Math Colloquium

### Speaker: Daniel Fernandez Moreno, University of Iceland

### Title: Entanglement entropy at non-equilibrium in holography

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Friday 7 July at 13:20

### Abstract:

In recent years, holographic models have proved to be successful at studying far-from-equilibrium physics. This provides a new approach to studying quantum quenches in strongly coupled systems. In this talk, based on ArXiv:1705.04696, I will focus on the local quench-like time evolution obtained by joining two 1+1 dimensional heat baths at different temperatures. I will present results for the entanglement entropy of different entangling regions obtained by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription. The interest of this study relies on the presence of emergent collective behavior, which can provide insight into the interplay between quantum effects and out of equilibrium physics.

Math Colloquium

### Speaker: Christopher Kellett, University of Newcastle (Australia)

### Title: Back and Forth in Lyapunov’s Second Method: Non-Uniform Subtleties

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Thursday 6 July at 13:20

### Abstract:

Lyapunov’s second or direct method provides an easy-to-check sufficient condition for stability properties of equilibria. The converse question – given a stability property, does there exist an appropriate Lyapunov function? – has been fundamental in differentiating and classifying different stability properties, particularly with regards to “uniform” stability.

In this talk, I will review the usual textbook definitions for Lyapunov functions for time-varying systems and describe where they are deficient. Some interesting new sufficient (and probably necessary) conditions pop up along the way.

Math Colloquium

### Speaker: Peter J. Olver, University of Minnesota

### Title: Equivalence, Invariants, Puzzles, and Cancer

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Friday 9 June at 16:00

### Abstract:

A fundamental issue in computer vision is recognizing when two objects in an image are the “same”. The underlying mathematical apparatus for studying such equivalence problems is transformation group (or, more generally, groupoid) theory. Cartan’s solution to the equivalence and symmetry problem for submanifolds relies on the associated geometric invariants, through what is now known as the differential invariant signature. Furthermore, the new equivariant approach to the method of moving frames provides a systematic and algorithmic approach that can be applied to very general Lie group and even Lie pseudo-group actions. The talk will conclude with recent applications to automated assembly of broken objects, such as jigsaw puzzles, and cancer detection.

PhD thesis defense rehearsal

### Speaker: Örn Arnaldsson, University of Minnesota

### Title: Involutive moving frames

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Tuesday 6 June at 10:50

### Abstract:

Cartan’s equivalence method and the method of the equivariant moving frames are the two best known methods for solving equivalence problems in differential geometry, differential equations, calculus of variations and control theory. My thesis demonstrates how the two methods are really two sides of the same coin and combines them in a powerful hybrid method that increases the computational efficiency of both of its progenitors. This novel viewpoint provides effortless proofs to some previously hard-to-prove results, such as the Lie-Tresse theorem. Furthermore, we obtain proof of a long standing conjecture of Cartan on the termination of his equivalence method.

Thesis presentation in Master of Applied Statistics (MAS)

### Guðmundur Helgason

Titill: Hversu lengi þarf ég að bíða? Forspárlíkön fyrir biðtíma í þjónustuveri CCP

Location: V-157, VRII

Time: Thursday 1. June at14:00.

### Abstrat:

Í þessari rannsókn, með hjálp ýmissa tölfræðiaðferða, spáum við fyrir um biðtíma eftir svari við tölvupósti með gögnum frá þjónustuveri CCP, framleiðanda tölvuleiksins EVE Online. Að mestu leyti er notast við tvíkosta tölfræðilíkön þar sem spáð er fyrir um hvort að svar sé gefið fyrir ákveðinn tímapunkt eða ekki. Samfelldar aðferðir eru þó einnig notaðar, bæði til að spá fyrir um biðtíma í sjálfu sér og hvort svar sé gefið fyrir ákveðinn tíma eða ekki. Auk greiningarlegra aðferða til forspáar er einnig notast við einfaldari empírískar aðferðir til að meta dreifingu biðtíma og líkindi á svari eftir ákveðinn tíma. Tiltækar rannsóknir á sviði þjónustuvera, gæða í þjónustu, áhrifa þess að bíða eftir þjónustu og aðferða sem notast hefur verið við til að spá fyrir um biðtíma eru skoðaðar. Aðferðirnar sem notast var við til biðtíma forspáar eru bornar saman, kostir þeirra og gallar ræddir, auk hugsanlegra hagnýtra eiginleika.

Leiðbeinendur:

Anna Helga Jónsdóttir

Matthías Kormáksson

Prófdómari: Thor Aspelund

http://www.hi.is/vidburdir/meistarafyrirlestur_hversu_lengi_tharf_eg_ad_bida_forsparlikon_fyrir_bidtima_i_thjonustuveri_ccp

Thesis presentation in Master of Applied Statistics (MAS)

### Stella Kristín Hallgrímsdóttir

Title: Samband veðurs og komufjölda á bráðamóttökur Landspítala

Location: V-157, VRII

Time: Monday 29. May at 14:00.

