Upper Secondary Teaching

**Development of projects on differentiation with emphasis on understanding and discovery**

**Advisors: ** Benedikt Steinar Magnússon and Bjarnheiður Kristinsdóttir

**Examiner:** Kristín Bjarnadóttir, Professor Emerita

**Abstract**

Mathematics in upper secondary schools is a challenging subject for many students, and many even become convinced they are unable to learn the subject. In order to counter such beliefs, it is important that teachers refuse to accept that sort of thinking. There are ways to help students overcome their pessimism and, according

to research, one of the best ways to help them is to guide them towards discovering their own connections between different elements of mathematics and using these connections to better their understanding. The objective with this thesis is, therefore, to create and develop projects for students in upper secondary schools

with this idea in mind. The projects focus on differentiation because the author is interested in that field and because studies conducted among upper secondary school graduates have shown they struggle most with differentiation and integration of all the mathematical fields. Continue reading 'Sóley Benediktsdóttir'»

Applications are invited for a postdoctoral position at the University of Iceland financed by The Icelandic Research Fund. The research project is called:

“Scaling limits of random enriched trees”

and is in the field of probabilistic combinatorics. The project includes studying scaling limits of random graphs, statistical mechanical models on random planar maps and related subjects. The application deadline is October 15, 2019, however applications will continue to be accepted until the position is filled.

We are looking for a candidate who has completed a PhD within the last 5 years or is close to defending a PhD thesis. Her/his specialization and interests should be in this area.

Applications should be sent directly by e-mail to sigurdur[at]hi.is, including a CV, list of publications or an abstract of a planned PhD thesis, a research statement and names and e-mail addresses of two referees, who have agreed to provide recommendation.

The appointment is for two years from the 1st of Novenber 2019, or otherwise according to agreement All applications will be answered.

For further information please contact:

Prof. Sigurdur Orn Stefansson (e-mail: sigurdur[at]hi.is)

### Speaker: Carolina Canales Gonzalez, Pontificia Universidad Católica de Chile

### Title: Looking for a complex Poincaré-Bendixson theorem

Location: V-258, VR-II

Time: Thursday February 28 at 11.40 am

### Abstract:

The goal of this talk is to introduce the study of holomorphic foliations.

First, we will recall some things about differential equations on $\mathbb{R}^2$, like the Poincaré-Bendixson theorem and Hilbert’s 16th problem and then we will pass to the complex context where we will introduce holomorphic foliations.

The idea is to talk about the problem of the exceptional minimal set, who is an analog of Poincaré-Bendixson theorem in this new context, and about the developments in complex geometry, analysis and dynamics related with the study of this problem.

### Speaker: Carlos Argaez Garcia, UI

### Title: Numerical methods for dynamic systems: Analysis of stability

Location: V-258, VR-II

Time: Thursday February 21 at kl. 11.40

### Abstract:

Dynamic systems describe the evolution over time of quantities governed by

differential equations. Therefore they are a powerful descriptive tool of

phenomena originated in applied disciplines.

A complete Lyapunov function describes the dynamic behavior of such

systems without requiring the explicit solution of the differential

equations. However, these have the disadvantage of being difficult to

obtain.

The algorithms proposed here, reduce the effort to obtain such functions

and even more, are able to isolate the regions whose dynamics have a

periodic behavior.

Throughout this talk, simple examples of applications in both two- and

three-dimensional systems will be given.

Math Phys/Phys seminar

### Speaker: Jens H. Bárðarson, KTH Stockholm

### Title: On the chiral anomaly in Weyl semimetals

Location: VR-II 158

Time: Tuesday December 4, at 13.30

### Abstract:

I will give an introduction to the physics of Weyl semimetals focussing on Fermi arcs and chiral anomaly. I will then discuss some transport properties of Weyl semimetals including strongly angular-dependent magnetotransport in the presence of long range disorder, and the difference between the longitudinal conductance in the presence of magnetic field and chiral pseudo-magnetic field. The latter points in opposite direction for opposite chiralities and can be induced, for example, by strain. This leads to a discussion of pseudo-landau levels and their connection with Fermi arcs and covariant and consistent chiral anomaly. I will also mention a new axial torsional contribution to the axial anomaly.