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.

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.

For further information please contact:
Prof. Sigurdur Orn Stefansson (e-mail: sigurdur[at]hi.is)

Fyrirlesari: Thomas Selig, University of Strathclyde

Titill: EW-tableaux, permutations and recurrent configurations of the sandpile model on Ferrers graphs.

Staðsetning: VRII, V-147
Tími: Miðvikudagur 27. júní kl. 10:30

Ágrip:

The Abelian sandpile model (ASM) is a dynamic process on a graph. More specifically, it is a Markov chain on the set of configurations on that graph. Of particular interest are the recurrent configurations, i.e. those that appear infinitely often in the long-time running of the model. We study the ASM on Ferrers graphs, a class of bipartite graphs in one-to-one correspondence with Ferrers diagrams. We show that minimal recurrent configurations are in one-to-one correspondence with a set of certain 0/1 fillings of the Ferrers diagrams introduced by Ehrenborg and van Willigensburg. We refer to these fillings as EW-tableaux, and establish a bijection between the set of EW-tableaux of a given Ferrers diagram and a set of permutations whose descent bottoms are given by the shape of the Ferrers diagram. This induces a bijection between these permutations and minimal recurrent configurations of the ASM. We enrich this bijection to encode all recurrent configurations, via a decoration of the corresponding permutation. We also show that the set of recurrent configurations over all Ferrers graphs of a given size are in bijection with the set of alternating trees of that size.

Fyrirlesari: Delphin Sénizergues, Université Paris 13

Titill: Random metric spaces constructed using a gluing procedure

Staðsetning: VRII-V147
Tími: Mánudagur 18. júní kl. 10:50

Ágrip:

I will introduce a model of random trees which are constructed by iteratively gluing an infinite number of segments of given length onto each other. This model can be generalized to a gluing of „blocks“ that are more complex than segments. We are interested in the metric properties of the limiting metric space, mainly its Hausdorff dimension. We will show that its Hausdorff dimension depends in a non-trivial (and surprising !) manner on the different scaling parameters of the model and the dimension of the blocks.

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 March 12, 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 temporary for two years from the 1st of August 2018, or otherwise according to agreement, with a possibility of an extension of one year. All applications will be answered.

For further information please contact:
Ass. Prof. Sigurdur Orn Stefansson (e-mail: sigurdur[at]hi.is)

Applications are invited for a three year PhD position in mathematics at the University of Iceland with a starting date in Fall 2018. The position is funded by a grant from the Icelandic Research Fund.

The successful candidate will work in the area of probabilistic combinatorics with emphasis on scaling limits of random graphs, statistical mechanical models on random planar maps and related subjects. A master degree, or equivalent, in mathematics is required. The application deadline is March 12, however applications will continue to be accepted until the position is filled.

Applications should be sent directly by e-mail to sigurdur[at]hi.is, including a CV, transcripts from undergraduate and master studies, a short description of research interests and names and e-mail addresses of two referees, who have agreed to provide recommendation.

For further information please contact:
Ass. Prof. Sigurdur Orn Stefansson (e-mail: sigurdur[at]hi.is)

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.

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: