GeoSTaR seminar

GeoSTaR is a traveling workshop/seminar focused on connections in symplectic, tropical, and real geometries. Previous editions have taken place at in Belalp, Switzerland and Sorbonne University. 

Registration

To register and submit a proposal for a talk please fill out this registration form

Speakers  

Ilia Itenberg (Sorbonne University) 

Felipe Rincón (Queen Mary London) 

Helge Ruddat (University of Stavanger) 

Talks and abstracts

Empty real plane sextic curves - Ilia Itenberg 

Many geometric questions about K3-surfaces can be restated and solved in purely arithmetical terms,by means of an appropriately defined homological type. We prove that the equisingular equivariant deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, that is, the polarization, exceptional divisors, and real structure recorded in the homology of the covering K3-surface. As an illustration,we obtain a deformation classification of real plane sextics with empty real part (for completeness, we consider the few non-simple ones as well). This is a joint work with Alex Degtyarev.

Tropicalising principal minors of positive definite matrices - Felipe Rincón

We study the tropicalisation of the image of the cone of positive definite matrices under the principal minor map. This polyhedral complex is a subset of M-concave functions on the discrete n-dimensional hypercube, and we show that it can be characterised as those functions that lie in the tropical flag variety, or equivalently, in a certain slice of the tropical Grassmannian. This is joint work with Abeer Al Ahmadieh, Cynthia Vinzant, and Josephine Yu. 

Canonical fans in the tangent spaces of the positive real locus of a cluster variety - Helge Ruddat

In the context of a joint work with Tom Bridgeland about the construction of twistor families, we discovered that the positive real locus of a finite type cluster variety has a canonical complete fan in each of its tangent spaces. The fans are typically not rational fans and they vary from point to point. Each cone in the fan is a tangent cone to the set of non-negative points as a subset of the real points for a particular cluster chart. There is also a deeper meaning to these fans as they are heart fans of the derived category of the Ginzburg path algebra of a quiver that underlies the cluster variety. Each fan can also be identified with the tropical cluster variety. The proof that the set of cones make a complete fan uses toric specialization.

Program

The program will consist of three talks followed by a discussion/open problem session in the afternoon. It will begin Friday morning and end in the afternoon.  

Organisers

Kris Shaw (University of Oslo)

Funding

This event is part of the CAS Young Fellows Project REACTIONS.