# MAM Seminars Autumn term 2013

Higher seminar in the subject Mathematics/Applied Mathematics, Autumn term 2013.

School of Education, Culture and Communication (UKK), Mälardalen University.

Autumn term 2013 (HT 2013)

**Program for MAM seminar. Autumn term 2013**

*Wednesdays** afternoon is the normal time for MTM seminars with deviations when necessary. The program is always provisional. The information about each specific talk at MTM seminar becomes final the day before. Suggestions for talks at MTM seminar are very welcome.*

**September 4, 2013, Wednesday, 14.00-15.00**

**Location: **U2-158, Västerås, Mälardalen University

**Speaker: **Bengt Aspvall, Blekinge Tekniska Högskola

**Contact at MDH:** Kimmo Eriksson, Division of Applied Mathematics, UKK

__Title__

**Sorting algorithms as special cases of a priority queue sort**

__Abstract __

We revisit the main sorting algorithms in a novel way. Our approach offers a review and exercise after the algorithms have been taught to students. It is done in a way that emphasizes relationships between the sorting algorithms, and shows how considering abstraction and extreme cases can lead to the generation of new algorithms. A number of authors (including textbook authors) have noted particular relationships between algorithms, such as an uneven split in merge sort being equivalent to insertion sort. We use a flexible priority queue, the d-heap, to derive three common sorting algorithms. We combine this with using a BST as a priority queue, plus prior observations in the literature, to show strong relationships between the main sorting algorithms that appear in textbooks. Using this approach students are able to revisit a number of algorithms and data structures and explore elegant relationships between them. This approach can also lead to exercises and exam questions that go beyond desk-checking to evaluate students’ understanding of these algorithms. (based on Bell & Aspvall, SIGCSE 2011)

**September 18, 2013, Wednesday, 15.30-16.30**

**Location: ** U3-083 (Hilbert rum UKK), Västerås, Mälardalen University

**Speaker: **Johan Richter, Center of Mathematical Sciences, Division of Mathematics and Numerical Analysis, Faculty of Engineering (LTH), Lund University

**Contact at MDH: **Sergei Silvestrov, Division of Applied Mathematics, UKK

__Title __

**Associativity of Ore extensions**

__Abstract __

Ore extensions are a non-commutative analogue of polynomial rings. In this talk I will review a combinatorial definition of Ore extensions. To verify that this definition gives an associative ring is slightly tricky. I will discuss how to prove this, focusing on a recent proof by Patrik Nystedt and myself. No previous knowledge of Ore extensions will be required.

**September 20, 2013, Friday, 15.15-16.30 (Obs! not Wednesday)**

** Location: **U3-104 (Turing rum UKK), Västerås, Mälardalen University

**Speakers (3 PhD students, two 30 min talks + discussion): **

Talk 1. Betuel Canhanga, Mälardalen University and Maputo EMU

Talk 2. Carolyne Adhiambo Ogutu, University of Nairobi and Mälardalen University;

Karl Lundengård, Division of Applied Mathematics, Mälardalen University

** Contact at MDH: **sergei.silvestrov@mdh.se, karl.lundengard@mdh.se

** Talk 1 **(Betuel Canhanga)

__Title__

**Black-Scholes and Black-Scholes like equations in Financial Engineering. **

__Abstract __

Black Scholes equation and other Black-Scholes like equations and models play important role for various mathematical methods and approaches to complex problems in Financial Engineering. In this seminar I will give an introductory review of several classes of such Black-Scholes like equations and their interconnections and appearance in Financial Engineering models.

** Talk 2 **(Carolyne Ogutu, Karl Lundengård)

__Title__

**Asian options, jump diffusion processes on a lattice and Vandermonde matrices**

__Abstract __

Jump diffusion processes can be used to model the value of options in a way that can be less biased than the Black-Scholes pricing model. One method of pricing options that involve these kinds of processes are lattice pricing algorithms. When describing the lattice pricing algorithm using matrices the well-known Vandermonde matrices appear. Applications of the inverse and other properties of these and related matrices will be presented within this context.

