## Hermann Þórisson (30/11/2018)

Math Colloquium

### Speaker: Hermann Þórisson, University of Iceland

### Title: What is typical?

Location: Naustið (Endurmenntun)

Time: Friday November 30 at 11.40

### Abstract:

Math Colloquium

Location: Naustið (Endurmenntun)

Time: Friday November 30 at 11.40

The word “typical” is often used in a loose sense for events in a stationary random process (such as occurrences of heads in repeated coin tosses). This concept can be made precise using so-called Palm version of the process. It is however not well known that there are in fact two Palm versions and that it is the less known version that captures the typicality property. So using the well known version is flawed except in the special case when the two versions coincide.

In this talk the elementary example of repeated coin tosses (indexed by the integers) will be used to make transparent what the issue is.

In the latter half of the talk we shift drastically to random measures on a rather general class of Abelian groups (in the coin tossing example the group is the integers under addition and the random measure is formed by mass points of size one at the heads). After giving the formal definition of the two Palm versions we present a theorem motivating the claim that it is the less known Palm version that captures the typicality property. If time allows we skim through the proof which relies on the concepts of shift-coupling and mass-stationarity.

Math colloquium

Location: Naustið (Endurmenntun)

Time: Friday November 23 at 11.40

Math Phys seminar

Location: VR-II 155

Time: Thursday November 22 at 13.30

TBA

Math colloquium

Location: Naustið (Endurmenntun)

Time: Friday November 16 at 11.40

Math Colloquium

Location: Naustið (Endurmenntun)

Time: Friday November 2 at 11.40

We show that there is a bijection between the spatial slices of 3-dimensional causal triangulations and a class of two-dimensional cell complexes satisfying some simple conditions. The talk will be preceded by a short introduction to the subject.

Math Phys seminar

Location: Naustið (Endurmenntun)

Time: Wednesday October 24, 13.30 – 14.30

We present holographic models realizing the pseudo-spontaneous breaking of translations. We study the electrical transport of these solutions finding that they reproduce features characteristic of the bad metallic transport observed in the cuprates.

Math Colloquium

Location: Naustið (Endurmenntun)

Time: Friday October 19 at 11.40

A real Banach algebra is a Banach algebra over the reals. We will only consider commutative Banach algebras with unit. An example is the algebra of continuous functions, f , on the unit disc, analytic in the interior of the disc, satisfying f (z) = f (z). The norm on the algebra is the sup-norm.

Another example is the algebra of continuously differentiable real-valued functions on the unit interval with the norm given by

∥f∥ = ∥f∥∞ +∥f′∥∞

According to Gelfand theory, a commutative Banach algebra A with unit, over the complex numbers, can be represented as an algebra of continuous complex valued functions on a compact Hausdorff space X, with

sup_{x ∈ X}|ã(x)| = r(a) := lim∥a^n∥^1/n

for a ∈ A. Here X is the space of multiplicative linear functionals on A, equipped with the w∗-topology, and ã(x) = x(a) for x ∈ X.

This result also holds for real Banach algebras. Furthermore, the representati- on consists of real valued functions if and only if

r(a^2) ≤ r(a^2 +b^2) a,b ∈ A.

We will prove this using only real Banach space theory. If there is time we

will also talk about the general case where there is no condition on A.

Math Colloquium

Location: Naustið (Endurmenntun)

Time: Friday October 12 at 11.40

A permutation graph is a graph whose edges are given by the inversions of a permutation. The Abelian sandpile model (ASM) is a Markov chain on the set of so-called configurations of a graph. Of particular interest are the recurrent configurations, i.e. those that appear infinitely often in the long-time running of the model. We exhibit a bijection between the set of recurrent configurations for the ASM on permutation graphs and the set of tiered trees, introduced by Duggan et al. This provides a new bijective proof of a famous result linking the level polynomial of the ASM to the ubiquitous Tutte polynomial. We also show a link between the minimal recurrent configurations and the set of complete non-ambiguous binary trees, introduced by Aval et al.

Math Phys seminar

Place: Aðalbygging A-069

Time: Thursday October 4, at 1.20 – 2.20 pm

The holographic correspondence can be extended to identify plasmonic excitations in strongly correlated systems. These modes have relevance in the growing field of plasmonics, and play also a crucial role in relating properties of holographic ‘screened’ density-density response response functions to ‘physical’ density-density response functions, with the latter being the quantity actually related to experimental observation.

Math Colloquium

Location: V-147 (VR-II)

Time: Monday 2 July at 10:30

In this talk I will give an overview of a set of techniques that allow us to define latent variable models of data generating distributions.

To this end we introduce neural networks as an efficient and a surprisingly effective way of finding variational parameters that best fit some specified objective.

I will discuss a couple of different approaches that can be taken to define this objective and show you some interesting results.