Nonarchimedean and Tropical Geometry

February 1-7, 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

Monday
Johan de Jong A remark on a paper of Thuillier
Dustin Cartwright On homotopy types of analytifications. (PDF)
Yuri Tschinkel Igusa integrals and volume asymptotics in analytic and adelic geometry (joint work with A. Chambert-Loir) (PDF)
Open Problem Session Moderator: Ravi Vakil
June Huh A tropical approach to a Hodge conjecture for positive currents (PDF)
Tuesday
Mircea Mustata Weight functions and skeleta (PDF)
Chenyang Xu Skeleton and dual complex (PDF)
Johannes Nicaise Poles of maximal order of Igusa zeta functions (PDF)
Michael Temkin Metrization of differential pluriforms on Berkovich spaces (PDF)
Wednesday
Mattias Jonsson Solution to a non-Archimedean Monge-Ampere equation I (PDF)
Sebastien Boucksom Solution to a non-Archimedean Monge-Ampere equation II (PDF)
Walter Gubler A tropical approach to non-archimedean Arakelov theory (PDF)
Thursday
Sam Payne Tropical Brill–Noether theory and its applications I (PDF)
David Jensen Tropical Brill–Noether theory and its applications II (PDF)
Open Problem Session Moderator: Antoine Chambert-Loir
Vladimir Berkovich Complex analytic vanishing cycles for formal schemes (PDF)
Friday
Antoine Ducros Piecewise monomial skeleta (PDF)
Kiran Kedlaya Convergence polygons for connections on nonarchimedean curves (PDF)
Annette Werner Skeletons and tropicalizations (PDF)
Dan Abramovich Artin fans (PDF)

→ Download full agenda PDF

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

→ Download Participants PDF

 
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