# MAM Seminars Spring term 2015

Higher seminars in the subject Mathematics/Applied Mathematics, Spring term 2015.

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

**Program for Mathematics and Applied Mathematics seminar. **

**Spring term 2015**

*Wednesdays afternoon is the normal time for MAM seminars with deviations when necessary. The program is always provisional. The information about each specific talk at MAM seminar becomes final the day before. Suggestions for talks at MAM seminar are very welcome to Prof. Sergei Silvestrov sergei.silvestrov@mdh.se.*

**February 18, 2015, Wednesday, 15.30-16.30**

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

Speakers: Waldemar Kocjan, Jeppesen (Boeing Company), Göteborg

(Seminar about PhD thesis)

__Title__

Mathematical models for cardinality constraints and container loading

__Abstract __

This presentation concerns mathematical models for two types of problems: cardinality constraints and flexible packing.

Cardinality constraints are described in terms of variables which takes their values as subsets of some value sets.

They constraint cardinality of set assigned to each variable to be in a specific interval and are frequently used in solving different types of assignment problems in Constraint Programming. The container loading problem aims at optimal packing of boxes of different dimensions into available containers with respect to some objective function.

The problem arises in areas like distribution and logistics. This work is motivated by a real-life problem and consider such aspects as container utilization, packing order and different aspects of physical stability of loading.

**February 25, 2015, Wednesday, 15.30-16.30**

Location: U2-158, Västerås, Mälardalen University

Speaker: Prof. Dmitrii Silvestrov, Department of Mathematics, Stockholm University, Sweden

__Title __

American-Type Options. Stochastic Approximation Methods

__Abstract __

The lecture presents the second volume of the comprehensive two-volume monograph. The first volume [1] was devoted to stochastic approximation methods for American-type options with general pay-off functions, for **discrete** time modulated Markov log-price processes. The second volume [2] gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions, for **continuous** time Markov log-price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic time-space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov log-price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov log-price processes and general pay-off functions, which can depend not only on log-price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also presents results of experimental studies and contains an extended bibliography of works in the area.

References

[1] Silvestrov, D.S. American-Type Options. Stochastic Approximation Methods. Vol. 1. De Gruyter Studies in Mathematics, 56, De Gruyter, Berlin, 2014, x+509 pp.

Flyer of the book:

[2] Silvestrov, D.S. American-Type Options. Stochastic Approximation Methods. Vol. 2. De Gruyter Studies in Mathematics, 57, De Gruyter, Berlin, 2015, xi+558 pp.

Flyer of the book:

**March 11, 2015, Wednesday, 15.30-16.30**

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

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

__Title__

The Perron-Frobenius theorem

__Abstract __

In this talk, I will give a proof of the Perron-Frobenius theorem. The theorem states that every non-negative irreducible matrix has a unique positive eigenvector, the eigenvalue of which is positive, and gives information on the spectrum of the matrix in terms of this eigenvalue. The presentation is based on a proof given by Wielandt in 1950.

**March 18, 2015, Wednesday, 15.30-16.30**

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

Speaker: Prof. Osamu Iyama, Nagoya University, Japan

(Visiting the Representation Theory Program (Spring 2015) at Institute Mittag-Leffler in Stockholm )

__Title __

Higher representation-finite algebras

__Abstract __

In representation theory of finite dimensional algebras, Auslander correspondence plays an important role. This gives a bijection between two classes of algebras. One is representation-finite algebras, that is, algebras which have only finitely many indecomposable modules, and the other is a certain class of algebras with global dimension 2, called Auslander algebras. I will discuss a higher dimensional analog of Auslander correspondence, and show basic examples of higher representation-finite algebras.

**March 25, 2015, Wednesday, 15.30-16.30**

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

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

__Title __

Graph partitioning and a component wise PageRank algorithm

__Abstract __

In this lecture we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known 'strongly connected components' as well as another type of component we call 'connected acyclic components'. We will give an algorithm of how such a partitioning can be found, as well as showing that the partitioning itself is unique and that the underlying graph can be represented as a directed acyclic graph (similar to a pure strongly connected component partitioning).

In the second part we will show how such a partitioning of a graph can be used to calculate PageRank of a graph effectively by calculating PageRank for different components in parallell as well as using different kinds of PageRank algorithms for different types of components. Results of the algorithm and comparison with a more basic approach will be shown on a collection of 4 large graphs.

