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SUMMARY:Sira Gratz
DTSTART:20210421T140000Z
DTEND:20210421T150000Z
DTSTAMP:20260423T022713Z
UID:TRAC/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TRAC/16/">Hi
 gher SL(k)-friezes</a>\nby Sira Gratz as part of The TRAC Seminar - Théor
 ie de Représentations et ses Applications et Connections\n\n\nAbstract\nC
 lassical frieze patterns are combinatorial structures which relate back to
  Gauss’ Pentagramma Mirificum\, and have been extensively studied by Con
 way and Coxeter in the 1970’s.\n\nA classical frieze pattern is an array
  of numbers satisfying a local (2 × 2)- determinant rule. Conway and Coxe
 ter gave a beautiful and natural classification of SL(2)-friezes via trian
 gulations of polygons. One way to generalise the notion of a classical fri
 eze pattern is to ask of such an array to satisfy a (k × k)-determinant r
 ule instead\, for k at least 2\, leading to the notion of higher SL(k)-fri
 ezes. While the task of classifying classical friezes yields a very satisf
 ying answer\, higher SL(k)-friezes are not that well understood to date.\n
 \nIn this talk\, we’ll discuss how one might start to fathom higher SL(k
 )-frieze patterns. The links between frieze patterns and cluster combinato
 rics encoded by triangulations of polygons in the k=2 case suggests a link
  to Grassmannian varieties under the Plücker embedding and the cluster al
 gebra structure on their homogeneous coordinate rings. We find a way to ex
 ploit this relation for higher SL(k)-friezes and provide an easy way to ge
 nerate SL(k)-friezes via Grassmannian combinatorics.\n\nThis talk is based
  on joint work with Baur\, Faber\, Serhiyenko and Todorov.\n
LOCATION:https://researchseminars.org/talk/TRAC/16/
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