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SUMMARY:Alex Fink (Queen Mary University of London)
DTSTART:20240605T160000Z
DTEND:20240605T170000Z
DTSTAMP:20260423T021422Z
UID:CG-BLT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CG-BLT/4/">S
 peyer's g conjecture and Betti numbers for a pair of matroids</a>\nby Alex
  Fink (Queen Mary University of London) as part of Combinatorics and Geome
 try BLT Seminar\n\n\nAbstract\nIn 2009\, looking to bound the face vectors
  of matroid subdivisions and tropical linear spaces\, Speyer introduced th
 e g-invariant of a matroid. He proved its coefficients nonnegative for mat
 roids representable in characteristic zero and conjectured this in general
 . Later\, Shaw and Speyer and I reduced the question to positivity of the 
 top coefficient. This talk will overview work in progress with Berget that
  proves the conjecture.\n\nGeometrically\, the main ingredient is a variet
 y obtained from projection away from the base of the matroid tautological 
 vector bundles of Berget--Eur--Spink--Tseng\, and its initial degeneration
 s. Combinatorially\, it is an extension of the definition of external acti
 vity to a pair of matroids and a way to compute it using the fan displacem
 ent rule. The work of Ardila and Boocher on the closure of a linear space 
 in (P^1)^n is a special case.\n
LOCATION:https://researchseminars.org/talk/CG-BLT/4/
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