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Michal Lason: On some structures on matroids and related algebraic problems

Tid: Ti 2018-02-27 kl 14.00 - 15.00

Plats: Seminar Hall Kuskvillan, Institut Mittag-Leffler

Medverkande: Michal Lason, University of Bern

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When an ideal is defined only by combinatorial means, one expects to have a combinatorial description of its algebraic invariants. An attempt to achieve this description often leads to surprisingly deep combinatorial questions. White's conjecture is an example. It asserts that the toric ideal associated to a matroid is generated by quadratic binomials corresponding to symmetric exchanges. Another example is a question of Herzog and Hibi about existence of a quadratic Gröbner basis of the toric ideal of a matroid. Both problems reduce to questions about arrangements of bases in a matroid. We will review recent progress and state some intriguing problems.