# Program for MAM research student seminar

MAM research student seminar (little MAM seminar) is a research student seminar in Mathematics and Applied Mathematics at Mälardalen University organized by the research environment MAM for research students in the subject. The main organizers are the research students in MAM.

**Organizer of MAM research student seminar is**

**Talks listed in reverse chronological order, that is future talks first**

**Duration of all talks is normally up to 30 minutes followed by questions and informal discussions **

**2019**

**January 16, 2019, Wednesday, 15:30**

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

Speaker: Per Bäck, MAM research environment, Division of Applied Mathematics, UKK, MDH

__Title__: Star semirings, formal languages, and graphs

__Abstract:__ In this talk, I will give a short introduction to star semirings, formal languages, and directed graphs describing so-called finite automata, relating the areas of algebra, computer science, and graph theory to one another.

This is based on a project conducted in the course *[MAA600] Graph theory, networks, and applications* in the autumn of 2018.

Lecture notes:

**Past doctoral students seminars in Mathematics and Applied Mathematics:**

**----------- 2017 -----------------------------------------------------**

**September 20, 2017, Wednesday, 15.30**

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

Speaker: Karl Lundengård, MAM research environment, Division of Applied Mathematics, UKK, MDH

__Title:__

Computation of B-splines and blossoming

__Abstract:__

Splines are parametric curves based on piecewise polynomials that were first introduced in the 1940s and developed more extensively in the 1960s. They are a very powerful tool for representing curves and surfaces, especially in geometric modelling since they have several properties that makes it easy to specify and modify a shape in an intuitive way.

In order to efficiently use splines to represent curves and surfaces a suitable base need to be chosen to avoid numerical instabilities, the best known alternative turns out to be the so-called B-splines. Traditionally B-splines are defined using divided differences and their most important properties were proved using this definition. It was quickly discovered that the most efficient and reliable algorithms for computing with B-splines should instead be based on recurrence relations, starting with work by De Casteljau in the 1950s and culminating with work by De Boor in the 1970s. The so-called De Boor algorithm will be described in detail.

**September 27, 2017, Wednesday, 15.30**

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

*Speaker 1 (20 minutes):*

Pitos Biganda, MAM research environment, Division of Applied Mathematics, UKK, MDH

__Title:__

Comparison-traditional PageRank, lazy PageRank and random walk with backstep for a line of nodes connected with complete graphs

__Abstract:__

PageRank was initially defined by S. Brin and L. Page for the purpose of measuring the importance of web pages (nodes) based on the structure of links between them. Lazy PageRank is used in clustering, where as random walk with backstep is similar to traditional PageRank except that there is an introduction of one more parameter to account for the back steps of a random walk on a graph. In this article we will examine how the PageRank changes when a complete graph is connected to a line of nodes whose links between the nodes are in one direction. We will consider theoretical aspect of PageRank as a random walk on a graph for three variants of PageRank: traditional PageRank, lazy PageRank and random walk with backstep for the purpose of comparing them. We will develop explicit formulas for the PageRank in each consideration, and use them to look at the behaviour of the ranking as the system changes.

*Speaker 2 (20 minutes):*

John Musonda, MAM research environment, Division of Applied Mathematics, UKK, MDH

__Title:__

Reordering formulas and deformed difference operator representations of deformed Lie type commutation relations

__Abstract:__

Multi-parameter deformation of symmetric difference and multiplication operators are shown to fulfill deformed Lie type relations with three generators defining a multi-parametric family of algebras deforming a Lie algebra into more general class of algebras. General reordering formulas, the center and families of commuting elements and subalgebras for this parametric family of algebras are considered in the algebra and in the representing operators. The operators of representation are studied for elements of the center and families of commuting elements and subalgebras. Matrix presentations of the deformed difference operator representation of the deformed commutation relations are studied depending on the parameters. This family of algebras is considered also in context of quasi-hom-Lie algebra quasi-deformations of Lie algebras.

**October 11, 2017, Wednesday, 15.30-16.30**

Location: U3-083 (Hilbert room)

Speaker: The Lanczos algorithm and Sturm–Liouville theory

__Title:__

The Lanczos algorithm and Sturm–Liouville theory

__Abstract:__

The two topics in the title are described, and it is examined whether they could be usefully combined (preliminary studies indicate they can)