Midway evaluation, Daniel Amankwah

Sigurður Örn Stefánsson, nóvember 30, 2020

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

Elisa Domínguez-Hüttinger, Universidad Nacional Autónoma de México

Carlos Argaez Garcia, nóvember 7, 2020

Math colloquium

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

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

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 13.nóvember kl.14:00

Ágrip:

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.

Juan Fernando Angel Ramelli

Valentina Giangreco, nóvember 4, 2020

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.

Watse Sybesma, Háskóli Íslands

Carlos Argaez Garcia, október 27, 2020

Math Phys seminar

Fyrirlesari: Watse Sybesma, Háskóli Íslands

Titill: Myndun svarthola og risamassinn í miðju sólkerfisins.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 30.október kl.12:00

Ágrip:

Nóbelsverðlaunin í eðlisfræði í ár snúast um svarthol, bæði út frá kenningum og rannsóknum. Breski eðlisfræðingurinn Roger Penrose setti fram kenningu sem tengir saman myndun svarthola og almennu afstæðiskenninguna og þýski stjarneðlisfræðingurinn 
Reinhard Genzel og bandaríski stjörnufræðingurinn Andrea Ghez hafa sýnt fram á að ósýnilegur og afar eðlisþungur hlutur stýrir hreyfingu stjarna í miðju sólkerfis okkar og risasvarthol er eina mögulega skýringin. Í fyrirlestrinum verður farið yfir þessar rannsóknir og þær kynntar. Athugið að fyrirlesturinn fer fram á ensku.

Adam Timar, University of Iceland

Carlos Argaez Garcia, október 23, 2020

Math colloquium

Fyrirlesari: Adam Timar, Háskóli Íslands

Titill: Uniform Spanning Forests of infinite graphs.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 30.október kl.10:00

Ágrip:

Consider a spanning tree of a given finite graph, chosen uniformly at random. The so-defined Uniform Spanning Tree (UST) has long been an object of interest, since it is intimately connected to harmonic functions on the graph and random walks.
Given an infinite graph G, such as a cubic lattice, one can take its exhaustion by finite graphs G_n and consider a suitably defined limit of the UST of G_n. The limiting measure is called the Uniform Spanning Forest of G. The resulting random object has had crucial importance in statistical physics on 2 dimensional lattices, but also turned out to be interesting when G is a Cayley graphs of a group. Among other uses, it allows for a simple probabilistic interpretation of an intricate geometric parameter.
The talk will be addressed to a general math audience. We will give a brief overview of the above topics, and present some recent results that are joint work with Gábor Pete.

Lukas Schneiderbauer

Valentina Giangreco, september 24, 2020

PhD defense, Friday September 25 at 14.00, in Veröld, room 023

Semi-Classical Black Hole Holography 

The defense will be streamed: https://www.youtube.com/user/HIvarp/live

Dissertation title: Semi-Classical Black Hole Holography 

Opponents: Dr. Veronika Hubeny, Professor of Physics at UC Davis,USA
Dr. Mukund Rangamany, Professor of Physics at UC Davis, USA

Advisor: Dr. Lárus Thorlacius, Professor at the Faculty of Physical Sciences, University of Iceland

Doctoral committee: Dr. Bo Sundborg, Professor at the Department of Physics at Stockholm University, Sweden
Dr. Valentina Giangreco M. Puletti, Professor at the Faculty of Physical Sciences, University of Iceland
Dr. Þórður Jónsson, Professor at the Faculty of Physical Sciences, University of Iceland

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

Abstract:
This thesis discusses two aspects of semi-classical black holes.
First, a recently improved semi-classical formula for the entanglement entropy of
black hole radiation is examined. This entropy is an indicator of information loss and determines whether black hole evaporation is an information preserving process or destroys quantum information. Assuming information conservation, Page expressed the entanglement entropy as a function of time, which is referred to as the “Page curve.” Using the improved formula for evaporating black hole solutions of a gravitational model introduced by Callan, Giddings, Harvey and Strominger (CGHS) and modified by Russo, Susskind and Thorlacius (RST), we find that the entanglement entropy follows the Page curve and thus is consistent with unitary evolution.
Second, the notion of quantum complexity is explored in the context of black holes. The quantum complexity of a quantum state measures how many “simple operations” are needed to create that state. Susskind conjectured that the quantum complexity of a black hole state corresponds to a certain volume inside the black hole. A modified conjecture equates the quantum complexity with the gravitational action evaluated for a certain region of spacetime which intersects the black hole interior. We test the complexity conjectures for semi-classical black hole solutions in the CGHS/RST model and find that both conjectures yield the expected behavior.

Kristján Jónasson, University of Iceland.

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Kristján Jónasson, University of Iceland.

