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SUMMARY:Lukas Kühne (Max Planck Institute of Mathematics in the Sciences)
DTSTART:20210318T151500Z
DTEND:20210318T170000Z
DTSTAMP:20260422T065511Z
UID:CJCS/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/9/">Inv
 estigating Terao's freeness conjecture with computer algebra</a>\nby Lukas
  Kühne (Max Planck Institute of Mathematics in the Sciences) as part of C
 openhagen-Jerusalem Combinatorics Seminar\n\n\nAbstract\nMotivated by sing
 ularity theory\, Hiroaki Terao introduced a module of logarithmic derivati
 ons associated with a hyperplane arrangement. This talk is concerned with 
 Terao’s freeness conjecture which asserts that the freeness of this deri
 vation module is determined by the underlying combinatorics of the arrange
 ment.\n\nTo investigate this conjecture\, we have enumerated all matroids 
 of rank 3 with up to 14 hyperplanes whose characteristic polynomial splits
  over the integers and saved it in a public database. Using the GAP packag
 e ZariskiFrames we have computed the moduli space and the free locus of th
 e derivation module of each of these matroids as a quasi-affine set. As th
 e main result\, this yields a computational proof of Terao’s freeness co
 njecture for rank 3 arrangements with up to 14 hyperplanes in arbitrary ch
 aracteristic.\n\nIn this talk\, I will explain the background of this conj
 ecture without assuming prior knowledge and demonstrate the database and h
 ighlights of the computations.\n\nThis talk is based on joint work with Mo
 hamed Barakat\, Reimer Behrends\, Christopher Jefferson\, and Martin Lerne
 r.\n
LOCATION:https://researchseminars.org/talk/CJCS/9/
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