Non-Archimedean and tropical geometry

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This is the webpage of a workshop on non-Archimedean and tropical geometry.
The event, originally scheduled to take place at the Institut für Mathematik of the Goethe-Universität Frankfurt am Main in 2020, will be replaced by a series of online talks between October and December 2021. More specifically, the seminars take place online on Zoom every other Friday afternoon (Central European Time) starting at the beginning of October, that is on the following dates: October 1st, 15th, and 29th, November 12th and 26th, and December 10th.
If the conditions allow it, the November 12th and the December 10th sessions will take place phisically in Frankfurt, and the November 26th session will take place at École Polytechnique. All the in-person seminars will also be livestreamed on Zoom.

Organizing committee: Lorenzo Fantini, Martin Ulirsch, Annette Werner.

Registration: Zoom links will be sent out by email to all registered participants. If you wish to be added to the mailing list please send an email to Lorenzo or to Martin.

Speakers

Schedule and abstracts

Friday, October 1st

This session will take place online on Zoom. Contact an organizer to receive a link.

14:00-15:00 (CET)
Antoine Ducros (Sorbonne University)
Non-standard analysis and non-archimedean geometry
In a joint work with E. Hrushovski and F. Loeser, we show that certain one-parameter families of complex integrals have a limit that can be expressed as an integral on a Berkovich space over the field ℂ((t)) (in the sense of the theory of integration of real differential forms on Berkovich spaces, developed by Chambert-Loir and myself). In this talk I will present this result, but rather focus on the general method we introduced to prove it, which we hope will be useful for a lot of other situations involving a "t-adic limit of one-parameter families of complex objects". It consists in introducing a huge non-standard model of ℂ also equipped with a non-archimedean absolute value; working on such a model enables by design to deal at the same time with limits of usual complex objects (through non-standard analysis) as well as with non-archimedean objects, allowing for a direct comparison between these two worlds.

15:15-16:15 (CET)
Joe Rabinoff (Duke University)
Weakly smooth forms and Dolbeault cohomology of curves
Gubler and I work out a theory of weakly smooth forms on non-Archimedean analytic spaces closely following the construction of Chambert-Loir and Ducros, but in which harmonic functions are forced to be smooth. We call such forms "weakly smooth". We compute the Dolbeault cohomology groups of rig-smooth, compact non-Archimedean curves with respect to this theory, and show that they have the expected dimensions and satisfy Poincaré duality. We carry out this computation by giving an alternative characterization of weakly smooth forms on curves as pullbacks of certain "smooth forms" on a skeleton of the curve. This yields an isomorphism between the Dolbeault cohomology of the skeleton, which can be computed using standard combinatorial methods, and the Dolbeault cohomology of the curve.
This work is joint with Walter Gubler.

16:30-17:30 (CET)
Tony Yue Yu (California Institute of Technology)
Title TBA
Coming soon!

Friday, October 15th

This session will take place online on Zoom. Contact an organizer to receive a link.

14:00-15:00 (CET)
Kris Shaw (University of Oslo)
Title TBA
Coming soon!

15:15-16:15 (CET)
Melody Chan (Brown University)
Title TBA
Coming soon!

16:30-17:30 (CET)
Daniele Turchetti (Durham University)
Title TBA
Coming soon!


Friday, October 29th

This session will take place online on Zoom. Contact an organizer to receive a link.

14:00-15:00 (CET)
Elise Goujard (Bordeaux University)
Title TBA
Coming soon!

15:15-16:15 (CET)
Walter Gubler (University of Regensburg)
Title TBA
Coming soon!

16:30-17:30 (CET)
Navid Nabijou (University of Cambridge)
Title TBA
Coming soon!


Friday, November 12th

If the conditions allow it, this session will take place in the Hilbertraum, Room 302 of the Institut für Mathematik (Robert-Mayer-Str. 6, Frankfurt am Main, Germany).
The talks will also be livestreamed on Zoom. Contact an organizer to receive a link.

14:00-15:00 (CET)
Jan Steffen Müller (University of Groningen)
Title TBA
Coming soon!

15:15-16:15 (CET)
Klaus Künnemann (University of Regensburg)
Title TBA
Coming soon!

16:30-17:30 (CET)
Stefan Wewers (Ulm University)
Title TBA
Coming soon!


Friday, November 26th

If the conditions allow it, this session will take place in the Seminar Room of the Centre de Mathématiques Laurent Schwartz of the École Polytechnique (Palaiseau, France). Information on how to reach the department with public transport can be found here.
The talks will also be livestreamed on Zoom. Contact an organizer to receive a link.

14:00-15:00 (CET)
Vlerë Mehmeti (University Paris-Saclay)
Title TBA
Coming soon!

15:15-16:15 (CET)
Erwan Brugallé (Nantes University)
Title TBA
Coming soon!

16:30-17:30 (CET)
Jérôme Poineau (University of Caen Normandy)
Title TBA
Coming soon!

Friday, December 10th

If the conditions allow it, this session will take place in the Hilbertraum, Room 302 of the Institut für Mathematik (Robert-Mayer-Str. 6, Frankfurt am Main, Germany).
The talks will also be livestreamed on Zoom. Contact an organizer to receive a link.

14:00-15:00 (CET)
Claudia Fevola (Max Planck Institute Leipzig)
Title TBA
Coming soon!

15:15-16:15 (CET)
David Holmes (Leiden University)
Title TBA
Coming soon!

16:30-17:30 (CET)
Dimitri Wyss (École Polytechnique Fédérale de Lausanne)
Title TBA
Coming soon!

Practical information

LOEWE

If you have any questions you can get in touch with Lorenzo Fantini and/or Martin Ulirsch.

The workshop is funded by the LOEWE Research Unit Uniformized structures in arithmetic and geometry and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) projects 456557832 and 444845124, the SFB 326 Geometry and Arithmetic of Uniformized Structures.


GAUS