Seminar Series in Mathematics and its Applications
Division of Mathematics, Luleå University of
Technology, Sweden
The Past Talks since November 2, 2016:

Speaker: John Fabricius, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, November 2, 2016
Place: E243
Title: On the Role of Functional Analysis in Continuum Mechanics
Abstract:
The theory of Hilbert spaces has a wide range of applications in
science and technology. In this talk we will focus on functional
analysis as a tool for analyzing boundary value problems in
continuum mechanics. Some topics that will be discussed are
definitions of weak (or generalized) solutions, variational
formulations, existence and uniqueness of solutions, continuous
dependence of solutions on boundary data, eigenvalue problems
and numerical methods for computing approximative solutions.
The slides of the talk.
Some Matlab examples.

Speaker: Per Bergström, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, November 23, 2016
Place: E243
Title: Shape Inspection by Vision in Production
Abstract:
Analysis of shape data from an optical measurement method will be discussed. The shape of a
measured object is to be compared to its nominal shape defined by a CADmodel. The measured
object is moving on a conveyer belt and is arbitrarily oriented. Using optical shape measurement
methods the background is measured as well and measurement errors are considerable.
A computational method for doing the shape analysis fast and robust from given shape data will be described.
The slides of the talk.

Speaker: Gunnar Söderbacka, Åbo Akademi, Finland
Date and Time: Wednesday 15:00, December 7, 2016
Place: A1545
Title: Dynamical Systems: Ecological Modeling
Abstract:
Ecological modeling is becoming increasingly more important for modern engineers.
The mathematical language of
dynamical systems has
been applied by engineering since ancient times.
In this seminar we introduce and discuss some main methods for studying
dynamical systems, in particular for the analysis
of nonlinear systems of predators and preys. We show how
important results can be obtained by simple
methods that are based on elementary mathematics.
Most models of predators and preys indicate cycles
where populations are becomming unrealisticly small. We point out that Deterministic
Models are heavily criticised, e.g. amongst
Swedish specialists in stochastics. On the other hand, subarctic biologists
confirm that predators are
not behaving stochasticly, but rather switching feeding between species.
This leads to dynamical
systems with switches, also well known in other engineering
applications. To conclude, we will also mention some challenging open problems in this subject.
The slides of the talk.
Note:
2018 is the "Year of Mathematical Biology"
as announced by the European Mathematical Society.

Speaker: Inge Söderkvist, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, 11 January 2017
Place: E246
Title: LeastSquares Fitting of Model Parameters to Experimental Data
Abstract: We will consider computational methods for fitting parameters to experimental
data using the leastsquares criteria. Linear, nonlinear, and separable problems will be
considered. The methods covered range from basic techniques, taught in undergraduate courses,
to techniques which are close to the state of the art in research and which often are adapted
to specific problems.
Special attention is given to the problem of determining a movement of a rigid body given
3Dpositions of some landmarks.
The slides of the talk.

Speaker: Daniel Kastinen, Department of Computer Science, Electrical and Space Engineering, LTU
Date and Time: Wednesday 15:00, 25 January 2017
Place: E246
Title: Meteors and Celestial Dynamics
Abstract:
The area of celestial dynamics has been and is ripe with applications of contemporary mathematics. However there has
been a distinct lack of formalism and applications of advanced methods in the more experimental areas of celestial
dynamics, such as meteor science. Thus we have developed a skeleton version of a new toolbox for statistical small
body dynamics in the Solar system. We will present the general idea and methods behind the software and its possible
applications. The celestial dynamics are handled by standard Hamiltonian splitting methods and common ODE solvers.
We also plan to implement stability analysis methods such as Lyapunov Indicators, Fast Lyapunov Indicators, and Mean
Exponential Growth factor of Nearby Orbits using the same solvers. Currently, the software is constructed to generate
clones of parent bodies drawn from multivariate probability distribution calculated from uncertainties in observational
parameters by Bayesian inversion theory. As we then sample the initial distributions in a MonteCarlo fashion we also
examine convergence and find both scenario configurations and their respective probability. We have used this to
examine the comet 21P/GiacobiniZinner and its generated meteoroid streams that produce the meteor showers on
Earth of the 1933, 1946, 2011, and 2012 October Draconids.
The slides of the talk.

Speaker: Damiano Varagnolo, Automatic Control Lab, LTU
Date and Time: Wednesday 15:00, 8 February 2017
Place: E246
Title: Solving IllPosed Estimation Problems
through Regularization: A Brief Introduction with Examples
Abstract: We will describe the concept of regularization in statistical estimation frameworks,
and give Bayesian interpretations of why regularizing illposed problems may lead to improved estimates.
More specifically we will start from introducing the Stein's phenomenon, to end connecting Tikhonov
regularization with reproducing kernel Hilbert spaces. In doing so we will show with practical examples and
Matlab codes the effect of applying regularization concepts in classical statistical problems such as the
identification of BIBO stable LTI systems and the estimation of unknown inputs.
For the slides, a zipped file and the video of the talk, please visit the following links:
slides
zipped
mp4

Speaker: Elena Miroshnikova, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, 22 February 2017
Place: E243
Title: Conservation Laws as Consequences of Fundamental Properties of Space and Time
Abstract:
Noether's theorem provides a strong connection between symmetry of space and time and conservation laws for some
dynamical systems. We'll show that certain physically important conservation laws are a direct consequence
of the spacetime symmetry admitted by the system. This theorem plays a fundamental role in the connection
between mathematics and physics. We consider some classical applications of the theorem, such as conservation
laws of energy, mass and momentum, and also show its effect on quantum physics.
The slides of the talk.

