{"id":1755,"date":"2024-07-17T12:37:03","date_gmt":"2024-07-17T10:37:03","guid":{"rendered":"https:\/\/www.dm.unipi.it\/phd\/?page_id=1755"},"modified":"2025-09-22T16:59:38","modified_gmt":"2025-09-22T14:59:38","slug":"ph-d-courses-2024-2025","status":"publish","type":"page","link":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/","title":{"rendered":"Ph.D. Courses 2024 &#8211; 2025"},"content":{"rendered":"  <div id=dm-manager-widget-69d99dd35ca4b><\/div>\n  <script>\n    (function () {\n      const el = document.getElementById(\"dm-manager-widget-69d99dd35ca4b\");\n      const props = {\"widget\":\"CourseList\",\"from\":\"2024-09-01\",\"to\":\"2025-08-30\",\"phd\":\"Matematica\"}\n      dmwidgets.loadComponent(el, \"CourseList\", props);\n    })();\n  <\/script>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">List of advanced MSc courses offered<\/h4>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17550\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Fall\/Winter Term<\/h4><div id=\"ac-17550\" class=\"c-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Analisi armonica (Harmonic analysis) taught by J. Bellazzini<\/li>\n\n\n\n<li>Analisi Gaussiana (Gaussian analysis) taught by D. Trevisan<\/li>\n\n\n\n<li>Calcolo delle variazioni B (Calculus of variations B: Regularity theory for minima of variational integrals) taught by A. Pratelli<\/li>\n\n\n\n<li>Determinazione orbitale (Orbital determination) taught by G. Tommei<\/li>\n\n\n\n<li>Curve Ellittiche (Elliptic curves) taught by T. Szamuely<\/li>\n\n\n\n<li>Geometria &#8211; Analisi complessa B (Complex analysis) taught by F. Bianchi<\/li>\n\n\n\n<li>Geometria Riemanniana (Riemannian Geometry) taught by D. Conti<\/li>\n\n\n\n<li>Gruppi algebrici lineari (Linear algebraic groups) taught by A. Maffei<\/li>\n\n\n\n<li>Metodi numerici per catene di Markov (Numerical methods for Markov chains) taught by B. Meini<\/li>\n\n\n\n<li>Metodi numerici per la grafica (Numerical methods for graphics) taught by P. Boito<\/li>\n\n\n\n<li>Modelli Matematici in Biomedicina e Fisica Matematica (Mathematical models in biomedicine and mathematical physics) taught by V. Georgiev<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17551\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Winter\/Spring Term<\/h4><div id=\"ac-17551\" class=\"c-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Algebra superiore A (Commutative algebra) taught by E. Sbarra<\/li>\n\n\n\n<li>Geometria algebrica F (Toric varieties) taught by M. Talpo<\/li>\n\n\n\n<li>Geometria differenziale complessa (Complex differential geometry) taught by G. Pearlstein<\/li>\n\n\n\n<li>Topologia algebrica B (Algebraic topology B: Algebraic and combinatorial topology, with application to Hyperplane Arrangements and related spaces) taught by M. Salvetti<\/li>\n\n\n\n<li>Teoria dei Nodi A (Knot theory A: Invariants of knots and links, theory of braids) taught by P. Lisca<\/li>\n\n\n\n<li>Equazioni della Fluidodinamica (Equations of fluid mechanics) taught by L. C. Berselli<\/li>\n\n\n\n<li>Equazioni ellittiche (Elliptic partial differential equations) by B. Velichkov<\/li>\n\n\n\n<li>Analisi dei dati (Data analysis) taught by M. Romito and A. Papagiannouli<\/li>\n\n\n\n<li>Meccanica Celeste (Celestial mechanics: Singularities and periodic orbits in the N-body problem) taught by L. Gronchi<\/li>\n\n\n\n<li>Fisica Matematica (Mathematical Physics: Insights in the Theory of Dynamical Systems and in the Hamiltonian) taught by C. Bonanno<\/li>\n\n\n\n<li>Meccanica Superiore (Advanced mechanics: Measure of chaos and ergodic methods in mechanics) taught by P. Giulietti<\/li>\n\n\n\n<li>Meccanica Spaziale (Space mechanics: Motion of artificial satellites and space probes, interplanetary space missions) taught by G. Ba\u00f9<\/li>\n\n\n\n<li>Metodi numerici per equazioni alle derivate parziali (Numerical methods for partial differential equations) taught by L. Heltai<\/li>\n<\/ul>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>List of advanced MSc courses offered&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":166,"featured_media":0,"parent":78,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1755","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Ph.D. Courses 2024 - 2025 - Ph.D. in Mathematics<\/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:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ph.D. Courses 2024 - 2025 - Ph.D. in Mathematics\" \/>\n<meta property=\"og:description\" content=\"List of advanced MSc courses offered&hellip;Read More...