workshop
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Les deux révisions précédentesRévision précédenteProchaine révision | Révision précédente | ||
workshop [2019/10/22 15:47] – weronika | workshop [2019/11/03 21:09] (Version actuelle) – weronika | ||
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====== Workshop "Real geometry in the footsteps of Gabriel Cramer" | ====== Workshop "Real geometry in the footsteps of Gabriel Cramer" | ||
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+ | ** Geneva, 2019 , October 28th - November 1st, Villa Battelle ** | ||
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Monday, October 28, 16:30, Battelle, Ilia Itenberg, " | Monday, October 28, 16:30, Battelle, Ilia Itenberg, " | ||
- | Tuesday, October 29, 11:45, Battelle, Nikita Kalinin, | + | Tuesday, October 29, 11:45, Battelle, Nikita Kalinin, |
- | Tuesday, October 29,14:45, Battelle, Kristin Shaw, Minicourse | + | Tuesday, October 29, 14:45, Battelle, Kristin Shaw, " |
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+ | | ||
- | Wednesday, October 30, 10:30, Battelle, Kristin Shaw, Minicourse | + | Wednesday, October 30, 10:30, Battelle, Kristin Shaw, " |
- | Thursday, October | + | Thursday, October |
- | Thursday, October | + | Thursday, October |
+ | Friday, November 1, 15:00, Battelle, Nikita Kalinin, " | ||
+ | |||
+ | ---- | ||
**Abstracts: | **Abstracts: | ||
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- | Kristin Shaw, Minicourse **Poincaré duality for tropical manifolds** | + | Ilia Itenberg (Sorbonne University) |
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+ | ** Planes in four-dimensional cubics ** | ||
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+ | We discuss possible numbers of 2-planes in a smooth cubic hypersurface in the 5-dimensional projective space. | ||
+ | We show that, in the complex case, the maximal number of planes is 405, the maximum being realized by the Fermat cubic. | ||
+ | In the real case, the maximal number of planes is 357. | ||
+ | |||
+ | The proofs deal with the period spaces of cubic hypersurfaces in the 5-dimensional complex projective space | ||
+ | and are based on the global Torelli theorem and the surjectivity of the period map for these hypersurfaces, | ||
+ | as well as on Nikulin' | ||
+ | |||
+ | Joint work with Alex Degtyarev and John Christian Ottem. | ||
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+ | |||
+ | ---- | ||
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+ | Kristin Shaw (University of Oslo) | ||
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+ | Minicourse: **Poincaré duality for tropical manifolds** | ||
The series of lectures will focus on the different formulations and approaches to Poincaré duality for the tropical homology group of tropical manifolds. | The series of lectures will focus on the different formulations and approaches to Poincaré duality for the tropical homology group of tropical manifolds. | ||
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- | Nikita Kalinin | + | Nikita Kalinin |
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+ | Talk 1: **Symplectic packing problem.** | ||
+ | This will be an introductory talk. I will mention several instances of symplectic packing problems and present simple geometric methods for tackling them. Based on (unpublished) survey of Felix Schlink. | ||
- | Talk 1: | + | Talk 2: **Symplectic packing problem and Nagata’s conjecture.** |
- | + | Curiously, the question of what is the maximal R such that we can embed k<10 symplectic balls of radius R in CP^2 is related to the question of what is the minimal degree d of an algebraic curve in CP^2 passing through given generic points with given multiplicities. Nagata’s conjecture (still open for all n>10 except squares) states that d>m\sqrt n if we draw a curve through n points of multiplicity m. I will highlight the connections between symplectic packing and Nagata’s conjecture (based on works of McDuff, Polterovich, | |
workshop.1571752079.txt.gz · Dernière modification : 2019/10/22 15:47 de weronika