{"http:\/\/dx.doi.org\/10.14288\/1.0384906":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Non UBC","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Luc\u00eda Mart\u00edn-Merch\u00e1n","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2019-11-03T10:23:06Z","type":"literal","lang":"en"},{"value":"2019-05-06T14:30","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"In this talk we explain how to describe pure types of $\\mathrm{Spin}(7)$ structures in terms of spinors and focus on the construction of balanced examples. An $8$-dimensional Riemannian manifold admitting a $\\mathrm{Spin}(7)$ structure determined by a $4$-form $\\Omega$ is spin and the structure can also be described in terms of a spinor $\\eta$. Balanced $\\mathrm{Spin}(7)$ structures are a pure class and are characterized by the equation $(\\ast d\\Omega)\\wedge \\Omega=0$ or, equivalently, by the condition that $\\eta$ is harmonic, that is, $D \\eta=0$ where $D$ is the Dirac operator. For our purposes, the description of balanced structures in terms of spinors turns out to be much simpler. Our examples are products $(N\\times T,g+g_k)$, where $(N,g)$ is a $k$-dimensional nilmanifold endowed with a left-invariant metric, $(T,g_k)$ is an $(8-k)$-dimensional flat torus, and $k=5,6$. Under these assumptions, the presence of a left-invariant balanced $\\mathrm{Spin}(7)$ structure on the product is equivalent to the fact that $(N,g)$ admits a left-invariant non-zero harmonic spinor. For this reason we search left-invariant metrics on $N$ that admit left-invariant harmonic spinors. The results of our investigation are a list of $5$ and $6$-dimensional nilmanifolds that verify this condition, and the description of the set of left-invariant metrics with left-invariant harmonic spinors in the particular case $k=5$.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/72172?expand=metadata","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/extent":[{"value":"59.0 minutes","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/elements\/1.1\/format":[{"value":"video\/mp4","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"","type":"literal","lang":"en"},{"value":"Author affiliation: Universidad Complutense de Madrid","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/spatial":[{"value":"Oaxaca (Mexico : State)","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt":[{"value":"10.14288\/1.0384906","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/language":[{"value":"eng","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#peerReviewStatus":[{"value":"Unreviewed","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/provider":[{"value":"Vancouver : University of British Columbia Library","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/publisher":[{"value":"Banff International Research Station for Mathematical Innovation and Discovery","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/rights":[{"value":"Attribution-NonCommercial-NoDerivatives 4.0 International","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#rightsURI":[{"value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#scholarLevel":[{"value":"Graduate","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/isPartOf":[{"value":"BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/subject":[{"value":"Mathematics","type":"literal","lang":"en"},{"value":"Differential Geometry, Geometry, Differential Geometry","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/title":[{"value":"A spinorial approach to the construction of balanced Spin(7) manifolds","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/type":[{"value":"Moving Image","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#identifierURI":[{"value":"http:\/\/hdl.handle.net\/2429\/72172","type":"literal","lang":"en"}]}}