{"id":295,"date":"2021-07-01T16:10:02","date_gmt":"2021-07-01T16:10:02","guid":{"rendered":"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/?page_id=295"},"modified":"2021-09-28T09:24:26","modified_gmt":"2021-09-28T09:24:26","slug":"analytic-methods-in-birational-geometry","status":"publish","type":"page","link":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/","title":{"rendered":"Analytic Methods in Birational Geometry"},"content":{"rendered":"[vc_row][vc_column][vc_column_text]The speakers for the sixth session,\u00a0<em>Analytic Methods in Birational Geometry<\/em>, are:<\/p>\n<ul>\n<li><a href=\"http:\/\/sebastien.boucksom.perso.math.cnrs.fr\/\">S\u00e9bastien Boucksom<\/a>\u00a0(CNRS \u2013 CMLS \u00c9cole Polytechnique): &#8220;<em>Valuations and singularities of plurisubharmonic functions<\/em>&#8220;<\/li>\n<\/ul>\n<p><em style=\"font-size: 1rem\">Abstract<\/em><span style=\"font-size: 1rem\">:\u00a0<\/span><span style=\"font-size: 1rem\">Plurisubharmonic (psh) functions can be viewed as a complex analytic analogue of convex functions, but they exhibit a much broader range of possible singularities, including those induced by ideals of holomorphic functions. Understanding psh singularities is a key issue in several questions of complex geometry, as illustrated by recent progress on the Yau-Tian-Donaldson conjecture. A powerful tool to do so is the classical notion of Lelong numbers and the theory of multiplier ideals, which open the way to a valuative approach that studies the analogue of psh functions on a (non-Archimedean) space of valuations. This lecture will present a gentle introduction to this circle of ideas.<\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/perso.pages.math.cnrs.fr\/users\/eleonora.di-nezza\/\">Eleonora Di Nezza<\/a>\u00a0(CMLS \u00c9cole Polytechnique): &#8220;<em>Pluripotential theory : how to get singular K\u00e4hler-Einstein metrics<\/em>&#8220;<\/li>\n<\/ul>\n<p><em>Abstract<\/em>:\u00a0In the last 50 years pluripotential theory has played a central role in order to solve geometric problems, such as the existence of special metrics (e.g. K\u00e4hler-Einstein, csck) on a compact K\u00e4hler manifold. In this talk I am going to present some recent developments in pluripotential theory. These new tools are so flexible that they allow to study \u201csingular\u201d settings : we will then be able to work with a singular variety and\/or to search for singular metrics. The talk is based on a series of joint papers with T\u00e1mas Darvas and Chinh Lu.<br \/>\n(Talk accessible for researchers in geometry).<\/p>\n<ul>\n<li><a href=\"https:\/\/math.unice.fr\/~hoering\/\">Andreas H\u00f6ring<\/a>\u00a0(Universit\u00e9 C\u00f4te d\u2019Azur): &#8220;<em>Stein complements in projective manifolds<\/em>&#8220;<\/li>\n<\/ul>\n<p><em>Abstract<\/em>:\u00a0Let X be a complex projective manifold, and let Y be a prime divisor in X. If Y is ample, it is well-known that the complement X\\Y is an affine variety. Vice versa, assume that X\\Y is affine, or more generally a Stein manifold. Then X\\Y does not contain any curve, in particular Y has positive intersection with every curve. This leads to our main question: if X\\Y is Stein, what can we say about the normal bundle of Y? After some general considerations I will focus on the case where Y is the projectivised tangent bundle of some manifold M, and X is a &#8220;canonical extension&#8221;. We will see that the Stein property leads to many restrictions on the birational geometry of M. This is work in progress with Thomas Peternell.<\/p>\n<ul>\n<li><a href=\"https:\/\/sites.google.com\/site\/jiansongrutgers\/home\">Jian Song<\/a>\u00a0(Rutgers University): &#8220;<em>Moduli space of K\u00e4hler-Einstein metrics of negative scalar curvature<\/em>&#8220;<\/li>\n<\/ul>\n<p><em>Abstract<\/em>:\u00a0\u00a0Let K(n, V) be the space of n-dimensional compact K\u00e4hler-Einstein manifolds with negative scalar curvature and volume bounded above by V. We prove that any sequence in K(n, V) converges in pointed Gromov-Hausdorff topology to a finite union of complete K\u00e4hler-Einstein metric spaces without loss of volume, which is biholomorphic to an algebraic semi-log canonical model with its non-log terminal locus removed. We further show that the Weil-Petersson metric extends uniquely to a K\u00e4hler current with continuous local potentials on the KSB compactification of the moduli space of canonically polarized manifolds. In particular, the Weil-Petersson volume of the KSB moduli space is finite.<\/p>\n<p>The schedule of the conference is the following:<\/p>\n<ul>\n<li>Release of the videos: June 23, 2021 (<a href=\"https:\/\/www.youtube.com\/channel\/UCeHQo5ia5gCj5EnCUfY3Obw\">YouTube<\/a>)<\/li>\n<li>Discussion: from June 23 to July 7, 2021 (<a href=\"https:\/\/gitter.im\/GTACOS-June2021\">Gitter<\/a>)<\/li>\n<li>Coffee break: July 7, 2021, at 17.00 CET (<a href=\"https:\/\/ubc.zoom.us\/j\/61250635720?pwd=QjFtYUZTVHVXdXEyK2hRYUdQNjI4QT09\">Zoom<\/a>)<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-306\" src=\"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-300x100.png\" alt=\"\" width=\"300\" height=\"100\" srcset=\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-300x100.png 300w, https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-768x256.png 768w, https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-1024x341.png 1024w, https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37.png 1314w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/li>\n<\/ul>\n[\/vc_column_text][\/vc_column][\/vc_row]\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text]The speakers for the sixth session,\u00a0Analytic Methods in Birational Geometry, are: S\u00e9bastien Boucksom\u00a0(CNRS \u2013 CMLS \u00c9cole Polytechnique): &#8220;Valuations and singularities of plurisubharmonic functions&#8220; Abstract:\u00a0Plurisubharmonic (psh) functions can be viewed as a complex analytic