### Upcoming Talks

#### Vortrag

Title: Capture-recapture for population size estimation based upon zero-truncated count distributions with one-inflation
Speaker: Dankmar Böhning (Statistical Sciences Research Institute, University of Southampton/UK)
Date: 28.05.2019, 17:15 Uhr
Room: SR für Statistik (NT03098), Kopernikusgasse 24/III
Abstract:

Abstract: Population size estimation by means of capture-recapture methods using zero-truncated count distributions has become popular. The estimator of Chao is likewise frequently used as it is asymptotically unbiased if the model holds and provides a lower bound in the case of population heterogeneity. However, if one-inflation occurs Chao’s estimator can seriously overestimate as it builds largely on the count of ones, the singletons, in the sample. The talk highlights how one-inflation can be detected and how it can be dealt with, and ultimately provides a more reasonable population size estimator. Two examples will motivate and illustrate one-inflated modelling: the size of a dice-snake population in Graz (Austria) as well as the size of the flare star cluster in the Pleiades.

#### Seminarvortrag

Title: Best Estimate Berechnung und Validierung in der Lebensversicherung
Speaker: Simon Hochgerner (FMA - Finanzmarktaufsicht Österreich)
Date: 24.05.2019, 14:15
Room: SR für Statistik (NT03098), Kopernikusgasse 24/III
Abstract:

Seit Inkrafttreten von Solvency II per 1.1.2016 sind Versicherungsunternehmen verpflichtet, den Wert der eingegangenen Verpflichtungen marktkonsistent und unter Berücksichtigung realistischer Annahmen zu bestimmen ("Best Estimate").
Speziell für die klassische Lebensversicherung führen diese Bedingungen zu besonderen Herausforderungen, da es bei diesen Produkten eine enge Verflechtung von Aktiv-, Passivseite und Managementregeln gibt.
Im Rahmen des Vortrags werden wir auf einige Probleme im Zusammenhang mit der Best Estimate Berechnung eingehen und die wichtigsten Validierungsschritte vorstellen.

#### Vorstellungsvortrag im Rahmen eines Habilitationsverfahrens

Title: High-dimensional connectedness: cores and components
Speaker: Oliver Cooley (TU Graz, Institut für Diskrete Mathematik)
Date: Freitag 24.5.2019, 11:00
Room: Seminarraum 2, Institut für Geometrie, Kopernikusgasse 24/IV
Abstract:

The talk will provide an overview of some of my recent research topics, with a common theme of generalising the standard graph notions of connectedness and components to higher-dimensional structures.

These include the $k$-core of a graph, i.e. the unique largest subgraph of minimum degree at least $k$, which we analyse by means of a message-passing algorithm introduced in physics literature. We show how an understanding of this local algorithm helps us to determine the global structure of the $k$-core and its interaction with other vertices.

We also consider $j$-tuple-connected components in $k$-uniform hypergraphs, a notion of connectedness related to $j$-tight paths. We observe some phase transition phenomena analogous to famous and classical graph results, but also discuss why the hypergraph case is richer and more complex.

#### Number Theory Seminar

Title: Khintchine's theorem with extra divergence instead of monotonicity
Speaker: Laima Kaziulyte (TU Graz)
Date: Tuesday, 21.5.2019, 11:15.
Room: Seminarraum Analysis-Zahlentheorie, Kopernikusgasse 24, 2.OG.
Abstract:

New results towards the Duffin-Schaeffer conjecture, which is a fundamental unsolved problem in metric number theory, have been established recently assuming extra divergence. Given a non-negative function $\psi: \mathbb{N}\to\mathbb{R}$ we denote by $W(\psi)$ the set of all $x\in\mathbb{R}$ such that $|nx-a|<\psi(n)$ for infinitely many $a,n$. Analogously, we write $W'(\psi)$ if we additionally require $a,n$ to be coprime.

Aistleitner et al. proved that $W'(\psi)$ is of full Lebesgue measure if there exists an $\varepsilon>0$ such that $\sum_{n=2}^\infty\psi(n)\varphi(n)/(n(\log n)^\varepsilon)=\infty$. This result seems to be the best one can expect from the method used. Assuming the extra divergence $\sum_{n=2}^\infty\psi(n)/(\log n)^\varepsilon=\infty$ we prove that $W(\psi)$ is of full measure. This could also be deduced from the results in Aistleitner et al., but we believe that our proof is of independent interest, since its method is totally different from theirs. As a further application of our method, we prove that a variant of Khintchine's theorem is true without monotonicity, if the support of $\psi$ can be restricted subject to a condition on the set of divisors.