{"id":25977,"date":"2025-04-17T16:15:56","date_gmt":"2025-04-17T19:15:56","guid":{"rendered":"http:\/\/localhost\/faci-wordpress\/?page_id=25977"},"modified":"2025-06-03T10:43:52","modified_gmt":"2025-06-03T13:43:52","slug":"doctorado-en-matematica-aplicada","status":"publish","type":"page","link":"https:\/\/ciencias.ubiobio.cl\/faci\/index.php\/doctorado-en-matematica-aplicada\/","title":{"rendered":"DOCTORADO EN MATEM\u00c1TICA APLICADA"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"25977\" class=\"elementor elementor-25977\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c258012 e-flex e-con-boxed e-con e-parent\" data-id=\"c258012\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-8011719 elementor-widget elementor-widget-heading\" data-id=\"8011719\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><h2 style=\"color:white\"> DOCTORADO EN MATEM\u00c1TICA APLICADA\n<\/h2>\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ce414b9 e-flex e-con-boxed e-con e-parent\" data-id=\"ce414b9\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-496bc19 elementor-widget elementor-widget-image\" data-id=\"496bc19\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1536\" height=\"569\" src=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-1536x569.png\" class=\"attachment-1536x1536 size-1536x1536 wp-image-26285\" alt=\"\" srcset=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-1536x569.png 1536w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-300x111.png 300w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-1024x379.png 1024w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-768x284.png 768w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-2048x759.png 2048w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/BANNER-Doctorado-Matematica-Aplicada-B-OK1-600x222.png 600w\" sizes=\"(max-width: 1536px) 100vw, 1536px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-f77c2d9 e-flex e-con-boxed e-con e-parent\" data-id=\"f77c2d9\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;shape_divider_bottom&quot;:&quot;waves&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 1000 100\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M421.9,6.5c22.6-2.5,51.5,0.4,75.5,5.3c23.6,4.9,70.9,23.5,100.5,35.7c75.8,32.2,133.7,44.5,192.6,49.7\n\tc23.6,2.1,48.7,3.5,103.4-2.5c54.7-6,106.2-25.6,106.2-25.6V0H0v30.3c0,0,72,32.6,158.4,30.5c39.2-0.7,92.8-6.7,134-22.4\n\tc21.2-8.1,52.2-18.2,79.7-24.2C399.3,7.9,411.6,7.5,421.9,6.5z\"\/>\n<\/svg>\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5b133d1 e-con-full e-flex e-con e-child\" data-id=\"5b133d1\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ef27308 elementor-widget elementor-widget-image-box\" data-id=\"ef27308\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><div class=\"elementor-image-box-content\"><p class=\"elementor-image-box-description\">El objetivo del Programa de Doctorado en Matem\u00e1tica Aplicada es formar graduados\/as altamente calificados\/as en teor\u00eda y m\u00e9todos matem\u00e1ticos, destinados a la investigaci\u00f3n original, que ayuden a ampliar el horizonte de conocimiento matem\u00e1tico, y puedan aportar en la formulaci\u00f3n, comprensi\u00f3n y resoluci\u00f3n de problemas provenientes de las m\u00e1s diversas \u00e1reas del conocimiento, participando eficientemente en actividades de investigaci\u00f3n y en el ejercicio profesional de acuerdo a las necesidades del pa\u00eds, as\u00ed como comunicar adecuadamente los resultados de su investigaci\u00f3n en reuniones cient\u00edficas o a trav\u00e9s de publicaciones. Los objetivos espec\u00edficos del Programa son: - Formar investigadores con conocimientos en teor\u00eda y m\u00e9todos matem\u00e1ticos para modelar y resolver problemas provenientes de distintas \u00e1reas del conocimiento de acuerdo con las exigencias y necesidades del medio - Producir conocimiento cient\u00edfico original en el \u00e1rea que ayude a ampliar el horizonte de conocimiento matem\u00e1tico. - Transferir conocimiento cient\u00edfico de frontera en Matem\u00e1tica Aplicada, comunicando adecuadamente los resultados de su investigaci\u00f3n a nivel nacional o internacional.<\/p><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21f2691 elementor-widget elementor-widget-image-box\" data-id=\"21f2691\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><div class=\"elementor-image-box-content\"><h2 class=\"elementor-image-box-title\">PERFIL DE EGRESO<\/h2><p class=\"elementor-image-box-description\">El\/la graduado\/a del programa de Doctorado en Matem\u00e1tica Aplicada de la Universidad del B\u00edo-B\u00edo se caracteriza por estar altamente calificado\/a en teor\u00eda y m\u00e9todos matem\u00e1ticos, trabajando en investigaci\u00f3n original, que ayuden a ampliar el horizonte de conocimiento matem\u00e1tico, aportando en la formulaci\u00f3n, comprensi\u00f3n y resoluci\u00f3n de problemas de diversas \u00e1reas del conocimiento. Los\/as graduados\/as ser\u00e1n investigadores capaces de desarrollar investigaci\u00f3n de acuerdo a las necesidades del pa\u00eds, as\u00ed como tambi\u00e9n comunicar adecuadamente los resultados de su investigaci\u00f3n en reuniones acad\u00e9micas nacionales o internacionales o a trav\u00e9s de publicaciones cient\u00edficas del \u00e1rea.