Différences

Ci-dessous, les différences entre deux révisions de la page.

--- workshop [2019/10/22 15:47] – weronika
+++ workshop [2019/11/03 21:09] (Version actuelle) – weronika
@@ Ligne 1: / Ligne 1: @@
 ====== Workshop "Real geometry in the footsteps of Gabriel Cramer"======
+** Geneva, 2019 , October 28th - November 1st, Villa Battelle **
 ----
@@ Ligne 5: / Ligne 7: @@
 Monday, October 28, 16:30, Battelle, Ilia Itenberg, "Planes in four-dimensional cubics".
-Tuesday, October 29, 11:45, Battelle, Nikita Kalinin, Talk 1
+Tuesday, October 29, 11:45, Battelle, Nikita Kalinin, "Symplectic packing problem".
-Tuesday, October 29,14:45, Battelle, Kristin Shaw, Minicourse
+Tuesday, October 29, 14:45, Battelle, Kristin Shaw, "Poincaré duality for tropical manifolds".
-Wednesday, October 30, 10:30, Battelle, Kristin Shaw, Minicourse
+Wednesday, October 30, 10:30, Battelle, Kristin Shaw, "Poincaré duality for tropical manifolds".
-Thursday, October 21, 11:00,Battelle, Kristin Shaw, Minicourse
+Thursday, October 31, 14:30,Battelle, Kristin Shaw, "Poincaré duality for tropical manifolds".
-Thursday, October 21,14:30, Battelle, Nikita Kalinin, Talk 2.
+Thursday, October 31, 16:00, Battelle, Nikita Kalinin,"Symplectic packing problem and Nagata's conjecture".
+Friday, November 1, 15:00, Battelle, Nikita Kalinin, "Symplectic packing problem and Nagata's conjecture".
+----
 **Abstracts:**
 ----
-Kristin Shaw, Minicourse **Poincaré duality for tropical manifolds**
+Ilia Itenberg (Sorbonne University)
+** Planes in four-dimensional cubics **
+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's theory of discriminant forms.
+Joint work with Alex Degtyarev and John Christian Ottem.
+----
+Kristin Shaw (University of Oslo)
+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.
@@ Ligne 33: / Ligne 58: @@
 ----
-Nikita Kalinin
+Nikita Kalinin (HSE University)
+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, Biran, among others).