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SUMMARY:Multilinear hyperquiver representations - Tommi Muller (University
  of Oxford)
DTSTART:20240118T143000Z
DTEND:20240118T151500Z
UID:TALK210622@talks.cam.ac.uk
DESCRIPTION:We count singular vector tuples of a system of tensors assigne
 d to the edges of a directed hypergraph. To do so\, we study the generalis
 ation of quivers to directed hypergraphs. Assigning vector spaces to the n
 odes of a hypergraph and multilinear maps to its hyperedges gives a hyperq
 uiver representation. Hyperquiver representations generalise quiver repres
 entations (where all hyperedges are edges) and tensors (where there is onl
 y one multilinear map). The singular vectors of a hyperquiver representati
 on are a compatible assignment of vectors to the nodes. We compute the dim
 ension and degree of the variety of singular vectors of a sufficiently gen
 eric hyperquiver representation. Our formula specialises to known results 
 that count the singular vectors and eigenvectors of a generic tensor.
LOCATION:Seminar Room 2\, Newton Institute
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