Organisateurs : Benoît Bertrand, Erwan Brugallé, Ilia Itenberg, Grigory Mikhalkin

Paris, 31 mars 2011

Institut de mathématiques de Jussieu, Jussieu, salle 1525-1-04

10h30 Accueil, café. (salle 1516-417)

11:00 Singular tropical hypersurfaces

Luis Felipe Tabera Alonso (Universidad de Cantabria)

Let us define a tropical singular point as the image, under the valuation, of a singular point over the field of Puiseux series.

We will present a pure tropical notion of singularity for a tropical hypersurface in arbitrary dimension. We will characterize the singular points of a hypersurface in terms of tropical Euler derivatives and show an algorithm to compute all singularities in a hypersurface.

As a related object, we will describe some non-transversal intersection of planar tropical curves (tangent intersection points). Joint work with Alicia dickenstein (U. Buenos Aires)

14:00 The phase limit set of a coamoeba

Frank Sottile (Texas A&M University)

A complex coamoeba is the image of a subvariety of a complex torus under the argument map to the real torus. Similarly, a non-archimedean coamoeba is the image of a subvariety of a torus over a complex Puiseaux field under its argument map. We describe the structure of non-archimedean coamoebae in terms of complex coamoebae and use the logarithmic limit set to describe the boundary of complex coamoebae. Detailed examples of lines in three-dimensional space illustrate and motivate these results. This is joint work with Mounir Nisse.

Plus de détails (page de Frank Sottile)

15h00 Pause café. (salle 1516-417)

15:30 Second cobounded cohomology and Hamiltonian group of surfaces

Rostislav Matveev (Universität Leipzig)