Zoom Link: 
https://huji.zoom.us/j/84511564169?pwd=SkJmY285YnFIWkZqNmxuaVZsVVQ2UT09

Meeting ID: 845 1156 4169

Passcode:    171220


Title: 4 approaches to the enumeration of dual defective finite sets


Abstract:

With every finite set on a lattice can be associated a toric variety by the monomial map.The dual variety to the corresponding toric is called A-discriminant. Usually, A-discriminant is a hypersurface, except for special configurations A, called dual defective. For the last 20 years, at least four approaches were invented to enumerate such finite sets via tropicalization, non-splitting flags, iterated circuits and Cayley configurations. In 2021, Cattani and Dickenstein showed the equivalence of all four approaches and derived
relations between the related invariants. We will review these approaches and equivalence results.

Main article: 2105.00302v, Non-splitting flags, Iterated Circuits, σ-matrices and Cayley configurations,
Eduardo Cattani, Alicia Dickenstein

Approach 1: 0510126v3, Tropical Discriminants,
Alicia Dickenstein, Eva Maria Feichtner, and Bernd Sturmfels,
Approach 2: 0510615v2, Restriction of A-Discriminants and Dual Defect Toric Varieties
Raymond Curran and Eduardo Cattani
Approach 3: 0810.4996v3, Newton polyhedra of discriminants of projections
Alexander Esterov
Approach 4: 1605.05801v2, A combinatorial description of dual defects of toric varieties
Katsuhisa Furukawa and Atusushi Ito