(University of Bonn)
Abstract
While the 2D Euler equations incorporate
neither dissipation nor entropy increase and
even possess a Hamiltonian structure, they
exhibit damping close to linear shear flows.
The mechanism behind this "inviscid
damping" phenomenon is closely related to
Landau damping in plasma physics.
In this talk I give a proof of linear stability,
scattering and damping for general
monotone shear flows, both in the setting
of an infinite periodic channel and a finite
periodic channel with impermeable walls.
Mon, 12 May 2014

14:15 - 15:15
Oxford-Man Institute

Optimal transport and Skorokhod embedding

MARTIN HEUSMANN
(University of Bonn)
Abstract

It is well known that several solutions to the Skorokhod problem

optimize certain ``cost''- or ``payoff''-functionals. We use the

theory of Monge-Kantorovich transport to study the corresponding

optimization problem. We formulate a dual problem and establish

duality based on the duality theory of optimal transport. Notably

the primal as well as the dual problem have a natural interpretation

in terms of model-independent no arbitrage theory.

In optimal transport the notion of c-monotonicity is used to

characterize the geometry of optimal transport plans. We derive a

similar optimality principle that provides a geometric

characterization of optimal stopping times. We then use this

principle to derive several known solutions to the Skorokhod

embedding problem and also new ones.

This is joint work with Mathias Beiglböck and Alex Cox.

Mon, 17 Feb 2014

17:00 - 18:00
L6

The Hilbert transform along vector fields

Christoph Thiele
(University of Bonn)
Abstract

An old conjecture by A. Zygmund proposes

a Lebesgue Differentiation theorem along a

Lipschitz vector field in the plane. E. Stein

formulated a corresponding conjecture about

the Hilbert transform along the vector field.

If the vector field is constant along

vertical lines, the Hilbert transform along

the vector field is closely related to Carleson's

operator. We discuss some progress in the area

by and with Michael Bateman and by my student

Shaoming Guo.

Thu, 10 May 2012

14:00 - 15:00
Gibson Grd floor SR

Frequency-independent approximation of integral formulations of Helmholtz boundary value problems

Professor Mario Bebendorf
(University of Bonn)
Abstract

We present recent numerical techniques for the treatment of integral formulations of Helmholtz boundary value problems in the case of high frequencies. The combination of $H^2$-matrices with further developments of the adaptive cross approximation allows to solve such problems with logarithmic-linear complexity independent of the frequency. An advantage of this new approach over existing techniques such as fast multipole methods is its stability over the whole range of frequencies, whereas other methods are efficient either for low or high frequencies.

Thu, 05 May 2011

13:00 - 14:00
SR1

Normal Forms, Factorability and Cohomology of HV-groups

Moritz Rodenhausen
(University of Bonn)
Abstract

A factorability structure on a group G is a specification of normal forms of group elements as words over a fixed generating set. There is a chain complex computing the (co)homology of G. In contrast to the well-known bar resolution, there are much less generators in each dimension of the chain complex. Although it is often difficult to understand the differential, there are examples where the differential is particularly simple, allowing computations by hand. This leads to the cohomology ring of hv-groups, which I define at the end of the talk in terms of so called "horizontal" and "vertical" generators.

Wed, 04 May 2011

16:00 - 17:00
SR2

Normal Forms, Factorability and Cohomology of HV-groups

Moritz Rodenhausen
(University of Bonn)
Abstract

A factorability structure on a group G is a specification of normal forms

of group elements as words over a fixed generating set. There is a chain

complex computing the (co)homology of G. In contrast to the well-known bar

resolution, there are much less generators in each dimension of the chain

complex. Although it is often difficult to understand the differential,

there are examples where the differential is particularly simple, allowing

computations by hand. This leads to the cohomology ring of hv-groups,

which I define at the end of the talk in terms of so called "horizontal"

and "vertical" generators.

Fri, 03 Jun 2011
14:15
DH 1st floor SR

Cross hedging with futures in a continuous-time model with a stationary spread

Prof Stefan Ankirchner
(University of Bonn)
Abstract

When managing risk, frequently only imperfect hedging instruments are at hand.

We show how to optimally cross-hedge risk when the spread between the hedging

instrument and the risk is stationary. At the short end, the optimal hedge ratio

is close to the cross-correlation of the log returns, whereas at the long end, it is

optimal to fully hedge the position. For linear risk positions we derive explicit

formulas for the hedge error, and for non-linear positions we show how to obtain

numerically effcient estimates. Finally, we demonstrate that even in cases with no

clear-cut decision concerning the stationarity of the spread it is better to allow for

mean reversion of the spread rather than to neglect it.

The talk is based on joint work with Georgi Dimitroff, Gregor Heyne and Christian Pigorsch.

Thu, 20 Nov 2008

14:00 - 15:00
Comlab

Approximation of harmonic maps and wave maps

Prof Soeren Bartels
(University of Bonn)
Abstract

Partial differential equations with a nonlinear pointwise constraint defined through a manifold occur in a variety of applications: The magnetization of a ferromagnet can be described by a unit length vector field and the orientation of the rod-like molecules that constitute a liquid crystal is often modeled by a vector field that attains its values in the real projective plane thus respecting the head-to-tail symmetry of the molecules. Other applications arise in geometric

modeling, quantum mechanics, and general relativity. Simple examples reveal that it is impossible to satisfy pointwise constraints exactly by lowest order finite elements. For two model problems we discuss the practical realization of the constraint, the efficient solution of the resulting nonlinear systems of equations, and weak accumulation of approximations at exact solutions.

Mon, 12 Feb 2007
14:15
DH 3rd floor SR

Stability of sequential Markov chain Monte Carlo methods

Prof Andreas Eberle
(University of Bonn)
Abstract

Sequential Monte Carlo Samplers are a class of stochastic algorithms for

Monte Carlo integral estimation w.r.t. probability distributions, which combine

elements of Markov chain Monte Carlo methods and importance sampling/resampling

schemes. We develop a stability analysis by functional inequalities for a

nonlinear flow of probability measures describing the limit behaviour of the

methods as the number of particles tends to infinity. Stability results are

derived both under global and local assumptions on the generator of the

underlying Metropolis dynamics. This allows us to prove that the combined

methods sometimes have good asymptotic stability properties in multimodal setups

where traditional MCMC methods mix extremely slowly. For example, this holds for

the mean field Ising model at all temperatures.

 

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