Non-Archimedean and Tropical Geometry (2015)
Organizers:
Matt Baker, Georgia Institute of Technology
Same Payne, Yale University
This symposium focused on setting a clear agenda for future developments in the related fields of tropical and nonarchimedean analytic geometry. One of the goals of the meeting was to produce high-quality expository material presenting the methods, results and ambitions of these active research areas. Another was to identify problems in other fields of mathematics that could be amenable to tropical and nonarchimedean analytic methods and establish new rigorous links with those neighboring fields.
Topics discussed included:
- Connections between birational geometry, minimal model program, and skeletons of Berkovich spaces
- The recent work of Mustata, Nicaise, and Xu, which relates Kontsevich-Soibelman skeletons of Berkovich spaces to skeletons of SNC formal models
- Existence and uniqueness of solutions to nonarchimedean Monge Ampere by Boucksom, Favre and Jonsson, and Yuan and Zhang
- Possible applications of existence and uniqueness for nonarchimedean partial differential equations in birational and arithmetic geometry
- Relations between as well as applications of various notions of higher dimensional potential theory on Berkovich spaces
Agenda, Notes & Materials
Organizers Matt Baker and Sam Payne provided the following documents that highlight open problems and topics discussed at the Non-Archimedean and Tropical Geometry symposium.
• Summary (PDF)
• Problem Session Notes (PDF)
Organizers’ site: http://users.math.yale.edu/~sp547/SimonsSymposium2015.html
Participants
| Dan Abramovich | Brown University |
| Matt Baker | Georgia Tech |
| Vladimir Berkovich | Weizman Institute |
| Sebastian Boucksom | Paris 6 |
| Dustin Cartwright | Yale University |
| Antoine Chambert-Loir | Université Paris-Sud |
| Johan de Jong | Columbia University |
| Antoine Ducros | Paris 6 |
| Tyler Foster | University of Michigan |
| Walter Gubler | University of Regensburg |
| June Huh | Princeton / IAS / Clay Math Institute |
| David Jensen | University of Kentucky |
| Mattias Jonsson | University of Michigan |
| Kiran Kedlaya | UC San Diego |
| Klaus Künnemann | Universität Regensburg |
| Mircea Mustata | University of Michigan |
| Johannes Nicaise | KU Leuven |
| Sam Payne | Yale University |
| Joe Rabinoff | Georgia Tech University |
| Michael Temkin | Einstein Institute of Mathematics |
| Yuri Tschinkel | Simons Foundation |
| Ravi Vakil | Stanford University |
| Annette Werner | Goethe-Universität Frankfurt |
| Chenyang Xu | Beijing International Center of Mathematics Research |