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 CAD-model. 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: Least-Squares Fitting of Model Parameters to Experimental Data
  
  Abstract: We will consider computational methods for fitting parameters to experimental data using the least-squares 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 3D-positions 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 Monte-Carlo fashion we also examine convergence and find both scenario configurations and their respective probability. We have used this to examine the comet 21P/Giacobini-Zinner 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 Ill-Posed 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 ill-posed 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 space-time 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: p-Harmonic Functions Near Low-Dimensional Hyperplanes
  
  Abstract: We first give some basics about the p-Laplace equation and p-harmonic functions including some applications. We then prove growth estimates of positive p-harmonic functions in n-dimensional space vanishing near an m-dimensional hyperplane, 0 < m < n-1. I.e. we consider "thin boundaries" of dimensions less than n-1. Our results imply the so called boundary Harnack's inequality, some estimates of p-harmonic measure and some results of Phragmen-Lindelöf type for p-subharmonic functions. We will briefly sketch the proofs of which the core is constructions of certain sub- and supersolutions to the p-Laplace 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 long-term 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 short-lived technical equipment, it is often more natural and convenient to place the time horizon at infinity than to specify a finite horizon. The infinite-horizon 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 non-linear 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 Hamilton-Jacobi equation
  
  Abstract: The Hamilton-Jacobi 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