{"id":1264,"date":"2018-11-04T14:28:20","date_gmt":"2018-11-04T12:28:20","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=1264"},"modified":"2018-11-14T20:50:31","modified_gmt":"2018-11-14T18:50:31","slug":"geometry-and-topology-seminar-8-nov-nicholas-meadows-title-quasi-categories-and-simpsons-theory-of-higher-stacks","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=1264","title":{"rendered":"Geometry and Topology Seminar, 8 NOV, Nicholas Meadows. Title “Quasi-Categories and Simpson’s Theory of Higher Stacks”"},"content":{"rendered":"

Department of Mathematics\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 University of \u00a0Haifa<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Geometry & Topology Seminar<\/u><\/strong><\/p>\n

Speaker:\u00a0\u00a0Nicholas Meadows(University of Haifa)<\/p>\n

Topic:\u00a0Quasi-Categories and Simpson’s Theory of Higher\u00a0Stacks<\/span><\/p>\n

Place:\u00a0\u00a0\u00a0 room 614 in the Science & Education Building<\/p>\n

Time\u00a0 \u00a012:10<\/p>\n

Date:\u00a0 Thursday, November 8, 2018<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Abstract<\/u><\/strong>:<\/u><\/strong><\/p>\n

Abstract: In their 2001 preprint, `Descent Pour Les N-Champs’ Hirschowitz and Simpson established a theory of $(\\infty, n)$-stacks<\/span>\u00a0for all integers n. Their work has had a large amount of influence on the Lurie and Toen approaches to derived algebraic geometry. The wider goal of Simpson’s research program was to develop tools to study non-abelian Hodge theory.<\/p>\n

<\/div>\n
<\/div>\n
In my thesis, I developed a model structure on simplicial presheaves on a small site in which the weak equivalences are maps that induce Joyal weak equivalences on stalks (the local Joyal model structure). The purpose of this talk is to explain how to reininterpret Simpson’s results on $(\\infty, 1)$-stacks<\/span>\u00a0using the Joyal and local Joyal model structure, which give a much more tractable presentation of the results.<\/div>\n
<\/div>\n
The results covered include a characterization of higher\u00a0stacks<\/span>\u00a0in terms of mapping space presheaves, and a general technique for constructing higher\u00a0stacks<\/span>\u00a0from presheaves of simplicial model categories on a site. This leads to the construction of the higher\u00a0stack<\/span>\u00a0of simplicial $\\mathcal{R}$-module spectra, where $\\mathcal{R}$ is a sheaf of rings on the site. This object is related to the problem of glueing together unbounded chain complexes along quasi-isomorphisms<\/div>\n","protected":false},"excerpt":{"rendered":"

Department of Mathematics\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 University of \u00a0Haifa \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Geometry & Topology Seminar Speaker:\u00a0\u00a0Nicholas Meadows(University of Haifa) Topic:\u00a0Quasi-Categories and Simpson’s Theory of Higher\u00a0Stacks Place:\u00a0\u00a0\u00a0 room 614 in the Science & Education Building Time\u00a0 \u00a012:10 Date:\u00a0 Thursday, November 8, 2018 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Abstract: Abstract: In their…
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