YouTube recording: https://www.youtube.com/watch?v=6hmhSYado9Q

Time: Thursday, Feb 16, 3pm EST (8pm GMT, 9am Fri NZDT)
Zoom: https://gatech.zoom.us/j/8802082683

Speaker: Relinde Jurrius, Netherlands Defense Academy
Title: The combinatorial derived matroid
Abstract: The question of “dependencies between dependencies” in matroids has been raised in the 1960’s by Rota and Crapo, in various formulations (here is a nice overview elsewhere on this blog: matroidunion.org/?p=2628). For a matroid $M$, the derived matroid is a matroid that has as ground set the set of (co)circuits of $M$. Over time, various definitions of a derived matroid have been proposed. However, none of them completely solved the question of Rota and Crapo: these definitions depend on a representation, for example, or are not unique, or don’t always exist.
In a recent paper with Olga Kuznetsova and Ragnar Freij-Hollanti, we proposed a definition of a derived matroid that is purely combinatorial. The combinatorial derived matroid is defined via the rank function of $M$, and via an operation that resembles a closure operation on the collection of dependent sets. It is therefore uniquely defined for any matroid. In this talk I will motivate this definition and discuss some examples and desirable properties of this definition. Time permitting we will discuss open questions and links to previous definitions.