**April 1, 2015, Wednesday, 15.30-16.30**

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

Speaker: Talat Nazir, COMSAT, Pakistan

__Title__

Common fixed point theorem for commuting maps

__Abstract__

In this talk, I will give some proofs of common fixed point results for various types of commuting maps satisfying generalized contractive conditions. I also obtain some coupled coincidence points and coupled fixed points of single-valued mappings. These results extend and improve various recent results in the existing literature.

**April 22, 2015, Wednesday, 15.30-16.30**

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

Speaker: Thomas Ernst, Department of Mathematics, Uppsala University

__Title:__

Generalized Vandermonde determinants

__Abstract:__

We present a new expression for the generalized Vandermonde determinant (from now on abbreviated as GVD). First we prove an expression for a GVD with λ_{1}=2 in terms of the elementary symmetric polynomials e_{n}. Then we prove an expression for an arbitrary GVD by induction. We also obtain an equivalence relation on the set of all generalized Vandermonde determinants.

**April 29, 2015, Wednesday, 15.30-16.30**

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

Speaker: Thomas Ernst, Department of Mathematics, Uppsala University

__Title:__

__Abstract:__

_{q}(n) as well as general q-spherical coordinates will be given. We show some Mathematica pictures of the most important objects.

**May 6, 2015, Wednesday, 13.30-16.30**

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

Speaker: Åke Brännström, Department of Mathematics and Mathematical Statistics, Umeå University

__Title:__

An evolutionary theory of food-web intervality.

(Presentation of work with Linus Carlsson, Ulf Dieckmann and Axel Rossberg).

__Abstract: __

Food webs represent trophic (feeding/foraging) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. A common interpretation of food-web intervality is that trophic interactions between two species can be predicted based on a single trait value assigned to each species, for example maximum body size. In ecological terms, one could say that the trophic niche space is close to one-dimensional. In this talk, I argue that food-web intervality emerges as a consequence of phylogenetic descent also in a high-dimensional niche space. The argument is based on neutral models of food-web evolution.

**May 11, 2015, Monday, 15.30-16.30 (Obs! not usual day and time)**

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

Speaker:

Prof. Vyacheslav Futorny, Department of Mathematics, University of Sao Paulo, Brasilia

__Title:__

Gelfand-Tsetlin representations of algebras

__Abstract: __

We will discuss the theory of Gelfand-Tsetlin modules for different classes of Lie and associative algebras. In particular, we will consider the cases of the Lie algebra gl(n) and the Weyl algebras. Our approach is based on the theory of Galois algebras which are the invariant subalgebras in certain skew group rings. We also will show how to construct new representations of Affine Kac-Moody algebras from representations of Weyl algebras.

**May 20, 2015, Wednesday, 15.30-16.30**

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

Speaker:

Gustavo Jasso, Max Planck Institute for Mathematics, Bonn, Germany

__Title:__

Cluster algebras

__Abstract: __

Cluster algebras are a class of commutative rings with unit equipped with a distinguished set of generators grouped in overlapping sets of the same finite cardinality which are called clusters. One can pass from one cluster to the other via a combinatorial operation called mutation. Since their introduction by Fomin-Zelevinsky in 2001, cluster algebras have appeared in a variety of contexts, from Lie theory to mathematical physics, passing through the representation theory of finite dimensional algebras. In this talk, I will give an elementary introduction to cluster algebras focusing on explaining their combinatorial nature.

**June 10, 2015, Wednesday, 15.30-16.30**

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

Speaker:

Kimmo Eriksson, Division of Applied Mathematics, Mälardalen University

__Title:__

Lord’s Paradox in a Continuous Setting and a Regression Artifact in Numerical Cognition Research

__Abstract: __

This talk should be of interest to, and accessible for, researchers of mathematics education as well as mathematicians. I will discuss Lord's paradox, a confusing phenomenon that arises in statistical analysis of change in test scores between a pre-test and a post-test. The paradox is that very different results can be obtained depending on whether the pre-test score is included as a covariate in the analysis. I will discuss conditions under which it is inappropriate to include the covariate in the analysis. I will illustrate the problem by discussing a paper about children's mathematical development by Booth and Siegler. This paper is considered to important in the literature on mathematical development (e.g., it has more than 250 citations). However, reanalysis of their data shows that the finding of the paper is simply wrong; it is just an artifact of inappropriately including the pre-test as a covariate. This is joint work with Olle Häggström.

**June 17, 2015, Wednesday, 15.30-16.30**

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

Speaker:

__Title:__

__Abstract: __