## Postdoctoral position in mathematics at the University of Iceland

Sigurður Örn Stefánsson, september 2, 2019

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.

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

## Björn Birnir

Carlos Argaez Garcia, ágúst 23, 2019

Math colloquium

#### Titill: When can we expect the Greenland glacier to melt?

Staðsetning: VR-II,V-258
Tími: Þriðjudag 27.ágúst kl. 11:00

#### Ágrip:

It was suggested by Rose (2005) that because of the migratory and responsive nature of the capelin, a small pelagic fish that is key to the ecology and fisheries of the North Atlantic, it can be viewed as the „canary in the coalmine“ to detect signals of environmental changes in the Arctic Ocean. In this talk we will combine analysis of data and extensive simulations of the migrations of the capelin and its physiology to analyze the changes in the ocean environment taking place over the last half-century. The environmental data for the last thirty year is obtained from a database called Copernicus, constructed by the European Union. Our goals will be to understand and predict the migrations of the capelin and its interactions with the ocean environment. We will explain how these have changed over time and how they are likely to change in the future. Then we will explain how our simulations can be compared with data, with the aim of finding out the rate of the temperature changes in the Arctic Ocean and when thresholds for major disruptions in Arctic environments are likely to be reached. The recent changes in the spawning routes of the capelin lead to a startling prediction.

## Hólmfríður Sigríðar Hannesdóttir

Valentina Giangreco, ágúst 23, 2019

Math Phys seminar

#### Titill: Infrared Finite S-matrix elements and Cross Sections

Staðsetning: A-050
Tími: Þriðjudag 27.ágúst kl. 14:00

#### Ágrip:

Quantum field theory (QFT) works remarkably well for making theoretical predictions in collider scattering experiments. One of the fundamental objects in these calculations, the scattering matrix (S-matrix), is inspired by a well defined operator in non-relativistic quantum mechanics, but is plagued with both ultraviolet (UV) and infrared (IR) divergences in QFT. The UV divergences are now understood through the program of renormalization, but IR divergences remain an active area of research. Three approaches have been explored to define IR finite quantities, which will all be discussed in this talk: i) The cross section method, ii) modification of the S-matrix, and iii) the dressed state formalism. The minimal set of processes required for a finite cross section will be examined, along with the need for forward scattering and disconnected diagrams. We will furthermore explore how the usual assumptions about evolution of the scattering states at asymptotic times are broken in a theory with massless particles, and how the universality of the interactions leading to IR divergences in such theories can be exploited to define finite S-matrix elements.

## Juan Fernando Angel Ramelli

, ágúst 22, 2019

PhD midway evaluation

#### Titill: Entanglement entropy of the quantum Lifshitz model

Staðsetning: A-050
Tími: Þriðjudag 27.ágúst kl. 09:00

#### Ágrip:

The quantum Lifshitz model (QLM) is a toy model used for studying scale invariant systems in which time and space scale on different footing. This type of behavior occurs, for example, in the context of critical phenomena. Entanglement entropy is a purely quantum measure of correlation between subsystems. It is a useful theoretical probe, as it encodes certain universal properties of critical models. I review the QLM as well as its generalization to higher dimensions, and show how to construct its excited states on compact manifolds. Through careful application of the replica method, I demonstrate that analytic results can be obtained for the entanglement entropy of both its ground state and its excited states.

## Mohab Abou Zeid

, ágúst 20, 2019

Math Phys seminar

#### Titill: T-duality in (2,1) superspace and SKT geometry

Staðsetning: VR-II, V-156
Tími: Föstudag 23.ágúst kl. 14:00

#### Ágrip:

I will explain our recent derivation of the T-duality transformation rules for two-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. To this end I will first review the gauging of sigma-models in (2,1) superspace and present a new manifestly real and geometric expression for the gauged action. I will  also discuss the obstructions to gauging (2,1) sigma-models and show that the obstructions to (2,1) T-duality are considerably weaker than the obstructions to gauging. Our complexified T-duality transformations are equivalent to the usual Buscher duality transformations (including an important refinement) together with diffeomorphisms. Time permitting, I will mention some possible applications of our results.