**October 9, 2013, Wednesday, 16.00-17.00**

**Location: **U3-083 (Hilbert rum UKK), Västerås, Mälardalen University

**Speaker: **Linus Carlsson, Division of Applied Mathematics, Mälardalen University

**Contact at MDH:** linus.carlsson@mdh.se

__Title __

**A mathematical approach for ecological systems**

__Abstract __

When studying ecological systems in nature, one has to decide what species to study and properties which are important to monitor. In the easiest setting one could predict for the amount of individuals of a certain species, knowing the total population today, treat all individuals as equal, with the property that the net growth is proportional to the number of individuals, this leads the an exponential solution. While this approach is easy it has a lot of obvious flaws.

Another way would be to try and monitor each individual separately and specify different properties for different types of individuals. For example, an ecological system could involve the population of trees in a forest or the population of different fishes in a lake. In these systems properties such as the type, age, size and competition for resources may be important. In this seminar we will look at a physiological structured population model called the Escalator boxcar train. The goal of this presentation will be to gather the important equations connecting the ecology to math and understand a mathematical approach to find solutions to such equations.

**October 16, 2013, Wednesday, 15.30-16.30**

**Location:** U3-083 (Hilbert rum UKK), Västerås, Mälardalen University

**Speaker:** Johan Richter, Center of Mathematical Sciences, Division of Mathematics and Numerical Analysis, Faculty of Engineering (LTH), Lund University

** Contact at MDH: **Sergei Silvestrov, Division of Applied Mathematics, UKK

__Title __

**A brief introduction to the Gelfand-Kirillov dimension**

__Abstract __

The purpose of this talk is to briefly explain the Gelfand-Kirillov dimension, an important way to measure the "size" of algebras. I will explain what the Gelfand-Kirillov dimension is and show how to compute it for certain important algebras, such as the Weyl algebra. I will also mention some results that illustrate why the Gelfand-Kirillov dimension is important.

**October 24, 2013, Thursday, 15.30-16.30 (Obs! not Wednesday)**

**Location: **Västerås, Mälardalen University

**Speaker: **Milica P. Rančić**, **Department of Theoretical Electrical Engineering, University of Niš and Division of Applied Mathematics, Mälardalen University

**Contact at MDH:** Sergei Silvestrov, Division of Applied Mathematics, UKK

__Title __

**Wire antenna structures in presence of semi-conducting ground: from image theory to nasty Sommerfeld's integrals**

__Abstract __

For a variety of research fields (surface wave propagation analysis, oceanography, geological mapping, submarine communications and detection, lightning discharge modelling and lightning protection) it is of great importance to, as accurately as possible, foresee effects that natural circumstances would have on propagation of radio waves. Finite specific conductivity and permittivity of the ground are one of the parameters that have an especially considerable influence on the characteristics of antenna structures, primarily noticeable in their near field. Since many antennas and antenna systems, depending on their purpose, are installed in close proximity to the ground or even directly on it, the impact of the lossy ground on antenna characteristics cannot be ignored. This means that the ground cannot be considered a perfectly conducting one, and therefore more stringent analysis is required. This results in a need to address a group of improper, so-called Sommerfeld's integrals that mathematically describe the influence of the finite conductivity of the soil on the electromagnetic field of the analyzed antenna structure. In this presentation, a new method for mathematical modelling of this group of integrals, which don’t have a closed-form solution, is going to be presented. Also, this model’s applicability to analysis of both the near and the far field of different antenna structures will be explored.

**SHORT BIO**

Milica P. Rančić was born in Niš, Serbia, in 1977. She received the dipl. eng. degree in Telecommunications from the University of Niš, Serbia in 2002, and finished the post-graduate studies and the PhD studies at the same University in 2008. and 2012, respectively. She holds the degree of Doctor of science - electrical engineering and computer science. In the period of 2003-2004 she has been employed as a teaching assistant at the Dept. of Metrology, University of Niš, Serbia. Since 2004, she has been working as a teaching assistant at the Dept. of Theoretical Electrical Eng. at the same University. Her research areas include Electromagnetics (Antennas and propagation, Computational Electromagnetics, EMC) and Illumination (Daylighting, Photometry, Road & Tunnel illumination).

