## Daniel Fernandez (05/12/16)

Anders Claesson, desember 1, 2016

Málstofa í stærðfræði

### Titill: Information geometry and Holography

Staðsetning: V-158, VRII
Tími: Mánudaginn 5. desember kl. 15:00

### Ágrip:

Information Geometry allows for families of probability distributions to be imbued with a natural measure: the Fisher metric. In particular, it is possible to define a Fisher metric on the instanton moduli space of field theories, which in many cases leads to hyperbolic geometries. Furthermore, Euclidean AdS emerges naturally as the metric of the SU(2) Yang Mills instanton moduli space. These are the first steps towards understanding the emergence of holographic dualities.

## Sara Zemljic (28/11/16)

Anders Claesson, nóvember 23, 2016

Málstofa í stærðfræði

### Titill: Generalized Sierpiński graphs

Staðsetning: V-158, VRII
Tími: Mánudaginn 28. nóvember kl. 15:00

### Ágrip:

(Generic) Sierpiński graphs are two parametric family of graphs, one parameter tells us what complete graph is the main building block for the graph, and the other parameter tells us in which iteration we are. A generalization of these graphs was proposed such that instead of taking a complete graph we start with an arbitrary graph G as our base graph and build the graph $$S_G^n$$ in the same iterative manner as generic Sierpiński graphs. We will examine many basic graph properties and standard graph invariants for generalized Sierpiński graphs.

## Hermann Þórisson (11/10/16)

Sigurður Örn Stefánsson, október 8, 2016

Málstofa í stærðfræði

### Fyrirlesari: Hermann Þórisson Titill: On the Skorohod Representation

Staðsetning: Naustið, Tæknigarði
Tími: Þriðjudaginn 11. október kl. 12:30-14:00

### Ágrip:

According to the Skorohod representation theorem, convergence in distribution to a limit in a separable set is equivalent to the existence of a coupling with elements converging a.s. in the metric. A density analogue of this theorem says that a sequence of probability densities on a general measurable space has a probability density as a pointwise lower limit if and only if there exists a coupling with elements converging a.s. in the discrete metric. In this talk the discrete-metric theorem is extended to stochastic processes considered in a widening time window. The extension is then used to prove the Skorohod representation theorem.

Benedikt Magnússon, október 6, 2016

Meistaraprófsfyrirlestur

### Arnbjörg Soffía Árnadóttir Titill: Grúpuverkanir á óendanleg stefnd net og hlutbrautafallið

Staðsetning: Naustið, Endurmenntun.
Tímasetning: Fimmtudagur 6. október 2016, klukkan 16:00.

### Ágrip:

Við notum grúpuverkanir til þess að skoða óendanleg stefnd net. Við byrjum á því að skilgreina grúpumótun sem við köllum hlutbrautafallið. Við notum svo þessa mótun til þess að skoða ýmsa eiginleika óendanlegra stefndra neta, þ.á.m. myndir netamótana, háörvavegagegnvirkni, Cayley-Abels net og vöxt neta.

Leiðbeinendur: Rögnvaldur G. Möller og Jón Ingólfur Magnússon, báðir prófessorar við Raunvísindadeild Háskóla Íslands.
Prófdómari: Peter M. Neumann, emerítus við The Queen’s College, Oxford University.

## Séverine Biard (10/10/16)

Anders Claesson, október 5, 2016

Málstofa í stærðfræði

### Titill: On pseudoconvex domains and some of their applications

Staðsetning: V-158, VRII
Tími: Mánudaginn 10. október kl. 15:00

### Ágrip:

One of the most commonly studied object in several complex variables is pseudoconvex domains, which I will introduce. Domains of holomorphy in $$\mathbb{C}^n$$, they are studied in more general complex manifolds thanks to a powerful notion: plurisubharmonicity. Those domains are the support of the famous inhomogeneous Cauchy-Riemann equation or also called $$\bar\partial$$-equation. Combined with the existence of a bounded plurisubharmonic function, I will also talk about some applications to complex geometry and complex dynamics.

## Erik Broman (03/10/16)

Anders Claesson, september 28, 2016

Málstofa í stærðfræði

### Titill: Infinite range continuum percolation models

Staðsetning: V-158, VRII
Tími: Mánudaginn 3. október kl. 15:00

### Ágrip:

In the classical Boolean percolation model, one distributes balls in $$R^d$$ in a random, homogeneous way. The density of these balls is controlled by a parameter $$\lambda.$$ Depending on this density, the collection of balls then either form an infinite cluster ($$\lambda$$ large) or consists of only small components ($$\lambda$$ small).

