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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.

FORMAT : The format of the conference changed due to the conditions related to the pandemic and the impossibility to maintain the funding for a further date. Unfortunately, for the same reasons, some of the original speakers have been obliged to canceled their participation. The list is not stable for the moment (we will be more precise about that as soon as possible).

In order to increase the connections between the participants, the new format includes chats and virtual rooms where everybody can ask questions about the talks. The talks are uploaded or performed in streaming.

Organizers:

Andrea Pulita (Université Grenoble Alpes, France) Ambrus Pal (Imperial College of London, UK)

Scientific Committee:

Konstantin Ardakov (Oxford University, UK) Jeffrey Giansiracusa (Swansea University, UK) Jérôme Poineau (Université de Caen Normandie, France)