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 post at the Mathematics Division of the Science Institute, University of Iceland. The successful candidate is expected to conduct research in mathematics, pure or applied, or mathematical physics.

See:
https://euraxess.ec.europa.eu/jobs/658209
https://www.stjornarradid.is/efst-a-baugi/laus-storf-a-starfatorgi/auglysing/?id=25274

Math colloquium

Speaker: Gestur Ólafsson, Louisiana State University

Title: Atomic decomposition of Bergman spaces on Hermitian Symmetric Spaces

Room: Zoom link will be sent by email
Time: Tuesday 16^th February, 16:00hrs

Abstract:

Hermitian symmetric spaces, bounded or unbounded, and spaces of functions or distributions on those spaces show up naturally in com- plex analysis, Lie theory, functional analysis and several other parts of mathematics. In this talk we will discuss some resent work on dis- cretization/atomic decomposition of Bergman spaces on those domains and their unbounded realization.

The story goes back to the work of Coifman and Rochberg in the 1980’s where they provided atomic decompositions for Bergman spaces on (the unbounded realization of) bounded symmetric domains as well as on the unit ball. Their atoms were build from the Bergman kernel. One of the shortcomings of their work was that their results did not readily transfer to the bounded realization of the domain except in the case of the unit ball.

By applying representation/coorbit theory we obtain a large family of new atoms, including those of Coifman and Rochberg, for Bergman spaces on bounded symmetric domains. Our approach also allows us to describe the relation between atoms for the bounded and unbounded realizations of the domain thus solving one of the issues raised by Coif- man and Rochberg. If time allows then we will list some open questions for domains of rank higher than one.

This year, the Nordic Network for Diversity in Physics is holding its annual meeting as a one-day online event on 29th January, from 9.00 to 15.30.
Attendance is free of charge, but registration is mandatory to get access to the Zoom link and the recorded videos.

Highlights of the event:

Angela Saini’s talk. Angela Saini is a British journalist whose highly-regarded books and broadcasts on important issues around representation and discrimination in science and society have received widespread praise. She will speak on “Racism in science and society”. This is a topic that Angela researched extensively for her book Superior: The Return of Race Science.

Round-table: How to work against harassment – A discussion from a Nordic perspective. There will be reports on harassment reporting practices in academia from all the Nordic countries, and a round table discussion. Jóhanna Ella Jónsdóttir will be be the speaker for Iceland. Professor Helen Dannetun from Linköping University will moderate the discussion on “How to work against harassment – A discussion from a Nordic perspective”.

For more details about the conference, program, and the NORNDiP network visit: https://www.norndip.net
Registration at this link: https://indico.cern.ch/event/979804/registrations/66795/

Math colloquium

Speaker: Anders Karl Claesson, University of Iceland

Title: On the problem of Hertzsprung and similar problems

Room: Via Zoom. Link to be sent.
Time: Tuesday January 19th, 10:00 hrs

Abstract:

Drawing on a problem posed by Hertzsprung in 1887 (sometimes called the n-kings problem), we say that a permutation w contains the Hertzsprung pattern u if there is factor w(d+1)w(d+2)…w(d+k) of w such that w(d+1)-u(1) = … = w(d+k)-u(k).  Using a combination of the Goulden-Jackson cluster method (which we explain) and the transfer-matrix method we determine the joint distribution of occurrences of any set of (incomparable) Hertzsprung patterns, thus substantially generalizing earlier results by Jackson et al. on the distribution of ascending and descending runs in permutations.  We apply our results to the problem of counting permutations up to pattern-replacement equivalences, and using pattern-rewriting systems—a new formalism similar to the much studied string-rewriting systems—we solve a couple of open problems raised by Linton et al. in 2012.

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Room: Via Zoom. Link to be sent.
Time: Friday, December 11, at 10:00.

Doctoral student: Daniel Amankwah

Project title: Scaling limits of random, face-weighted, tree like planar maps.

Project description: The doctoral project lies in the scope of random planar maps. We investigate scaling limits of various classes of discrete planar maps which are by construction “tree-like”. These include Halin maps, outerplanar maps, series-parallel maps and more. The Brownian Continuum Random tree (CRT), introduced by David Aldous has been known to be the limit of various different discrete models of planar maps uniformly sampled. We focus on the case when each face in the maps is assigned a heavy tailed weight so that a typical face is in the domain of attraction of a stable law. It is known that for several such models for treelike graphs the scaling limits are the so-called stable looptrees. We aim to understand how generically this happens. For this reason we will consider classes of maps which have not been studied in this scope in the literature. Examples include Halin maps, Series-Parallel maps and Maps of bounded tree-width.

Supervisor: Sigurður Örn Stefánsson

Math colloquium

Speakers: Elisa Domínguez-Hüttinger, Universidad Nacional Autónoma de México

Title: A “triple-switch” hybrid mathematical model of epidermal homeostasis.