Contact info:

e-mail: __milica.rancic@elfak.ni.ac.rs__

web: __http://www.milicarancic.com/__

**November 6, 2013, Wednesday, 15.30-16.30**

**Location: **U2-158, Västerås, Mälardalen University

**Speaker: **Linus Carlsson, Division of Applied Mathematics, Mälardalen University

**Contact at MDH:** linus.carlsson@mdh.se

__Title __

Geometry of Domains

__Abstract __

When studying mathematical problems in higher dimensions, the domain of definition plays an important role, for example when integrating a function of two real variables, it is much easier to do this if the boundary of the domain of definition is a square or perhaps a circle (using polar coordinates). But in general the domains of definitions need not to be this nice. In this seminar we will talk a bit about properties of convex domains and their counterpart pseudoconvex domains which arise when dealing with holomorphic functions of several complex variables.

**November 12, 2013, Tuesday, 15.30-16.30 (Obs! not Wednesday)**

**OBS! The talk is cancelled since speaker informed being sick. This talk will be given at later occasion. **

**Location: **U2-145, Västerås, Mälardalen University

**Speaker: **Lars Hellström, Division of Applied Mathematics, Mälardalen University

**Contact at MDH: **lars.hellstrom@mdh.se

__Title __

Rewriting and the Diamond Lemma

__Abstract __

An important and recurring activity in many branches of mathematics and related sciences is the step-by-step transformation of one symbolic expression to another according to given rules. This is usually taught more as a craft than as a science, making it a matter of individual skill to find a sequence of steps that reach the wanted goal, but there is no fundamental reason why it cannot be studied systematically. Indeed, that idea has been executed many times over the years, often with a particular problem domain in mind, which has resulted in a sometimes confusing proliferation of terminology where fairly simple and general ideas run a significant risk of drowning in technicalities.

This talk aims to give an overview of and introduction to the field, which sits on the boundary between mathematics and computer science. Topics I (time permitting) hope to address are equational reasoning, rewrite systems, confluence and termination, the Diamond Lemma, Gröbner bases, words/terms/graphs/networks, universal algebra, linear structure, normal forms, and the word problem (not necessarily in that order). Familiarity with abstract algebra is not necessary.

**November 20, 2013, Wednesday, 13.15-14.15 (Obs! time)**

**Location: **U3-083 (Hilbert room, UKK), Västerås, Mälardalen University

**Speaker: **Daniel Andrén, Division of Applied Mathematics, Mälardalen University

**Contact at MDH: **daniel.andren@mdh.se

__Title __

**Gaussian elimination is not optimal**

__Abstract __

In the talk I will discuss problems concerning Gaussian elimination and matrix multiplication in finite fields.

This is joint work with Klas Markström, Umeå university and Lars Hellström, Mälardalen University.

**December 4, 2013, Wednesday, 13.15-14.15 (Obs! time)**

**Location: **U3-083,Västerås, Mälardalen University

**Speaker: **Christopher Engström, Division of Applied Mathematics, Mälardalen University

**Contact at MDH: **christopher.engstrom@mdh.se

__Title __

Page rank for evolving link structures

__Abstract __

In this talk, we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines as for example Google. This focus of the talk will be on understanding of the behaviour of PageRank as the link system dynamically evolves. We will look at PageRank as the solution of a linear system of equations and consider both the ordinary normalized version of PageRank as well as the non-normalized version found by solving the linear system. We will see that it’s possible to find explicit formulas for the PageRank in some simple link (graph) structures and using these formula’s take a more in depth look at the behaviour of the ranking as the system changes. Some open problems will be indicated. This talk is based on the recent article by Christopher Engström and Sergei Silvestrov.

**December 11, 2013, Wednesday, 15.30-16.30**

**Location: **Västerås, Mälardalen University

**Speaker: **Erik Darpö, Division of Applied Mathematics, Mälardalen University

**Contact at MDH: **__erik.darpo@mdh.se__

__Title __

Generalizations of complex and real numbers and non-associativity

__Abstract__

In this talk I shall give an introductory review of some generalisations of the fields of complex and real numbers. Several interesting algebraic structures, such as the quaternion and octonion algebras, arise in this way. While most of these new structures do not satisfy the commutative and associative laws, some of them still have important applications in geometry and physics, as well as computer graphics and coding theory.

In my talk I will introduce some of the more classical structures, along with some classification results. If time permits, I will also present some more recent developments and open research problems in the field.