<\/p><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6ffc418 e-flex e-con-boxed e-con e-parent\" data-id=\"6ffc418\" data-element_type=\"container\" data-settings=\"{&quot;shape_divider_bottom&quot;:&quot;waves&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 1000 100\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M421.9,6.5c22.6-2.5,51.5,0.4,75.5,5.3c23.6,4.9,70.9,23.5,100.5,35.7c75.8,32.2,133.7,44.5,192.6,49.7\n\tc23.6,2.1,48.7,3.5,103.4-2.5c54.7-6,106.2-25.6,106.2-25.6V0H0v30.3c0,0,72,32.6,158.4,30.5c39.2-0.7,92.8-6.7,134-22.4\n\tc21.2-8.1,52.2-18.2,79.7-24.2C399.3,7.9,411.6,7.5,421.9,6.5z\"\/>\n<\/svg>\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-408198d e-con-full e-flex e-con e-child\" data-id=\"408198d\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-547500f elementor-widget elementor-widget-image-box\" data-id=\"547500f\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><div class=\"elementor-image-box-content\"><h2 class=\"elementor-image-box-title\">LINEAS DE INVESTIGACI\u00d3N<\/h2><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4a79e3e elementor-widget__width-initial elementor-widget elementor-widget-accordion\" data-id=\"4a79e3e\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-7801\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-7801\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">An\u00e1lisis Num\u00e9rico de Ecuaciones Diferenciales Parciales\t<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7801\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-7801\"><p><strong>Claustro:\u00a0<\/strong>Ver\u00f3nica Anaya,\u00a0\u00a0David Mora, Ricardo Oyarz\u00faa, Luis Villada, Pablo Venegas<\/p><p><strong>Colaboradores:\u00a0<\/strong>Eligio Colmenares, Felipe Lepe<\/p><p><strong>Visitantes:\u00a0\u00a0<\/strong>Mauricio Sepulveda, Lourenco Beirao da Veira, Sergio Caucao<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-7802\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-7802\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">An\u00e1lisis de Ecuaciones Diferenciales Parciales<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7802\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-7802\"><p><strong>Claustro:\u00a0<\/strong>Luis Friz, Anibal Coronel,\u00a0Jaime Mu\u00f1oz Rivera<\/p><p><strong>Colaboradores:\u00a0<\/strong>Patricio Cumsille,<\/p><p><strong>Visitantes:\u00a0<\/strong>Emilio Porcu, Marko Rojas<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-7803\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-7803\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Sistemas Din\u00e1micos y Aplicaciones<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7803\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-7803\"><p><strong>Claustro:<\/strong>\u00a0Dante Carrasco, Claudio Vidal, Yuki Yayama, Jaime Andrade, Francisco Crespo, Salomon Rebollo,<\/p><p><strong>Colaboradores:\u00a0<\/strong>Samuel Castillo,<br \/>Adri\u00e1n G\u00f3mez, Paulina Mart\u00ednez<\/p><p><strong>Visitantes:\u00a0<\/strong>Manuel\u00a0 Zamora,\u00a0Jaume Llibre,\u00a0Ernesto Perez-Chavela,\u00a0Jes\u00fas Palaci\u00e1n, Manuel Pinto, Carlos Morales,\u00a0 Robert Hakl, Patricia Yanguas, Esther Barrabes, Josep Cors, Claudia Valls<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-7804\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-7804\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">F\u00edsica-Matem\u00e1tica\t<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-7804\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-7804\"><p><strong>Claustro:<\/strong>\u00a0Carlos Maniatis, York\u00a0 Schr\u00f6der<\/p><p><strong>Colaboradores:\u00a0\u00a0<\/strong>Igor Kondrashuk, Carlos Reyes,\u00a0Cristian Villavicencio<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-da1eebd e-flex e-con-boxed e-con e-parent\" data-id=\"da1eebd\" data-element_type=\"container\" data-settings=\"{&quot;shape_divider_bottom&quot;:&quot;waves&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" aria-hidden=\"true\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 1000 100\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M421.9,6.5c22.6-2.5,51.5,0.4,75.5,5.3c23.6,4.9,70.9,23.5,100.5,35.7c75.8,32.2,133.7,44.5,192.6,49.7\n\tc23.6,2.1,48.7,3.5,103.4-2.5c54.7-6,106.2-25.6,106.2-25.6V0H0v30.3c0,0,72,32.6,158.4,30.5c39.2-0.7,92.8-6.7,134-22.4\n\tc21.2-8.1,52.2-18.2,79.7-24.2C399.3,7.9,411.6,7.5,421.9,6.5z\"\/>\n<\/svg>\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-62359bf e-con-full e-flex e-con e-child\" data-id=\"62359bf\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9282e85 elementor-widget elementor-widget-image-box\" data-id=\"9282e85\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><div class=\"elementor-image-box-content\"><h2 class=\"elementor-image-box-title\">Director del Programa<\/h2><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-18b8fdd e-con-full e-flex e-con e-child\" data-id=\"18b8fdd\" data-element_type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-efd75ac e-con-full e-flex e-con e-child\" data-id=\"efd75ac\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c2fdee6 elementor-widget elementor-widget-image\" data-id=\"c2fdee6\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas.jpg\" class=\"attachment-large size-large wp-image-26189\" alt=\"\" srcset=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas.jpg 1024w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas-300x300.jpg 300w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas-150x150.jpg 150w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas-768x768.jpg 768w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas-600x600.jpg 600w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/06\/pvenegas-100x100.jpg 100w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">DIRECTOR - Pablo Venegas Tapia<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3fa4e62 e-con-full e-flex e-con e-child\" data-id=\"3fa4e62\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2a92e7a elementor-widget