[vc_row][vc_column][vc_column_text]El Departamento de An\u00e1lisis Matem\u00e1tico y\u00a0 el Instituto de Matem\u00e1ticas y Aplicaciones de la Universidad de La Laguna organizan Seminarios de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada con car\u00e1cter semanal.[\/vc_column_text][\/vc_column][\/vc_row][vc_row][vc_column][vc_tta_accordion c_icon=\u00bbchevron\u00bb c_position=\u00bbright\u00bb active_section=\u00bb1″ no_fill=\u00bbtrue\u00bb collapsible_all=\u00bbtrue\u00bb][vc_tta_section title=\u00bb14 de octubre: What is… a multiple orthogonal polynomial on the unit circle?\u00bb tab_id=\u00bb14-octubre\u00bb][vc_column_text]Conferenciante: Marcus Vaktn\u00e4s\u00a0(Uppsala U., Suecia)<\/p>\n
Multiple orthogonal polynomials extend the notion of orthogonal polynomials, allowing broader applications to e.g. rational approximation, numerical integration, and random matrix theory. These polynomials have been studied extensively over the last few decades, but nearly all of this research concerns orthogonality with respect to measures supported on the real line.<\/p>\n
Quite surprisingly, there were only two papers studying multiple orthogonality with respect to unit circle measures prior to 2024 (M\u00ednguez-Van Assche, 2008 and Cruz-Barroso\u2013D\u00edaz Mendoza-Orive, 2015). Since then the list has quickly expanded, with nine papers currently, including some work from my PhD thesis. Part of my work takes an alternative approach to the topic, introducing a different notion of multiple orthogonal polynomial. The new approach reveals fundamental results that had previously not been established, most importantly about the uniqueness and zero location of the polynomials.<\/p>\n
The goal of the talk will be to explain these new ideas, which I will compare with less technical notions from the usual orthogonal polynomial theory, in an attempt to give context and make the topic accessible to the audience. I will also illustrate connections to Pad\u00e9 approximation, Szeg\u0151-type quadrature rules, and point processes on the unit circle. Some open problems will likely be mentioned as well.<\/p>\n
Actividad financiada por el Vicerrectorado de Investigaci\u00f3n y Transferencia de la Universidad de la Laguna y de la Agencia Canaria de Investigaci\u00f3n, Innovaci\u00f3n y Sociedad de la Informaci\u00f3n (ACIISI) del Gobierno de Canarias.[\/vc_column_text][\/vc_tta_section][vc_tta_section title=\u00bb8 de octubre: Una introducci\u00f3n a procesamiento de lenguaje natural y LLMs\u00bb tab_id=\u00bb1791373298997-770ebe4d-fdb8″][vc_column_text]Conferenciante: Aythami Bethencourt de Le\u00f3n (ULL)<\/p>\n
Introduciremos las ideas fundamentales del procesamiento del lenguaje natural y los modelos de lenguaje. Veremos c\u00f3mo se representa matem\u00e1ticamente un texto, c\u00f3mo aprende un modelo a predecir palabras y qu\u00e9 papel desempe\u00f1an conceptos como los embeddings o la atenci\u00f3n. Explicaremos tambi\u00e9n de forma intuitiva c\u00f3mo funcionan los grandes modelos de lenguaje actuales.<\/p>\n
[\/vc_column_text][\/vc_tta_section][vc_tta_section title=\u00bb1 de octubre: Debate y taller sobre Inteligencia Artificial para probar resultados de matem\u00e1ticas (II)\u00bb tab_id=\u00bb1790673351220-201c21f4-4029″][vc_column_text]Conferenciante: Sara Embid & friends (ULL)<\/p>\n
Esta segunda parte retomar\u00e1 las ideas abiertas en el primer seminario desde un enfoque m\u00e1s pr\u00e1ctico. Exploraremos herramientas espec\u00edficas para la investigaci\u00f3n matem\u00e1tica y comentaremos art\u00edculos en los que varios agentes de inteligencia artificial colaboran entre s\u00ed. Prestaremos especial atenci\u00f3n a la educaci\u00f3n, a las dificultades que plantea la integraci\u00f3n de estas tecnolog\u00edas y a las respuestas que podemos ofrecer desde nuestras instituciones. Tambi\u00e9n revisaremos iniciativas en marcha y compararemos el uso de modelos instalados localmente con el de grandes modelos de lenguaje externos, teniendo en cuenta aspectos como la privacidad, el coste, los recursos y el control sobre los datos.<\/p>\n
