Matroid Theory Seminar - Ahmad Abdi

Title Minimally non-ideal clutters

Abstract: Together with Bertrand Guenin, we recently proved that, the lines of the Fano plane as well as the odd circuits of K5, constitute the only binary clutters with a triangle that are minimally non-ideal. Having taken us more than three years, our proof is just as interesting as the statement, and it uses many tools from different areas. While proving an important special case of Seymour's 1977 Flowing Conjecture, this result as well as the developed tools pave the way for attacking the general case. In this talk, I will sketch our proof.