\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/\" \/>\n<meta property=\"og:site_name\" content=\"Ph.D. in Mathematics\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-22T14:59:38+00:00\" \/>\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=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/past-courses\\\/ph-d-courses-2024-2025\\\/\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/past-courses\\\/ph-d-courses-2024-2025\\\/\",\"name\":\"Ph.D. Courses 2024 - 2025 - Ph.D. in Mathematics\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/#website\"},\"datePublished\":\"2024-07-17T10:37:03+00:00\",\"dateModified\":\"2025-09-22T14:59:38+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/past-courses\\\/ph-d-courses-2024-2025\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/past-courses\\\/ph-d-courses-2024-2025\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/past-courses\\\/ph-d-courses-2024-2025\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Ph.D. Courses\",\"item\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Past Courses\",\"item\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/ph-d-courses\\\/past-courses\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Ph.D. Courses 2024 &#8211; 2025\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/#website\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/\",\"name\":\"Ph.D. in Mathematics\",\"description\":\"Dipartimento di Matematica - Universit\u00e0 di Pisa\",\"publisher\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/#organization\",\"name\":\"Ph.D. in Mathematics\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/wp-content\\\/uploads\\\/sites\\\/4\\\/2023\\\/05\\\/matematica_dx_bianco-2.png\",\"contentUrl\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/wp-content\\\/uploads\\\/sites\\\/4\\\/2023\\\/05\\\/matematica_dx_bianco-2.png\",\"width\":1612,\"height\":463,\"caption\":\"Ph.D. in Mathematics\"},\"image\":{\"@id\":\"https:\\\/\\\/www.dm.unipi.it\\\/phd\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Ph.D. Courses 2024 - 2025 - Ph.D. in Mathematics","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:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/","og_locale":"en_US","og_type":"article","og_title":"Ph.D. Courses 2024 - 2025 - Ph.D. in Mathematics","og_description":"List of advanced MSc courses offered&hellip;Read More...","og_url":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/","og_site_name":"Ph.D. in Mathematics","article_modified_time":"2025-09-22T14:59:38+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/","url":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/","name":"Ph.D. Courses 2024 - 2025 - Ph.D. in Mathematics","isPartOf":{"@id":"https:\/\/www.dm.unipi.it\/phd\/#website"},"datePublished":"2024-07-17T10:37:03+00:00","dateModified":"2025-09-22T14:59:38+00:00","breadcrumb":{"@id":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/ph-d-courses-2024-2025\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.dm.unipi.it\/phd\/"},{"@type":"ListItem","position":2,"name":"Ph.D. Courses","item":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/"},{"@type":"ListItem","position":3,"name":"Past Courses","item":"https:\/\/www.dm.unipi.it\/phd\/ph-d-courses\/past-courses\/"},{"@type":"ListItem","position":4,"name":"Ph.D. Courses 2024 &#8211; 2025"}]},{"@type":"WebSite","@id":"https:\/\/www.dm.unipi.it\/phd\/#website","url":"https:\/\/www.dm.unipi.it\/phd\/","name":"Ph.D. in Mathematics","description":"Dipartimento di Matematica - Universit\u00e0 di Pisa","publisher":{"@id":"https:\/\/www.dm.unipi.it\/phd\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.dm.unipi.it\/phd\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.dm.unipi.it\/phd\/#organization","name":"Ph.D. in Mathematics","url":"https:\/\/www.dm.unipi.it\/phd\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.dm.unipi.it\/phd\/#\/schema\/logo\/image\/","url":"https:\/\/www.dm.unipi.it\/phd\/wp-content\/uploads\/sites\/4\/2023\/05\/matematica_dx_bianco-2.png","contentUrl":"https:\/\/www.dm.unipi.it\/phd\/wp-content\/uploads\/sites\/4\/2023\/05\/matematica_dx_bianco-2.png","width":1612,"height":463,"caption":"Ph.D. in Mathematics"},"image":{"@id":"https:\/\/www.dm.unipi.it\/phd\/#\/schema\/logo\/image\/"}}]}},"publishpress_future_action":{"enabled":false,"date":"2026-04-18 03:03:15","action":"change-status","newStatus":"draft","terms":[],"taxonomy":"","extraData":[]},"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/pages\/1755","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/users\/166"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/comments?post=1755"}],"version-history":[{"count":10,"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/pages\/1755\/revisions"}],"predecessor-version":[{"id":1952,"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/pages\/1755\/revisions\/1952"}],"up":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/pages\/78"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/phd\/wp-json\/wp\/v2\/media?parent=1755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}