Teden Matematičnih kolokvijev: Hansjoerg Albrecher, Alfred Geroldinger in Patrick Gérard
V dneh od 14. do 17. aprila bodo v okviru Matematičnih kolokvijev na sporedu tri predavanja:
**Hansjoerg Albrecher (Université de Lausanne): Matrix Distributions and Insurance Risk Models **
In this talk some recent developments on matrix distributions and their connection to absorption times of inhomogeneous Markov processes will be discussed, in particular how and why such constructions are natural tools for modelling in non-life and life insurance applications. We illustrate the approach for the modelling of mortality in both a single- and multi-population context, as well as modelling of joint lifetimes of couples. Finally, it is shown how certain extensions to the non-Markovian case involve fractional calculus and lead to matrix Mittag-Leffler distributions, which turn out to be a flexible and parsimonious class for the modelling of large but rare insurance loss events.
Torek, 14. april 2026, 15:15, predavalnica 2.02
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Alfred Geroldinger (University of Graz): On Length Sets in Krull Monoids
Let $H$ be a Krull monoid (e.g., the multiplicative monoid of nonzero elements of a Krull domain). Then every non-invertible element can be factored into irreducible elements. If $a = u_1 \cdot \ldots \cdot u_k$, with $k \in \mathbb N_0$ and irreducibles $u_1, \ldots, u_k$, then $k$ is a factorization length and the set $\mathsf L (a)$ of all factorization lengths of $a$ is called the length set of $a$. The system $\mathcal L (H) = {\mathsf L (a) \colon a \in H }$ of length sets is an infinite family of finite subsets of $\mathbb N_0$. The structure of $\mathcal L (H)$ depends only on the class group of $H$ and on the distribution of prime divisors in the classes. We provide an overview of the current state of knowledge regarding $\mathcal L(H)$ and present some new results for the case of torsion class groups.
Četrtek, 16. april 2026, 15:15, predavalnica 2.02
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Patrick Gérard (Paris-Saclay University): Long-time dynamics for the Benjamin-Ono equation on the line
Introduced in 1967 as a model of fluid mechanics, the Benjamin-Ono equation turns out to be a striking example of an infinite-dimensional integrable system. I will review its main properties, including a Lax pair and an explicit representation formula for its solutions, and I will try to explain how they have been recently used to prove a conjecture on the role of soliton solutions in the long-time dynamics on the line.
Petek, 17. april 2026, 14.15, predavalnica 2.02 ZOOM povezava: https://uni-lj-si.zoom.us/j/95924275545
