Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems
algebraic geometry number theory
| Audience: | Advanced learners |
| Conference dates: | 08-Dec-2020 to 10-Dec-2020 |
| Organizers: | ANDREA PULITA*, AMBRUS PAL |
| *contact for this listing |
DESCRIPTION
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 switched to a virtual form due to the conditions related to the pandemic and the impossibility to maintain the funding for a further date. We also decided to shrink the global time in front of the screen, because in this exceptional period almost everybody has personal or teaching duties. Moreover, we need to take into account the fact that the speakers come from different time zones. For this reason the schedule of live-talks is reduced to the short interval of time which is (relatively) compatible with European and US working time. The other talks are pre-recorded and can be watched by the audience in the complement of the schedule time. In order to increase the connections between the participants, the new format includes a system of chats where the participants can communicate and ask questions about the talks. For every talk, you find a link to a dedicated virtual room that permits to the audience to communicate with the speakers using ZULIP (an open source chat and collaborative software). You will be asked to register to ZULIP. We will maintain ZULIP ongoingly active for the total time of the conference (day and night) in order to permit exchanges between people of different time zones. All talks will be recorded and uploaded as soon as possible (ideally few time after the talk) in the dedicated page.