Lorentz Center - Mathematical Facets of Crystallization from 8 Sep 2014 through 12 Sep 2014
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    Mathematical Facets of Crystallization
    from 8 Sep 2014 through 12 Sep 2014

 

Solid-state physics is largely about crystals. In spite of the enormous achievements and numerous applications of solid-state physics, it remains unclear mathematically how crystals come into existence. Different areas of mathematics have contributed towards a rigorous picture of crystallization, but there still is a long way to go. This workshop focused on four topics that are closely connected with crystallization, and approached these topics from different mathematical angles. These four topics are:

Spatial symmetry breaking at positive temperature

Crystallization and surface effects at zero temperature

Metastability of continuum particle systems

Elasticity and quasi-crystals.

 

Any mathematical theory of crystallization must be rooted in analysis, probability theory and statistical physics. Analytic approaches typically consider only ground states of crystals (i.e., crystals at zero temperature). At positive temperature, defects occur and probabilistic approaches are needed. The workshop focused on the modeling of thermal effects through Gibbs measures, which requires a deep understanding of statistical mechanical techniques as well.

 

The workshop brought together researchers from different backgrounds: Analysis, Probability, Stochastic Geometry and Statistical Mechanics. In order to facilitate the different backgrounds, we asked four prominent researchers from different communities to give an extended overview talk and identify open problems. These keynote speakers were Michael Baake (Bielefeld), Aernout van Enter (Groningen), Marek Biskup (Los Angeles), and Florian Theil (Warwick). Apart from that, we kept a light schedule of talks, with ample room for individual discussion and three plenary discussion rounds. In particular the overview talks and the plenary discussions were very fruitful and were well received by the participants.

 

Our goal was to make participants aware of relevant developments and to stimulate collaboration between different mathematical communities. Indeed, several new research projects were initiated during the week. Moreover, a list of key challenges towards a rigorous understanding of crystallization has been comprised.

 

There were 25 participants in total, most of them from the United Kingdom, Germany and The Netherlands, but also from Czech Republic, France and the US.

 

Markus Heydenreich (Leiden, Netherlands)

Frank den Hollander (Leiden, Netherlands)

Sabine Jansen (Bochum, Germany)

 



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