elementor-widget-accordion\" data-id=\"2a92e7a\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-4461\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-4461\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Correo<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-4461\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-4461\"><p>pvenegas@ubiobio.cl<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-4462\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-4462\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Fono<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-4462\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-4462\"><p>(41) 311 1793<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-4463\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-4463\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Ubicaci\u00f3n<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-4463\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-4463\"><p>Concepci\u00f3n: Avda. Collao 1202<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-4464\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-4464\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-caret-right\" viewBox=\"0 0 192 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M0 384.662V127.338c0-17.818 21.543-26.741 34.142-14.142l128.662 128.662c7.81 7.81 7.81 20.474 0 28.284L34.142 398.804C21.543 411.404 0 402.48 0 384.662z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-caret-down\" viewBox=\"0 0 320 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Web Oficial<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-4464\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-4464\"><p>https:\/\/ciencias.ubiobio.cl\/doctorado-mat\/<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6bef0db e-flex e-con-boxed e-con e-parent\" data-id=\"6bef0db\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-75ac922 elementor-arrows-position-inside elementor-pagination-position-outside elementor-widget elementor-widget-image-carousel\" data-id=\"75ac922\" data-element_type=\"widget\" data-settings=\"{&quot;slides_to_show&quot;:&quot;1&quot;,&quot;navigation&quot;:&quot;both&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;pause_on_hover&quot;:&quot;yes&quot;,&quot;pause_on_interaction&quot;:&quot;yes&quot;,&quot;autoplay_speed&quot;:5000,&quot;infinite&quot;:&quot;yes&quot;,&quot;effect&quot;:&quot;slide&quot;,&quot;speed&quot;:500}\" data-widget_type=\"image-carousel.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-image-carousel-wrapper swiper\" role=\"region\" aria-roledescription=\"carousel\" aria-label=\"Carrusel de im\u00e1genes\" dir=\"ltr\">\n\t\t\t<div class=\"elementor-image-carousel swiper-wrapper\" aria-live=\"off\">\n\t\t\t\t\t\t\t\t<div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"1 de 2\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/IMG_74561583759653782-768x512.jpg\" alt=\"IMG_74561583759653782\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"2 de 2\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/IMG_73871583759773299-768x512.jpg\" alt=\"IMG_73871583759773299\" \/><\/figure><\/div>\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-prev\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-left\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M646 125C629 125 613 133 604 142L308 442C296 454 292 471 292 487 292 504 296 521 308 533L604 854C617 867 629 875 646 875 663 875 679 871 692 858 704 846 713 829 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e-con e-parent\" data-id=\"ce58a26\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-faf56f7 e-con-full e-flex e-con e-child\" data-id=\"faf56f7\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-57ef9ac elementor-widget elementor-widget-image-box\" data-id=\"57ef9ac\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><div class=\"elementor-image-box-content\"><h2 class=\"elementor-image-box-title\">MALLA PROGRAMA<\/h2><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2e2ee70 e-con-full e-flex e-con e-child\" data-id=\"2e2ee70\" data-element_type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-2bcddea e-con-full e-flex e-con e-child\" data-id=\"2bcddea\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a375fc9 elementor-widget elementor-widget-image\" data-id=\"a375fc9\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"496\" src=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-1024x496.png\" class=\"attachment-large size-large wp-image-25985\" alt=\"\" srcset=\"https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-1024x496.png 1024w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-300x145.png 300w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-768x372.png 768w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-1536x745.png 1536w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-2048x993.png 2048w, https:\/\/ciencias.ubiobio.cl\/faci\/wp-content\/uploads\/2025\/04\/MALLA-DOCTORADO-MATEMATICA-06-061578341683418-600x291.png 600w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0abf9d0 e-flex e-con-boxed e-con e-parent\" data-id=\"0abf9d0\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-a7beab2 e-con-full e-flex e-con e-child\" data-id=\"a7beab2\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a2fba21 elementor-widget elementor-widget-image-box\" data-id=\"a2fba21\" data-element_type=\"widget\" data-widget_type=\"image-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-image-box-wrapper\"><div class=\"elementor-image-box-content\"><h2 class=\"elementor-image-box-title\">Contacto<\/h2><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6bb3a2d e-con-full e-flex e-con e-child\" data-id=\"6bb3a2d\" data-element_type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-b97ca4e e-con-full e-flex e-con e-child\" data-id=\"b97ca4e\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t<div 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