Program

Thursday, February 7, 2013

Friday, February 8, 2013

Abstracts

Mario Amrein
An adaptive Newton method based on ODE solvers
The Newton method for solving nonlinear operator equations F(x) = 0 in a Banach space
X is discussed within the context of the continuous Newton method. This framework
makes it possible to reformulate the scheme by means of an adaptive step size control
procedure that aims at reducing the chaotic behaviour of the original method without
losing the quadratic convergence close to the roots. The performance of the modified
scheme is ilustrated with a few examples.

Chidambaram Annamalai
Linear and Semidefinite Hierarchies in Discrete Optimization
Hierarchies encompass a broad class of approaches that have
been successfully used by researchers to solve optimization problems.
We will take a gentle tour through some of the more recent and
exciting results in this area that provide insights into the strength
of this approach. The talk will be aimed at a broad (but
mathematically mature) audience providing a glimpse into what some
researchers in Discrete Optimization spend time with.

Filip Misev
How to see 4D
We present a way of drawing pictures of objects in complex two-dimensional space. On the way we will encounter so-called A'Campo divides and monodromy of plane curve singularities.

Christoph Röthlisberger
Checking Admissibility in Finite Algebras
Checking if a quasiequation is admissible in a finite algebra
is a decidable problem, but the naive approach, i.e., checking validity in
the corresponding free algebra, is computationally unfeasible. We give
an algorithm for obtaining smaller algebras to check admissibility and
some examples to demonstrate the advantages of this approach.

Raphaël Huser
Statistical modelling of extreme rainfall in space and time
We consider a precipitation dataset over Switzerland and we focus on analysing the behaviour of extreme events, with special interest in the space-time dependence properties of this complex phenomenon. The cornerstone of extreme value theory (EVT) is the extremal types theorem of Fisher and Tippett, which describes the asymptotic probability distribution of the maximum or upper order statistics of a given sample (see Coles, 2001). However, univariate EVT is not enough once we want to model extremes spatially and max-stable processes are the natural extension. The characterization of max-stable processes was discussed in de Haan (1984), and models for them have been proposed by Schlather (2002) or Kabluchko et al. (2009). In this talk, a short introduction on EVT and max-stable processes will be given, and the methods will be applied to a real dataset of rainfall in Switzerland.

Sabine Bögli
Behaviour of eigenvalues under strong resolvent convergence
Around 1970 Stummel published three papers about the notion of discrete convergence of operators. His main result states that if a sequence (A_n)_n converges discretely to an operator A, then the spectrum of A_n converges (in an appropriate sense) to the spectrum of A. We reformulate the result for a sequence of closed operators on varying domains whose resolvents are discretely compact and converge strongly. Then we present some perturbation results for discrete compactness and for strong convergence of the resolvents.

Laurent Michel
Estimating the ice thickness of mountain glaciers with a shape optimization algorithm using surface topography and mass-balance
We present a shape optimization algorithm to estimate the ice thickness distribution within a two-dimensional, non-sliding mountain glacier, given a transient surface geometry and a mass-balance distribution. The approach is based on the minimization of the surface misfit at the end of the glacier's time evolution in the Shallow Ice Approximation of ice flow with a limited memory variable metric method. No filtering of the surface topography is involved where its gradient vanishes and no particular interpolation of the basal shear stress is used.
The novelty of the presented Shape Optimization Algorithm consists in the use of surface topography and mass-balance only within a time-dependent Lagrangian approach for moving-boundary glaciers.

Marcel Wirz
Mixed hp-discontinuous Galerkin FEM for linear elasticity and Stokes flow in three dimensions
I will give a brief introduction to the mixed hp-discontinuous Galerkin finite element method (FEM) as applied to linear elasticity. FEM is one of the most widely used methods to solve partial differential equations numerically. Further, I will show that the method is able to achieve exponential convergence rates.

Adrian Bock
The School Bus problem
We consider the problem of designing a school bus service in an abstract mathematical setting and study its complexity. Our main goals are to find approximation algorithms and hardness results, but  we also use our algorithms to solve instances from practice.