In the talk I will discuss two variants of this model, both which are infinite range. In the first case, the balls are replaced by bi-infinite cylinders with radius 1. We then investigate what the connectivity structure of the resulting set is, and how this depends on $$\lambda$$ as well as on the underlying geometry (Euclidean vs hyperbolic).

In the second case, we replace the balls with attenuation functions. That is, we let $$l:(0,\infty) \to (0,\infty)$$ be some non-increasing function and for every $$y\in R^d$$ we define $$\Psi(y):=\sum_{x\in \eta}l(|x-y|)$$. We study the level sets $$\Psi_{\geq h}$$, which is simply the set of points where the random field $$\Psi$$ is larger than or equal to $$h.$$ We determine for which functions $$l$$ this model has a non-trivial phase transition in $$h.$$ In addition, we will discuss some classical results and whether these can be transferred to this setting.

The aim is that the talk should be accessible to anyone with a mathematical, but not necessarily probabilistic, background.

## Rögnvaldur Möller (19/09/16)

Anders Claesson, september 13, 2016

Málstofa í stærðfræði

### Titill: Highly-arc-transitie digraphs of prime out-valency

Staðsetning: V-158, VRII
Tími: Mánudaginn 19. september kl. 15:00

### Ágrip:

Joint work with Primoz Potocnik, Ljubljana, and Norbert Seifter, Leoben.
The concept of a highly-arc-transitive digraph was defined by Cameron, Praeger and Wormald in a paper that appeared in 1993. Examples constructed by various people have shown that suggestions put forward in that paper are wrong. But if it assumed that the highly-arc-transitive digraph has prime out-valency then some of the suggestions of Cameron, Praeger and Wormald are correct. The second part of the talk is about a general method to construct k-arc-transitive digraphs that are not (k+1)-arc-transitive. This construction gives examples that limit the possibilities of extending the results in the first part and also give examples of digraphs with polynomial growth that are k-arc-transitive but not (k+1)-arc-transitive

## Daniel Friedan (26/08/16)

Sigurður Örn Stefánsson, ágúst 22, 2016

Málstofa í stærðfræði

### Fyrirlesari: Daniel Friedan, Rutgers University and University of Iceland Titill: Quasi Riemann Surfaces

Staðsetning: TG-227 (Tæknigarður, 2. hæð)
Tími: Föstudagur 26. ágúst kl. 13:20.

### Ágrip:

This will be a talk about some speculative mathematics (analysis) with
possible applications in quantum field theory. I will leave any mention
of quantum field theory to the end. I will try to define everything
from scratch, but it probably will help to have already seen the basics
of manifolds, differential forms, and Riemann surfaces.

The talk is taken from my recent paper
„Quantum field theories of extended objects“, arXiv:1605.03279 [hep-th]
which is a mixture of speculative quantum field theory and speculative
mathematics. In the talk, the speculative mathematics will be presented
on its own, without the motivations from quantum field theory.

Below is the abstract from a note I am presently writing to try to
interest mathematicians in looking at this structure:

## Brittany A. Erickson (08/08/16)

Sigurður Örn Stefánsson, ágúst 4, 2016

Málstofa í stærðfræði

### Fyrirlesari: Brittany A. Erickson Titill: A Finite Difference Method for Plastic Response with an Application to the Earthquake Cycle

Staðsetning: V-157, VR-II.
Tími: Mánudagur 8. ágúst kl. 13:20.

### Ágrip:

We are developing an efficient, computational framework for simulating multiple earthquake cycles with off-fault plastic response. Both rate-independent and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The constitutive theory furnishes a nonlinear elliptic partial differential equation which must be solved through an iterative procedure. A frictional fault lies at an interface in the domain. The off-fault volume is discretized using finite differences satisfying a summation-by-parts rule and interseismic loading is accounted for at the remote boundaries through weak enforcement of boundary conditions. Time-stepping is done through an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm to obtain stresses consistent with the constitutive theory. Solutions are verified by convergence tests along with comparison to a finite element solution. I will conclude with some application problems related to earthquake cycle modeling.

## Anthony Bonato (30/06/16)

Sigurður Örn Stefánsson, júní 27, 2016

Málstofa í stærðfræði

### Fyrirlesari: Anthony Bonato Titill: Conjectures on Cops and Robbers Games on Graphs

Staðsetning: TG-227 (Tæknigarður, 2. hæð)
Tími: Fimmtudagur 30. júní kl. 13:20.

### Ágrip:

The game of Cops and Robbers gives rise to a rich set of conjectures, mainly associated with the cop number of a graph. Arguably the most important such conjecture is Meyniel’s, which posits a $$O(n^{1/2})$$ upper bound on the cop number of a connected graph of order n. We discuss the state-of-the-art on Meyniel’s conjecture, and explore other conjectures on cop number ranging from topics within computational, probabilistic, and topological graph theory.