Session II.6 - Computational Algebraic Geometry
Poster
Multilinear Hyperquiver Representations
Tommi Muller
University of Oxford, United Kingdom - This email address is being protected from spambots. You need JavaScript enabled to view it.
We count singular vector tuples of a system of tensors. We do so by studying the generalisation of quivers to directed hypergraphs. Assigning vector spaces to its nodes and multilinear maps to the its hyperedges gives a hyperquiver representation. Hyperquiver representations generalise quiver representations (where all hyperedges are edges) and tensors (where there is only one multilinear map). The singular vectors of a hyperquiver representation are a compatible assignment of vectors to the nodes. We compute the dimension and degree of the the variety of singular vectors of a hyperquiver representation. Our formula specialises to the result of Friedland and Ottaviani to count the singular vector tuples of a generic tensor, as well as to the formula of Cartwright and Sturmfels to count the eigenvectors of a generic tensor.
Joint work with Vidit Nanda (University of Oxford, United Kingdom) and Anna Seigal (Harvard University, United States).