Date:
Thu, 26/01/202313:00-14:00
Location:
Levy 6 hall and Zoom
Location: Levy 6 hall and Zoom
Zoom Link: https://huji.zoom.us/j/84511564169?pwd=SkJmY285YnFIWkZqNmxuaVZsVVQ2UT09
Meeting ID: 845 1156 4169
Passcode: 171220
Title: On the strongly robustness property of toric ideals
Abstract: To every toric ideal one can associate an oriented matroid structure, consisting of a graph and another toric ideal, called bouquet ideal. The connected components of this graph are called bouquets. Bouquets are of three types: free, mixed and non mixed. We prove that the cardinality of the following sets - the set of indispensable elements, minimal Markov bases, the Universal Markov basis and the Universal Gröbner basis of a toric ideal - depends only on the type of the bouquets and the bouquet ideal. These results enable us to introduce the strongly robustness simplicial complex and show that it determines the strongly robustness property. For codimension 2 toric ideals, we study the strongly robustness simplicial complex and prove that robustness implies strongly robustness. This is joint work with Apostolos Thoma and Marius Vladoiu.
Zoom Link: https://huji.zoom.us/j/84511564169?pwd=SkJmY285YnFIWkZqNmxuaVZsVVQ2UT09
Meeting ID: 845 1156 4169
Passcode: 171220
Title: On the strongly robustness property of toric ideals
Abstract: To every toric ideal one can associate an oriented matroid structure, consisting of a graph and another toric ideal, called bouquet ideal. The connected components of this graph are called bouquets. Bouquets are of three types: free, mixed and non mixed. We prove that the cardinality of the following sets - the set of indispensable elements, minimal Markov bases, the Universal Markov basis and the Universal Gröbner basis of a toric ideal - depends only on the type of the bouquets and the bouquet ideal. These results enable us to introduce the strongly robustness simplicial complex and show that it determines the strongly robustness property. For codimension 2 toric ideals, we study the strongly robustness simplicial complex and prove that robustness implies strongly robustness. This is joint work with Apostolos Thoma and Marius Vladoiu.