{"id":1090,"date":"2025-01-20T23:25:28","date_gmt":"2025-01-20T23:25:28","guid":{"rendered":"https:\/\/sites.rutgers.edu\/bin-guo\/?page_id=1090"},"modified":"2025-01-20T23:37:03","modified_gmt":"2025-01-20T23:37:03","slug":"topic-on-complex-analysis-spring-2025","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/","title":{"rendered":"Topic on complex analysis Spring 2025"},"content":{"rendered":"

This topic course will (tentatively) cover the following topics, and we will update the detailed materials as the course progresses.<\/p>\n

    \n
  1. Complex and differential geometry: Riemannian\/Kahler metrics, curvatures, vector bundles…<\/li>\n
  2. basic PDE theory: maximum principle, Schauder estimates, regularity theory for linear equations<\/li>\n
  3. Complex Monge-Ampere equations: a complete proof of Calabi conjecture<\/li>\n
  4. Hormander’s L^2 estimates for solving d-bar equations: Kodaira’s embedding theorem, partial C0 estimates, expansion of Bergman kernel<\/li>\n
  5. Existence of special Kahler metrics on Kahler manifolds: KE metrics, constant scalar curvature Kahler (cscK) metrics, Kahler-Ricci solitons<\/li>\n<\/ol>\n

    If time permits, we will explain briefly:<\/p>\n

      \n
    1. Metric geometry: Gromov-Hausdorff topology, introductory Cheeger-Colding theory<\/li>\n
    2. Recent development on the geometry of Kahler metrics from the works of Guo-Phong-Song-Sturm<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

      This topic course will (tentatively) cover the following topics, and we will update the detailed materials as the course progresses. Complex and differential geometry: Riemannian\/Kahler metrics, curvatures, vector bundles… basic … Read More<\/a><\/p>\n","protected":false},"author":814,"featured_media":0,"parent":160,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-custom.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1090","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\nTopic on complex analysis Spring 2025 - Bin Guo<\/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:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Topic on complex analysis Spring 2025 - Bin Guo\" \/>\n<meta property=\"og:description\" content=\"This topic course will (tentatively) cover the following topics, and we will update the detailed materials as the course progresses. 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Complex and differential geometry: Riemannian\/Kahler metrics, curvatures, vector bundles… basic … Read More","og_url":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/","og_site_name":"Bin Guo","article_modified_time":"2025-01-20T23:37:03+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/","url":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/","name":"Topic on complex analysis Spring 2025 - Bin Guo","isPartOf":{"@id":"https:\/\/sites.rutgers.edu\/bin-guo\/#website"},"datePublished":"2025-01-20T23:25:28+00:00","dateModified":"2025-01-20T23:37:03+00:00","breadcrumb":{"@id":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/topic-on-complex-analysis-spring-2025\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sites.rutgers.edu\/bin-guo\/"},{"@type":"ListItem","position":2,"name":"Courses","item":"https:\/\/sites.rutgers.edu\/bin-guo\/courses\/"},{"@type":"ListItem","position":3,"name":"Topic on complex analysis Spring 2025"}]},{"@type":"WebSite","@id":"https:\/\/sites.rutgers.edu\/bin-guo\/#website","url":"https:\/\/sites.rutgers.edu\/bin-guo\/","name":"Bin Guo","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sites.rutgers.edu\/bin-guo\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/pages\/1090"}],"collection":[{"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/users\/814"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/comments?post=1090"}],"version-history":[{"count":3,"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/pages\/1090\/revisions"}],"predecessor-version":[{"id":1099,"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/pages\/1090\/revisions\/1099"}],"up":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/pages\/160"}],"wp:attachment":[{"href":"https:\/\/sites.rutgers.edu\/bin-guo\/wp-json\/wp\/v2\/media?parent=1090"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}