Together with Clélia Mulatier (physics) and Patrick Forré (informatics), I
have an opening for a PhD position at the University of Amsterdam. Could
you please share this with any potential candidates? The underlying
mathematics involves the Tutte polynomial/Potts model and also hypergraphs.
PhD position at the frontier of Statistical Physics, Information Theory and
Mathematics (uva.nl)
<https://vacatures.uva.nl/UvA/job/PhD-position-at-the-frontier-of-Statistical-Physics%2C-Information-Theory-and-Mathematics/790845002/>
More details about the project: The main challenge in developing a general
theory of emergence is to understand how the complex behaviors of many
interacting units can give rise to a simpler macroscopic behaviour while
abstracting away the mechanistic details of the complex interactions. Over
the past century, the research on complex systems has focused on
identifying the microscopic interactions that may lead to such emergent
behavior, and emergence has been mainly studied on a case-by-case
basis. However,
the last decades have seen fast development in experimental techniques that
have enabled recording data from complex systems at both large scales and
high resolutions. This opens up the possibility to understand emergent
phenomena in real systems through the lens of data analysis, instead of
systems modeling.
During your PhD, you will explore a new approach to a theory of emergence,
by studying the structure of information in data from a topological
perspective and tackling the question of how *simpler *information
structures emerge. The project will build upon recent developments in two
different lines of research: on the topological structure of information
and statistical models on one hand, and on the information-theoretic
characterisation of what *simplicity *means on the other hand. We will
study in more detail the case of binary data, for which there exists a
well-understood complete family of statistical models (the physics-inspired
spin models with high-order interactions). To illustrate our approach, we
finally aim to apply it to artificial and real-world datasets.
All the best,
*Jo*
Jo Ellis-Monaghan
Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam
Editor, PRIMUS
Editor, Annales de l'Institut Henri Poincare D, Combinatorics, Physics and
their Interactions
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