Room:  Via Zoom. Link to be sent.
Time: Friday 13^th  November, 14:00

Abstract:

The epidermis is the outermost layer of the skin. It is a stratified epithelium, constituted by layers of epithelial cells (keratinocytes) with increasing levels of differentiation. The basal layer is formed by undifferentiated cells with proliferative capacity, while the most external layer, termed skin barrier, is formed by terminally differentiated cells that are embedded in a lipid matrix. This skin barrier hinders the invasion of pathogens and other aggressors, protecting the organism from environmental disturbances. Transient environmental perturbations that increase the pathogen load or damage the skin barrier can trigger both immune and tissue remodelling responses, resulting in increased pathogen elimination but also affecting its infiltration rate. Under healthy conditions, this complex feedback control structure effectively counteracts environmental aggressors.  However, perturbations by genetic and environmental factors can lead to the loss of homeostasis and the onset and progression of complex epidermal tissue diseases including atopic dermatitis, psoriasis and skin carcinomas. Characterizing the responses of the epidermis to these perturbations is pivotal to uncover pathogenic mechanisms and improve strategies for diagnosis, prevention and treatment of these diseases.  However, this task is difficult to achieve from a purely experimental or clinical perspective, because these perturbations: (1) Often lead to synergic and non-linear responses that are hard to predict experimentally; (2) Can affect several regulatory processes that operate at different time scales; (3) May result in symptoms that are clinically subtle; and (4) Can affect disease progression  in a history-dependent manner. Here we propose a triple-switch mathematical model that couples a bistable motifs describing the activation of innate and adaptive immune responses as well as the differentiation of skin cells with the dynamically changing tissue level properties. We will show how mathematical analysis of this hybrid model has allowed us to: (1) Characterize the effects of genetic and environmental perturbations on epithelial homeostasis; (2) Identify risk factors that increase the vulnerability to environmental aggressors, and (3) Design new strategies for early detection and prevention of complex epidermal diseases.

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PhD defense, Friday November 6 at 14.00, in Veröld, room 023

Entanglement in Quantum Lifshitz Theories

The defense will be streamed

Live stream:https://www.youtube.com/user/HIvarp/live

Opponents: 
Dr. Stefan Vandoren, Professor at Utrecht University, The Netherlands.
Dr. Jens Hjörleifur Bárðarson, Associate Professor at KTH Royal Institute of Technology, Sweden

Advisor: Dr. Valentina Giangreco Puletti, Professor at the Faculty of Physical Sciences, University of Iceland 

Doctoral committee: 

Dr. Lárus Thorlacius, Professor at the Faculty of Physical Sciences, University of Iceland
Dr. Þórður Jónsson, Professor at the Faculty of Physical Sciences, University of Iceland
Dr. Erik Tonni, Associate Professor at SISSA, Italy.

Chair of Ceremony: Dr. Einar Örn Sveinbjörnsson, Professor and the Head of the Faculty of Physical Sciences, University of Iceland

Abstract:
In recent years, the study of entanglement properties of quantum field theories has led to deep insights in fields as diverse as quantum gravity and condensed matter physics. Originating as effective field theories for certain quantum dimer models, the Quantum Lifshitz Model (QLM) and its generalizations are bosonic quantum field theories with anisotropic scaling symmetry between space and time. Being closely related to conformal field theories, they provide a fruitful playground, where diverse entanglement calculations can be performed analytically.

In this thesis, we concentrate on two entanglement measures, the entanglement entropy and logarithmic negativity. Motivated to extract subleading universal behavior, we perform analytic calculations in two and higher even dimensions. In order to make the calculations tractable, we put the QLM on compact manifolds, such as spheres and tori, where the spectrum of a certain operator appearing in the ground state of the theory is explicitly known. Mostly by means of the replica method, we then find analytic expressions for the finite subleading terms of the entanglement entropy and logarithmic negativity of the ground state, as well as the entanglement entropy of the excited states of the QLM. In the case of the ground state entanglement entropy, we provide analytic expressions for the sub-leading terms as functions of the dimension and the dynamical critical exponent. For the excited states we provide analytic formulae of the sub-leading coefficients as functions of the excitation numbers.

Math Phys colloquium

Speakers: Watse Sybesma, University of Iceland

Title: The formation of black holes and the supermassive object at the center of our galaxy.

Room:  Via Zoom. Link to be sent.
Time: Friday 30^th October, 12:00am

Abstract:

This year’s Nobel Prize in Physics is all about black holes with a narrative that covers both the theoretical and observational point of view. On the theoretical side: Roger Penrose, who showed that the theory of general relativity allows the formation of black holes. On the observational side: Reinhard Genzel and Andrea Ghez, who provided evidence that an invisible and extremely heavy object governs the orbits of stars at the center of our galaxy. A supermassive black hole is the only currently known explanation. In this talk an introductory overview is provided. Watse Sybesma (born in 1989 in the Netherlands) obtained his PhD degree at the university of Utrecht in the Netherlands, where he worked on black holes related topics. Afterwards, he obtained a grant from the Icelandic research fund (Rannís) to further pursue this line of research at the mathematical physics group of the university of Iceland as a postdoctoral researcher.