{"id":183,"date":"2020-09-16T06:17:37","date_gmt":"2020-09-16T06:17:37","guid":{"rendered":"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/?page_id=183"},"modified":"2021-09-28T09:23:33","modified_gmt":"2021-09-28T09:23:33","slug":"hyperkahler-geometry","status":"publish","type":"page","link":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/hyperkahler-geometry\/","title":{"rendered":"Hyperk\u00e4hler Geometry"},"content":{"rendered":"<p>The speakers for the third session, <em>Hyperk\u00e4hler Geometry<\/em>, are:<\/p>\n<ul>\n<li><a href=\"http:\/\/www.math.uni-bonn.de\/~huybrech\/\">Daniel Huybrechts<\/a> (Universit\u00e4t Bonn): &#8220;<em>3 families of K3 surfaces<\/em>&#8221;<br \/>\n<em>Abstract.<\/em> I will review three one-dimensional families of K3 surfaces (twistor, Brauer or Tate-Shafarevich, and Dwork) and explain how, from a purely Hodge-theoretic perspective, they fit into one picture. I am particularly interested in understanding how certain properties propagate along those families.<\/li>\n<li><a href=\"https:\/\/bakker.people.uic.edu\/\">Benjamin Bakker<\/a> (University of Illinois at Chicago): &#8220;<em>Towards a BBDGGHKP decomposition theorem for nonprojective Calabi\u2013Yau varieties<\/em>&#8221; &#8211; <a href=\"https:\/\/drive.google.com\/file\/d\/1CV7WS4pCoLihAErFeNEdte9nLA1oELsW\/view?usp=sharing\"><em>slides<\/em><\/a><br \/>\n<em>Abstract.<\/em> Calabi-Yau manifolds are built out of simple pieces by the Beauville\u2013Bogomolov decomposition theorem: any Calabi\u2013Yau Kahler manifold up to an etale cover is a product of complex tori, irreducible holomorphic symplectic manifolds, and strict Calabi-Yau manifolds (which have no holomorphic forms except a holomorphic volume form). Work of Druel\u2013Guenancia\u2013Greb\u2013Horing\u2013Kebekus\u2013Peternell over the last decade has culminated in a generalization of this result to projective Calabi\u2013Yau varieties with the kinds of singularities that arise in the MMP, and the proofs heavily use algebraic methods. In this talk I will describe some work in progress with C. Lehn and H. Guenancia extending the decomposition theorem to nonprojective varieties via deformation theory. I will also discuss applications to the K-trivial case of a conjecture of Peternell asserting that any minimal Kahler space can be approximated by algebraic varieties.<\/li>\n<li><a href=\"https:\/\/users-math.au.dk\/swann\/\">Andrew Swann<\/a> (Aarhus University): &#8220;<em>HyperK\u00e4hler metrics and symmetries<\/em><span style=\"font-size: 1rem\">&#8221; &#8211; <a href=\"https:\/\/users-math.au.dk\/swann\/talks\/TACoS-2020.pdf\"><em>slides<\/em><\/a><br \/>\n<\/span><em>Abstract.<\/em> HyperK\u00e4hler metrics are surveyed and discussed from the point of view of Lie group symmetries, so principally in the non-compact case. This includes the Gibbons-Hawking ansatz in dimension four, cotangent bundles, coadjoint orbits. A common theme is quotient constructions and various ideas related to symplectic reduction. Relations to other geometric structures naturally arise and show that metrics of indefinite signature have an important role.<\/li>\n<li><a href=\"https:\/\/webusers.imj-prg.fr\/~claire.voisin\/\">Claire Voisin<\/a> (Coll\u00e8ge de France): &#8220;<em>On the Lefschetz standard conjecture for hyper-K\u00e4hler manifolds<\/em>&#8221;<br \/>\n<em>Abstract.<\/em> The Lefschetz standard conjecture is of major importance in the theory of motives. It is open starting from degree 2 and in that degree, it predicts that any holomorphic 2-form on a smooth projective manifold is induced from a 2-form on a surface by a correspondence. I will discuss some results and further expectations in the hyper-K\u00e4hler setting.<\/li>\n<\/ul>\n<p>The schedule of the conference is the following:<\/p>\n<ul>\n<li><em>Release of the videos:<\/em> November 3rd, 2020 &#8211; Taco Tuesday (<a href=\"https:\/\/www.youtube.com\/playlist?list=PLOtduZ_kVlcguqpbsNqlvVo7BaQjAmDrK\">YouTube<\/a>)<\/li>\n<li><em>Discussion:<\/em> November 3rd through November 18th, 2020 (<a href=\"https:\/\/gitter.im\/GTACOS-November2020\/\">Gitter<\/a>)<\/li>\n<li><em>Coffee break:<\/em> November 18th, 2020, at 17:00(CET &#8211; <em><a href=\"https:\/\/www.timeanddate.com\/worldclock\/converter.html?iso=20201118T160000&amp;p1=341\">check your local time<\/a>!<\/em>) (<a href=\"https:\/\/lmu-munich.zoom.us\/j\/92108810695?pwd=ejY1N3c5TDk5UXAwVCtkdHBJOWt0UT09\">Zoom<\/a>)\u00a0\u2013 <em>the ID and password for the zoom meeting are the following:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-207 aligncenter\" src=\"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2020\/11\/tacos3.png\" alt=\"\" width=\"166\" height=\"39\" \/><\/em><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The speakers for the third session, Hyperk\u00e4hler Geometry, are: Daniel Huybrechts (Universit\u00e4t Bonn): &#8220;3 families of K3 surfaces&#8221; Abstract. I will review three one-dimensional families of K3 surfaces (twistor, Brauer or Tate-Shafarevich, and Dwork) and explain how, from a purely Hodge-theoretic perspective, they fit into one picture. I am particularly interested in understanding how certain &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/hyperkahler-geometry\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Hyperk\u00e4hler Geometry&#8221;<\/span><\/a><\/p>\n","protected":false},"author":15,"featured_media":0,"parent":93,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-183","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Hyperk\u00e4hler Geometry - Geometry and TACoS<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/hyperkahler-geometry\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hyperk\u00e4hler Geometry - Geometry and TACoS\" \/>\n<meta property=\"og:description\" content=\"The speakers for the third session, Hyperk\u00e4hler Geometry, are: Daniel Huybrechts (Universit\u00e4t Bonn): &#8220;3 families of K3 surfaces&#8221; Abstract. I will review three one-dimensional families of K3 surfaces (twistor, Brauer or Tate-Shafarevich, and Dwork) and explain how, from a purely Hodge-theoretic perspective, they fit into one picture. 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