analogue of convex functions, but they exhibit a much broader range of possible singularities, including those induced by ideals of holomorphic functions. &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Analytic Methods in Birational Geometry&#8221;<\/span><\/a><\/p>\n","protected":false},"author":11,"featured_media":0,"parent":93,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-295","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>Analytic Methods in Birational 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\/analytic-methods-in-birational-geometry\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Analytic Methods in Birational Geometry - Geometry and TACoS\" \/>\n<meta property=\"og:description\" content=\"[vc_row][vc_column][vc_column_text]The speakers for the sixth session,\u00a0Analytic Methods in Birational Geometry, are: S\u00e9bastien Boucksom\u00a0(CNRS \u2013 CMLS \u00c9cole Polytechnique): &#8220;Valuations and singularities of plurisubharmonic functions&#8220; Abstract:\u00a0Plurisubharmonic (psh) functions can be viewed as a complex analytic analogue of convex functions, but they exhibit a much broader range of possible singularities, including those induced by ideals of holomorphic functions. &hellip; Continue reading &quot;Analytic Methods in Birational Geometry&quot;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/\" \/>\n<meta property=\"og:site_name\" content=\"Geometry and TACoS\" \/>\n<meta property=\"article:modified_time\" content=\"2021-09-28T09:24:26+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-300x100.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/\",\"url\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/\",\"name\":\"Analytic Methods in Birational Geometry - Geometry and TACoS\",\"isPartOf\":{\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-300x100.png\",\"datePublished\":\"2021-07-01T16:10:02+00:00\",\"dateModified\":\"2021-09-28T09:24:26+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#primaryimage\",\"url\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37.png\",\"contentUrl\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37.png\",\"width\":1314,\"height\":438},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Sessions\",\"item\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Analytic Methods in Birational Geometry\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/#website\",\"url\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/\",\"name\":\"Geometry and TACoS\",\"description\":\"Online sessions on the Geometry and Topology of (Almost) Complex Structures\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Analytic Methods in Birational Geometry - Geometry and TACoS","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/","og_locale":"en_US","og_type":"article","og_title":"Analytic Methods in Birational Geometry - Geometry and TACoS","og_description":"[vc_row][vc_column][vc_column_text]The speakers for the sixth session,\u00a0Analytic Methods in Birational Geometry, are: S\u00e9bastien Boucksom\u00a0(CNRS \u2013 CMLS \u00c9cole Polytechnique): &#8220;Valuations and singularities of plurisubharmonic functions&#8220; Abstract:\u00a0Plurisubharmonic (psh) functions can be viewed as a complex analytic analogue of convex functions, but they exhibit a much broader range of possible singularities, including those induced by ideals of holomorphic functions. &hellip; Continue reading \"Analytic Methods in Birational Geometry\"","og_url":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/","og_site_name":"Geometry and TACoS","article_modified_time":"2021-09-28T09:24:26+00:00","og_image":[{"url":"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-300x100.png"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/","url":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/","name":"Analytic Methods in Birational Geometry - Geometry and TACoS","isPartOf":{"@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/#website"},"primaryImageOfPage":{"@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#primaryimage"},"image":{"@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#primaryimage"},"thumbnailUrl":"http:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37-300x100.png","datePublished":"2021-07-01T16:10:02+00:00","dateModified":"2021-09-28T09:24:26+00:00","breadcrumb":{"@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#primaryimage","url":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37.png","contentUrl":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-content\/uploads\/sites\/16\/2021\/06\/Schermata-2021-07-01-alle-15.54.37.png","width":1314,"height":438},{"@type":"BreadcrumbList","@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/analytic-methods-in-birational-geometry\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/"},{"@type":"ListItem","position":2,"name":"Sessions","item":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/sessions\/"},{"@type":"ListItem","position":3,"name":"Analytic Methods in Birational Geometry"}]},{"@type":"WebSite","@id":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/#website","url":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/","name":"Geometry and TACoS","description":"Online sessions on the Geometry and Topology of (Almost) Complex Structures","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/pages\/295"}],"collection":[{"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/comments?post=295"}],"version-history":[{"count":5,"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/pages\/295\/revisions"}],"predecessor-version":[{"id":309,"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/pages\/295\/revisions\/309"}],"up":[{"embeddable":true,"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/pages\/93"}],"wp:attachment":[{"href":"https:\/\/silicio.math.unifi.it\/wordpress\/tacos\/wp-json\/wp\/v2\/media?parent=295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}