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The theory of?Berkovich spaces?is a powerful and elegant approach to analytic geometry over non-archimedean fields. Over the past decade it has found many striking applications in areas such as?arithmetic geometry, p-adic differential equations, and dynamics. Running through many of these recent developments is a thread of tropical geometry. In some cases the tropical link is already firmly established, while in others it is not yet more than a promising hint. Our view is that there is now an exciting potential to forefront the role of?Tropical geometry?while exploring the application of Berkovich theory in the intersecting areas of?arithmetic D-modules, non-archimedean representation theories?and?p-adic local systems. This conference brings together leading experts in each of these areas in order to energize this vision and establish appropriate links.

With this workshop we would like to promote the interaction between the following five fields:
Berkovich spaces
Tropical geometry
p-adic differential equations
Arithmetic D-modules and representations of p-adic Lie groups
Arithmetic applications of p-adic local systems

While the first two are already tightly linked, the role of Berkovich spaces in the last ones is only emerging and within this, the role of tropical geometry has not yet been explored. More generally, we consider this conference to be a good opportunity to study new techniques recently introduced into the field. We are convinced that each of these areas has plenty of potential and that a fruitful interaction between them might nourish their development. The aim of the conference is precisely to give leading experts in these each of these domains the opportunity to meet, present their last results and open challenges, and encourage an exchange that will drive forward these exciting and rapidly developing subjects.

Workshop organisers

Dr Ambrus Pal
Professor Andrea Pulita

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For more information including list of invited speakers, registration, programme and practical details please see the workshop website

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