## Ro Jefferson

, ágúst 20, 2019

Math Phys seminar

#### Titill: Black hole interiors and modular inclusions

Staðsetning: VR-II, V-156
Tími: Fimmtudag 22.ágúst kl. 14:00

#### Ágrip:

We show how the traversable wormhole induced by a double-trace deformation of the thermofield double state can be understood as a modular inclusion of the algebras of exterior operators. The effect of this deformation is the creation of a new region of spacetime deep in the bulk, corresponding to a non-trivial center between the left and right algebras. This set-up provides a precise framework for investigating how black hole interiors are encoded in the CFT. In particular, we use modular theory to demonstrate that state dependence is an inevitable feature of any attempt to represent operators behind the horizon. Building on this geometrical structure, we propose that modular inclusions may provide a more precise means of investigating the nascent relationship between entanglement and geometry in the context of the emergent spacetime paradigm.

Carlos Argaez Garcia, ágúst 20, 2019

Math Phys seminar

#### Titill: Continuous Quantum Walks

Staðsetning: VR-II, V-158
Tími: Fimmtudag 22.ágúst kl. 11:00

#### Ágrip:

Continuous quantum walks arise naturally as quantum analogues of continuous random walks, but in contrast to their classical counterparts, they exhibit some curious and counter-intuitive properties. I will give an introductory talk on continuous quantum walks and present some of these exciting properties.
The motivation for studying quantum walks largely comes from quantum physics and quantum computing, however, the emphasis of this talk will be on the mathematics. In particular, no prior knowledge of anything quantum is assumed.

## Jorge Laraña Aragon

Carlos Argaez Garcia, ágúst 15, 2019

Math Phys seminar

#### Titill: Quenched coupling, effective thermalization and evanescence in the free $O(N)$ vector model

Staðsetning: VR-II, V-156
Tími: Fimmtudag 15.ágúst kl. 14:00

#### Ágrip:

In this project we study two coupled free $O(N)$ vector models implementing the coupling via a quench of mixing. Since the theory is integrable pure thermalization does not occur but the quantum modes thermalize independently. Generalized thermal behavior is obtained at late times in the limit of weak initial mixing. We investigate this from both the effective density matrix and the spectral density function. When computing the latter, we observe that late-time correlation functions of composite operators in the post-quench free QFT surprisingly share interesting properties with correlators in strongly coupled systems. We discuss a possible holographic interpretation in terms of the so called evanescent modes.

## Finnur Lárusson

Valentina Giangreco, júní 7, 2019

Málstofa í stærðfræði

### Titill: Chaotic holomorphic automorphisms of Stein manifolds with the volume density property

Staðsetning: VR-II, V-158
Tími: þriðjudagur 9. júlí kl. 11.00

### Ágrip:

I will report on joint work with Leandro Arosio.  Let $X$ be
a Stein manifold of dimension $n\geq 2$ satisfying the volume density
property with respect to an exact holomorphic volume form.  For example,
$X$ could be $\C^n$, any connected linear algebraic group that is not
reductive, the Koras-Russell cubic, or a product $Y\times\C$, where $Y$
is any Stein manifold with the volume density property. We prove that
chaotic automorphisms are generic among volume-preserving holomorphic
automorphisms of $X$.  In particular, $X$ has a chaotic holomorphic
automorphism. Forn\ae ss and Sibony proved (but did not explicitly
state) this for $X=\C^n$ in 1997.  We follow their approach closely.
Peters, Vivas, and Wold showed that a generic volume-preserving
automorphism of $\C^n$, $n\geq 2$, has a hyperbolic fixed point whose
stable manifold is dense in $\C^n$.  This property can be interpreted as
a kind of chaos.  We generalise their theorem to a Stein manifold as above.

## Christiana Pantelidou

Valentina Giangreco, júní 7, 2019

Math Phys seminar

### Titill: Incoherent hydrodynamics and density waves

Staðsetning: VR-II, V-258
Tími: mánudagur 24. júní kl. 14.00

### Ágrip:

I will consider thermal phases of holographic lattices at finite chemical potential in which a continuous internal bulk symmetry can be spontaneously broken. In the normal phase, translational symmetry is explicitly broken by the lattice and the long wavelength excitations are captured by incoherent hydrodynamics describing two perturbative diffusive modes. In the broken phase an additional diffusive hydrodynamic degree of freedom appears. In this talk I will use holography to write an effective theory describing the coupling of incoherent hydrodynamics to this goldstone mode.