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On the toric ideal of a matroid
Termin:
21.10.2014, 17:00 Uhr bis 21.10.2014, 18:00 Uhr
Typ:
Kolloquium
Ort:
Universitätsplatz 2, G03 Raum 214, 39106 Magdeburg
Veranstalter:
Otto-von-Guericke-Universität Magdeburg Institut für Algebra und Geometrie (IAG)
Kontakt:
Jun.-Prof. Dr. Thomas Kahle
Im Rahmen unseres Oberseminares trägt vor Herr Michal Lason (Polish Academy of Sciences).
Der Vortrag findet statt im Raum G03-214.
Alle Interessierten sind herzlich eingeladen.
Abstract: Toric ideals is a certain class of ideals constructed using combinatorial data. When an ideal is defined only by combinatorial means, one expects to have a combinatorial description of its set of generators. An attempt to achieve this goal often leads to surprisingly deep combinatorial questions.
A conjecture of White is an example. It asserts that the toric ideal associated to a matroid is generated by quadratic binomials corresponding to symmetric exchanges. In the combinatorial language it means that if two multisets of bases of a matroid have equal union (as a multiset), then one can pass between them by a sequence of symmetric exchanges.
White's conjecture resisted numerous attempts since its formulation in 1980. We will discuss our (joint with Mateusz Michalek) recent results and present some related combinatorial problems.