Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems

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algebraic geometry number theory

Imperial College London

Audience: Advanced learners
Conference dates: 08-Dec-2020 to 10-Dec-2020
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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.


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.

Upcoming talks
Past talks
Your timeSpeakerTitle
ThuDec 1017:00Kiran S. KedlayaDrinfeld's lemma for F-isocrystals.
ThuDec 1017:00Andreas BodeBornological D-modules on rigid analytic spaces.
ThuDec 1017:00Michel GrosTwisted local Simpson correspondence and crystals on the $q$-crystalline and prismatic sites.
ThuDec 1017:00Christian Liedtkep-adic Tate conjectures and abeloid varieties.
ThuDec 1017:00Tobias SchmidtD-modules and irreducibility results for locally analytic representations.
ThuDec 1017:00Veronika ErtlPoincaré duality in rigid analytic Hyodo-Kato theory.
ThuDec 1017:00Richard CrewIntegral p-adic cohomology theories.
ThuDec 1017:00Martin UlirschNon-Archimedean uniformization and tropicalization: Teichmueller space and the moduli space of curves.
ThuDec 1017:00Michael TemkinTropical reduction and lifting theorems.
ThuDec 1017:00Annette WernerOn p-adic vector bundles and local systems.
ThuDec 1015:00Roman BezrukavnikovDerived Cartier transform, derived Satake equivalence and cohomology.
ThuDec 1014:00Wiesława NiziołComparison theorems for p-adic analytic varieties.
ThuDec 1013:00Tomoyuki AbeArithmetic D-modules and rigid cohomologies
WedDec 0915:00Jeffrey GiansiracusaA general theory of tropical differential equations.
WedDec 0914:00Masha VlasenkoDwork's congruences and p-adic cohomology.
WedDec 0913:00Christine HuygheArithmetic differential operators with overconvergent coefficients.
TueDec 0815:00HELENE ESLAULTConnections and symmetric differentials.
TueDec 0814:00ALEX FINKTropical differential equations and their solutions.
TueDec 0813:00Mattias JonssonK-stability from a non-Archimedean perspective.
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