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DTSTART;TZID=America/Toronto:20260116T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-tamas-schwarcz-interaction-between-skew
SUMMARY:Tutte Colloquium - Tamas Schwarcz- Interaction between\nskew-repre
 sentability\, tensor products\, extension properties\, and rank\ninequalit
 ies
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Tamas Schwarcz\n\nAFFILIATION:\n London School of Ec
 onomics\n\nLOCATION:\n MC 5501\n\nABSTRACT:  The study of matroid tensor
  products dates back to the\n1970s\, extending the tensor operation from l
 inear algebra to the\ncombinatorial setting. While any two matroids repres
 entable over the\nsame field admit a tensor product via the Kronecker prod
 uct of\nmatrices\, Las Vergnas showed that such products do not exist for\
 nmatroids in general\, leaving the area underexplored. In this work\, we\n
 utilize this operation to study skew-representability —\nrepresentation 
 over division rings that need not be commutative — by\nproving that a ma
 troid is skew-representable if and only if it admits\niterated tensor prod
 ucts with specific test matroids. A key\nconsequence is the existence of a
 lgorithmic certificates for\nnon-representability. We further show that ev
 ery rank-3 matroid admits\na tensor product with any uniform matroid\, con
 structing the unique\nfreest such product. Finally\, we demonstrate the po
 wer of this\nframework by deriving the first known linear rank inequality 
 for\n(folded skew-)representable matroids that is independent of the commo
 n\ninformation property. \n\nJoint work with Kristóf Bérczi\, Boglárka
  Gehér\, András Imolay\,\nLászló Lovász\, and Carles Padró.
DTSTAMP:20260418T113639Z
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