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SUMMARY:Oliver Lorscheid (IMPA)
DTSTART:20201125T183000Z
DTEND:20201125T200000Z
DTSTAMP:20260423T021705Z
UID:BRAG/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BRAG/34/">Th
 e moduli space of matroids</a>\nby Oliver Lorscheid (IMPA) as part of Braz
 ilian algebraic geometry seminar\n\n\nAbstract\nMatroids are combinatorial
  gadgets that reflect properties of linear algebra in situations where thi
 s latter theory is not available. This analogy prescribes that the moduli 
 space of matroids should be a Grassmannian over a suitable base object\, w
 hich cannot be a field or a ring\; in consequence usual algebraic geometry
  does not provide a suitable framework. In joint work with Matt Baker\, we
  have used algebraic geometry over the so-called field with one element to
  construct such moduli spaces. As an application\, we streamline various r
 esults of matroid theory and find simplified proofs of classical theorems\
 , such as the fact that a matroid is regular if and only if it is binary a
 nd orientable.\n\nWe will dedicate the first part of this talk to an expos
 ition of matroids. Then we will briefly outline how to construct the modul
 i space of matroids. In a last part\, we will explain with some care why t
 his theory is useful to simplify classical results in matroid theory.\n
LOCATION:https://researchseminars.org/talk/BRAG/34/
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