Speaker: Norbert Euler, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, 8 March 2017
Place: E243
Title: Nonlinear Mathematical Physics and Differential Equations: A Personal Perspective and a First Step in Symmetry Analysis
Abstract:
This talk will consist of two main parts. In Part I
we will give a general overview on some of the subjects in nonlinear mathematical physics. In particular we'll consider the problem of the
integrability
(or solvability) of nonlinear differential equations and discuss the theories that are available to address this problem. We'll concentrate on two
main theories, namely the Lie symmetry analysis and the Painlev\'e analysis, applicable to both ordinary and partial differential equations.
Although the two approaches that are described by these theories are
essentially different in their mathematical structure, they both address the integrability of nonlinear equations and serve as
useful criteria for identifying integrable equations. In Part II of this talk
we will concentrate on the Lie symmetry analysis theory. As an introduction to this theory, we will derive the invariance condition that
determines Lie point symmetry transformations for differential equations. This part will be presented in the form of a lecture,
and some exercises will also be included for the interested reader.
The slides of the talk.

Speaker: Niklas Lundström, Department of Mathematics and Statistics, Umeå University
Date and Time: Wednesday 15:00, 22 March 2017
Place: E246
Title: pHarmonic Functions Near LowDimensional Hyperplanes
Abstract: We first give some basics about the pLaplace equation and pharmonic
functions including some applications. We then prove growth estimates of positive
pharmonic functions in ndimensional space vanishing near an mdimensional
hyperplane, 0 < m < n1. I.e. we consider "thin boundaries" of dimensions less than n1.
Our results imply the so called boundary Harnack's inequality, some
estimates of pharmonic measure
and some results of PhragmenLindelöf type for psubharmonic functions.
We will briefly sketch the proofs of which the core is constructions of
certain sub and supersolutions to the pLaplace equation.

Speaker: Adam Jonsson, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, 5 April 2017
Place: E246
Title: An Application of Classical Analysis to Intertemporal Choice
Abstract:
There are many problems of longterm management and control arising in engineering, economics,
and other areas, where it is not desirable to set an exact time horizon or terminal date.
For example, in finding optimal replacement times for shortlived technical equipment, it is
often more natural and convenient to place the time horizon at infinity than to specify a
finite horizon. The infinitehorizon model leads to difficulties however, as concepts like
maximal aggregate payoff or utility need to be replaced with new ones. In this talk I will
discuss some philosophical and computational aspects of these difficulties and show how
ideas from classical analysis can be used to partially resolve them.
The slides of the talk.

Speaker: Ove Edlund, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, 19 April 2017
Place: E246
Title: The Conjugate Gradient Method for Solving Systems of Linear Equations
Abstract: The conjugate gradient method is one of the most widely used methods for finding approximate solutions to systems of linear equations. It serves its purpose well when there are so many unknowns that factorization methods (with sparse representation no less) require computational resources that simply are not available. An example of when the conjugate gradient method is commonly used, is in numerical approximation of PDE.
The conjugate gradient method is a Krylov subspace method, that solves nxn systems with symmetric positive definite matrices in n iterations. In practice much fewer iterations are used, for two reasons: Often a good approximation is reached after a limited number of iterations, drastically lowering the computation time, and secondly, as the solution process approaches n iterations, rounding errors from the floating point representation may influence the solution in a bad way.
During the seminar, it will be explained why the solution always can be found in the Krylov subspace, and how the conjugate gradient step, that generates a Krylov sequence, can be so simple. If time permits, some properties of the system matrix that are favourable for the conjugate gradient method will be accounted for, as well as the connection to the nonlinear conjugate gradient method for optimization.
The slides of the talk.

Speaker: Thomas Strömberg, Division of Mathematics, LTU
Date and Time: Wednesday 15:00, May 17, 2017
Place: E246
Title: Singular dynamics for the HamiltonJacobi equation
Abstract: The HamiltonJacobi equation arises, e.g, in optimal control theory and classical mechanics. Solutions of this nonlinear partial differential equation develop singularities in finite time, in general. By definition, singularities are points where the viscosity solution in study fails to be differentiable. The singularities are known to propagate forward in time, at least in some finite time interval, along curves that are generalized characteristics in a specific sense. The propagation is governed by differential inclusions. In the talk I will present some known results about the spreading of singularities along generalized characteristics. An open problem is the following: once it starts, does the propagation of singularities always continue indefinitely or can it halt at some moment of time?
The slides of the talk.
The Schedule of the Current Seminars are posted
HERE
Back to the Seminar Series Main Page.