Titill: Maximum likelihood estimation of multivariate normal parameters when values are missing.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 18.September kl.10:00

Ágrip:

I have been working on a program to estimate the covariance matrix of a multivariate normal distribution in the presence of missing values via maximum likelihood. Many programs offer to do this by computing pairwise covariances (giving a potentially non-positive-definite matrix). There is a package in R (mvnmle) to do the ML-computation, but it is inefficient on several counts. Matlab’s statistical toolbox has a function mvnmle, and its financial toolbox has ecmnmle which are both quite fast, but they lack flexibility, for example to incorporate REML to eliminate bias, to use regularization (when many values are missing), or to reduce the number of parameters by incorporating some variance structure.

This work is in progress and still unpublished but preliminary results are promising. In the talk I shall tell you a little about the program and the underlying algorithms.

Bobby Cheng, University of Sussex, UK

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Bobby Cheng, University of Sussex, UK

Titill: Quantum Resonances in Relativistic Systems.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 9.október kl.10:00

Ágrip:

Significant amounts of research have been completed on mathematical quantum resonances in the non-relativistic setting. However success in generalizing these results to the relativistic setting have been limited. In this talk I will describe the work undertaken to study resonances of the Dirac operator, perturbed by an electric potential with certain ‘nice’ properties, and establish two key trace formulae.

Peter Giesl, University of Sussex, UK

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Peter Giesl, University of Sussex, UK

Titill: Existence and construction of a contraction metric as solution of a matrix-valued PDE.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 2.október kl.10:00

Ágrip:

A contraction metric is a Riemannian metric, with respect to which the distance between adjacent solutions of an ordinary differential equation (ODE) decreases.

A contraction metric can be used to prove existence and uniqueness of an equilibrium of an autonomous ODE and determine a subset of its basin of attraction without requiring information about its location. Moreover, a contraction metric is robust to small perturbations of the system. 

We will prove a converse theorem, showing the existence of a contraction metric for an equilibrium by characterising it as a matrix-valued solution of a certain linear partial differential equation (PDE). This leads to a construction method by numerically solving the matrix-valued PDE using mesh-free collocation. We use and present a recent extension of mesh-free collocation of scalar-valued functions, solving linear PDEs, to matrix-valued ones. Finally, we briefly discuss a method to verify that the computed metric satisfies the conditions of a contraction metric.

This is partly work with Holger Wendland, Bayreuth as well as Sigurdur Hafstein and Iman Mehrabinezhad, Iceland.

Joachim Toft , Department of mathematics, Faculty of Technology, Linnæus University, Växjö, Sweden

Carlos Argaez Garcia, september 11, 2020

Math colloquium

Fyrirlesari: Joachim Toft , Department of mathematics, Faculty of Technology, Linnæus University, Växjö, Sweden

Titill: Analytic pseudo-differential calculus via the Bargmann transform.

Staðsetning: Via Zoom. Link to be sent.
Tími: Föstudag 25.September kl.10:00

Ágrip:

The Bargmann transform is a transform which maps Fourier-invariant function spaces and their duals to certain spaces of formal power series expansions, which sometimes are convenient classes of analytic functions.

In the 70th, Berezin used the Bargmann transform to translate problems in operator theory into a pseudo-differential calculi, where the involved symbols are analytic functions, and the corresponding operators map suitable classes of entire functions into other classes of entire functions.

Recently, some investigations on certain Fourier invariant subspaces of the Schwartz space and their dual (distribution) spaces have been performed by the author. These spaces are called Pilipovi ́c spaces, and are defined by imposing suitable boundaries on the Hermite coefficients of the involved functions or distributions. The family of Pilipovi ́c spaces contains all Fourier invariant Gelfand- Shilov spaces as well as other spaces which are strictly smaller than any Fourier invariant non-trivial Gelfand-Shilov space. In the same way, the family of Pilipovi ́c distribution spaces contains spaces which are strictly larger than any Fourier invariant Gelfand-Shilov distribution space.

In the talk we show that the Bargmann images of Pilipovi ́c spaces and their distribution spaces are convenient classes of analytic functions or power series expansions which are suitable when investigating analytic pseudo-differential operators (i. e. Berezin or Wick operators).

We deduce continuity properties for such pseudo-differential operators when the symbols and target functions possess certain (weighted) Lebesgue estimates. We also show that the counter image with respect to the Bargmann transform of these results generalise some continuity results for (real) pseudo-differential operators with symbols in modulation spaces, when acting on other modulation space.

The talk is based on collaborations with Nenad Teofanov and Patrik Wahlberg, and parts of the content of the talk is available at:

N. Teofanov, J. Toft Pseudo-differential calculus in a Bargmann setting, Ann. Acad. Sci. Fenn. Math. 45 (2020), 227–257.