{"id":1460,"date":"2025-11-19T08:48:39","date_gmt":"2025-11-19T07:48:39","guid":{"rendered":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/?p=1460"},"modified":"2026-01-23T11:24:21","modified_gmt":"2026-01-23T10:24:21","slug":"phd-course-riemann-surfaces","status":"publish","type":"post","link":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/2025\/11\/19\/phd-course-riemann-surfaces\/","title":{"rendered":"PhD Course: Riemann Surfaces"},"content":{"rendered":"<h1>Riemann Surfaces<\/h1>\n<p><span class=\"moz-txt-star\"><strong>Prof. Roberto Mossa<\/strong><br \/>\n<\/span>University of Cagliari, Italy<\/p>\n<p><strong>Abstract<\/strong><\/p>\n<p>This 16-hour PhD course is devoted to algebraic functions on Riemann surfaces, following Forster\u2019s\u00a0<em>Lectures on Riemann Surfaces<\/em>\u00a0up to \u00a78 (<em>Algebraic Functions<\/em>), with emphasis on the construction of the associated Riemann surfaces and on Puiseux expansions near branch points.<\/p>\n<p>In the final part we will explain how these classical tools naturally appear in recent problems in K\u00e4hler geometry, notably in the study of Nash\u2013algebraic functions, simultaneous normalization, and rigidity of holomorphic isometries into K\u00e4hler manifolds. As a case study we will discuss the paper A. Loi, R. Mossa,\u00a0<em>Rigidity properties of holomorphic isometries into homogeneous K\u00e4hler manifolds<\/em>, Proc. Amer. Math. Soc. 152 (2024), no. 7.<\/p>\n<p><strong>Schedule<\/strong><\/p>\n<p>The course will take place in January-February 2026. The course consists of 16 hours divided into 8 lectures.<\/p>\n<ul>\n<li>\n<p class=\"p1\">27\/01, 11:45\u201313:45 (Room III)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">28\/01, 11:00\u201313:00 (Room C)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">29\/01, 11:00\u201313:00 (Room C)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">30\/01, 11:00\u201313:00 (Room C)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">03\/02, 11:45\u201313:45 (Room II)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">04\/02, 11:00\u201313:00 (Room II)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">05\/02, 11:00\u201313:00 (Room II)<\/p>\n<\/li>\n<li>\n<p class=\"p1\">06\/02, 11:00\u201313:00 (Room C)<\/p>\n<\/li>\n<\/ul>\n<p><strong>Exam<\/strong><\/p>\n<p>The final exam consists in a seminar on a topic building on the content of the course. The topic for the final exam may be proposed by the students themselves or chosen from a list provided at the end of the lectures.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Riemann Surfaces Prof. Roberto Mossa University of Cagliari, Italy Abstract This 16-hour PhD course is devoted to algebraic functions on Riemann surfaces, following Forster\u2019s\u00a0Lectures on Riemann Surfaces\u00a0up to \u00a78 (Algebraic Functions), with emphasis on the construction of the associated Riemann surfaces and on Puiseux expansions near branch points. In the final part we will explain how these classical tools naturally appear in recent problems in K\u00e4hler geometry, notably in the study of Nash\u2013algebraic functions, simultaneous normalization, and rigidity of holomorphic isometries into K\u00e4hler manifolds. As a case study we will discuss the paper A. Loi, R. Mossa,\u00a0Rigidity properties of holomorphic <a href='https:\/\/dottorati.unica.it\/matematicaeinformatica\/2025\/11\/19\/phd-course-riemann-surfaces\/' class='excerpt-more'>[&#8230;]<\/a><\/p>\n","protected":false},"author":244,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,11,10,2],"tags":[],"class_list":["post-1460","post","type-post","status-publish","format-standard","hentry","category-dipartimento-matematica-informatica","category-dottorato-matematica-informatica","category-events","category-news","category-9-id","category-11-id","category-10-id","category-2-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1460","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/comments?post=1460"}],"version-history":[{"count":4,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1460\/revisions"}],"predecessor-version":[{"id":1485,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1460\/revisions\/1485"}],"wp:attachment":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/media?parent=1460"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/categories?post=1460"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/tags?post=1460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}