### Abstract:

The objective of this project is to study the seasonal and weekly fluctuations in number of arrivals to the emergency departments of the University Hospital of Iceland and also to assess the influence of weather on the number of arrivals. Four emergency departments were examined; the Emergency Department in Fossvogur, the Emergency Unit in the Children‘s Hospital Department, Hjartagátt which is the emergency department for people with suspected acute heart problems, and the Psychiatry Emergency Department. The weather variables that were mostly looked into are temperature, wind speed, precipitation and cloudiness. Seasonal fluctuations were modeled with sine and cosine waves and with the help of linear regression a new variable was made that describes the seasonal fluctuations and linear increase in the number of arrivals. A few ARIMA models were built to predict the number of arrivals in the Emergency Department in Fossvogur and in the Children‘s Emergency Department. The models were compared to find the best prediction model for each department. To assess whether weather affects the number of arrivals in the emergency departments, the weather variables were added one by one to the best prediction model for each department to see if the model‘s prediction root-mean squared error (RMSE) decreases when information about weather is added to the model. Principal components analysis was also used to combine the weather variables into fewer new variables. The new variables were then added to the ARIMA models to assess their effect on the goodness of the models. The results show that adding the weather information slightly decreases prediction RMSE in the Emergency Department in Fossvogur but increases it for the Children‘s Emergency Department. That both applies to when each weather variable was looked into separately and when the principal components were used. Therefore, it can be concluded that weather does not affect the number of arrivals to the Children‘s Emergency Department but it has a minor effect on the number of arrivals to the Emergency Department in Fossvogur. Furthermore, the results show that a good prediction model for the number of arrivals to the emergency departments can be developed only using calendar variables.

Advisors: Dr. Sigrún Helga Lund and Dr. Tryggvi Helgason

Examiner: Dr. Ólafur Pétur Pálsson

http://www.hi.is/vidburdir/meistarafyrirlestur_samband_vedurs_og_komufjolda_a_bradamottokur_landspitala

Math Colloquium

### Speaker: Valentina Giangreco, University of Iceland

### Title: Non-analyticity of holographic Rényi entropy in Lovelock gravity

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Friday 26 May at 13:20

### Abstract:

In the first part of my talk I will introduce the definition of Rényi entropy, and some basic concepts of the so-called holographic principle (AdS/CFT). The second part of the talk is devoted to the analysis of certain black hole instabilities in gravity theories with higher derivative corrections (Lovelock gravity theories) and their implications for the holographic Rényi entropy.

Math Colloquium

### Speaker: Ayan Mukhopadhyay, Vienna University of Technology

### Title: The mogul pistes of non-equilibrium causal correlations in strongly interacting holographic systems: universal features and how they reveal the microscopic theory.

Location: V-158 (VR-II)

Time: Thursday 11 May at 13:30

### Abstract:

I will report exact calculations of holographic retarded (causal) correlation function away from equilibrium in states driven from one thermal equilibrium to another by a homogeneous energy injection. Our calculations reveal universal features of thermalization of the retarded propagator. Furthermore, I will discuss how the measurement of the non-equilibrium retarded propagator (possible by techniques such as pump-probe spectroscopy) enables us to learn a lot about the dual gravity description (i.e. the microscopic theory) by establishing novel connections between quantum information content of non-equilibrium density matrices and the classical dynamics of the apparent and event horizons in the dual geometries.

Math Colloquium

### Speaker: Jason Smith, University of Strathclyde

### Title: Poset Fibrations and Their Applications to Pattern Posets

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Friday 21 April at 13:30

### Abstract:

A poset fibration is a rank and order preserving surjective map between posets. It was shown by Quillen that many properties of posets can be maintained across a fibration, we introduce some of these results. Pattern occurrence has been studied on a wide range of combinatorial objects, and using the notion of pattern containment we can define a poset on these objects. Many such pattern posets have been studied in the literature and the results on these posets often have a similar theme. Using poset fibrations we introduce some results that show why such similarities arise between different pattern posets.

Math Colloquium

### Speaker: Friðrik Freyr Gautason, K.U. Leuven

### Title: Large field inflation in string theory

Location: Tg-227 (Tæknigarður, 2. hæð)

Time: Friday 7 April at 13:20

### Abstract:

I start by motivating that certain questions in cosmology, in particular dark energy and large field inflation, should be addressed in a quantum model that includes gravity such as string theory. I will give an overview how these questions are translated to dynamics in the extra dimensions of string theory and what challenges one encounters. I then present a novel model for inflation in string theory and discuss some of the stringent consistency constraints the parameters of the model must satisfy and how these constraints affect cosmological observables.