Universiteit Leiden

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This Week’s Discoveries | 1 November 2016

1 November 2016
Oort Building
Niels Bohrweg 2
2333 CA Leiden
De Sitterzaal

First Lecture

Universal elliptic curves and torsion points
Maarten Derickx (MI)

Maarten defended his PhD thesis, supervised by Bas Edixhoven, on 21 September 2016.
Quote from the PhD announcement: 'Barry Mazur famously classified the finitely many groups that can occur as a torsion subgroup of an elliptic curve over the rationals. This thesis deals with generalizations of this to higher degree number fields.'

Second Lecture, Lorentz Center highlight

The sandpile model – a simple model for cascades
Wioletta Ruszel (TU Delft)

Wioletta Ruszel is assistant professor in Applied Probability and a Delft Female Fellow at the Technical University Delft. Her main research interest are interacting particle systems and statistical mechanics. She was one of the organizers of the Lorentz Center workshop 'Transformations in Statistical Mechanics: Pathologies and Remedies' that was held from 10 October 2016 through 14 October.

The abelian sandpile model (ASM) is a toy model for 'self-organised criticality', a concept used to describe systems which drive themselves into a critical state without tuning a parameter. The ASM was also used in different disciplines such as biology or economy to model cascading failures. Since its birth year 87 this model has been extensively studied and different variants considered. This model is very interesting because of its many connections to different models and questions, such as chip-firing games, conformal field theory, bi-Laplacian Gaussian Fields and uniform spanning trees.
In this talk we will introduce the basic model and review some of the many connections.