El seminario combinar\u00e1 debate, an\u00e1lisis de art\u00edculos y actividades pr\u00e1cticas.[\/vc_column_text][\/vc_tta_section][vc_tta_section title=\u00bb24 de septiembre: Debate y taller sobre Inteligencia Artificial para probar resultados de matem\u00e1ticas\u00bb tab_id=\u00bb1790320720110-3402b70c-1b42″][vc_column_text]<\/p>\n
El verano de 2026 ha sido revolucionario en la historia de las matem\u00e1ticas y hemos visto c\u00f3mo cada semana ca\u00eda una conjetura famosa por medio de la colaboraci\u00f3n entre inteligencia artificial e investigadores en matem\u00e1ticas. No debemos quedarnos atr\u00e1s de este cambio aunque cabe decidir l\u00edmites pr\u00e1cticos y \u00e9ticos al mismo para evitar la jerarquizaci\u00f3n de nuestra investigaci\u00f3n en base a la disponibilidad de recursos econ\u00f3micos o el malgasto de recursos naturales.<\/p>\n
Por todo ello, algunas de las sesiones del seminario de este cuatrimestre se dedicar\u00e1n a debatir conjuntamente esta nueva realidad y practicar para formarnos sobre cu\u00e1les son buenas estrategias y t\u00e9cnicas para utilizar la IA en el trabajo de investigaci\u00f3n en matem\u00e1ticas.<\/p>\n
En esta primera sesi\u00f3n dedicaremos el tiempo necesario para debatir las implicaciones de este tsunami para posteriormente plantear un listado de problemas\u00a0de dificultades muy diversas\u00a0que estudiaremos por equipos con varios modelos IA, en cooperaci\u00f3n entre los asistentes con el objetivo de identificar inicialmente qu\u00e9 modelos y qu\u00e9 tipos de problemas son m\u00e1s adecuados para su soluci\u00f3n con IA.<\/p>\n
En sesiones posteriores estudiaremos qu\u00e9 prompts dan mejores resultados, c\u00f3mo configurar cada modelo, c\u00f3mo construir un agente o por qu\u00e9 algunas veces la IA parece negarse a colaborar.<\/p>\n
Qui\u00e9n lo desee podr\u00e1 proponer problemas que se puedan contar r\u00e1pido a no-expertos, que puedan estar bien enfocados a su soluci\u00f3n con IA y para los que est\u00e9 dispuest@ a compartir el m\u00e9rito de su resoluci\u00f3n.<\/p>\n
[\/vc_column_text][\/vc_tta_section][\/vc_tta_accordion][\/vc_column][\/vc_row]<\/p>","excerpt":"","slug":"seminario-de-analisis-matematico-y-matematica-aplicada-2026-2027","image":{"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos-.png","id":50007,"extension":"png","width":750,"height":370,"filesize":66198,"sizes":{"medium":{"width":300,"height":148,"mime-type":"image\/png","filesize":23800,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--300x148.png"},"thumbnail":{"width":150,"height":150,"mime-type":"image\/png","filesize":13226,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--150x150.png"},"mug-shot":{"width":150,"height":250,"mime-type":"image\/png","filesize":18350,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--150x250.png"},"sidebar":{"width":375,"height":185,"mime-type":"image\/png","filesize":29919,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--375x185.png"},"half":{"width":375,"height":185,"mime-type":"image\/png","filesize":29919,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--375x185.png"},"thimble":{"width":50,"height":50,"mime-type":"image\/png","filesize":3024,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--50x50.png"},"thumbnail-large":{"width":300,"height":300,"mime-type":"image\/png","filesize":33581,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--300x300.png"},"rss":{"width":108,"height":81,"mime-type":"image\/png","filesize":7088,"url":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos--108x81.png"}}},"all_day":false,"start_date":"2026-10-14 15:00:00","start_date_details":{"year":"2026","month":"10","day":"14","hour":"15","minutes":"00","seconds":"00"},"end_date":"2026-10-14 16:00:00","end_date_details":{"year":"2026","month":"10","day":"14","hour":"16","minutes":"00","seconds":"00"},"utc_start_date":"2026-10-14 15:00:00","utc_start_date_details":{"year":"2026","month":"10","day":"14","hour":"15","minutes":"00","seconds":"00"},"utc_end_date":"2026-10-14 16:00:00","utc_end_date_details":{"year":"2026","month":"10","day":"14","hour":"16","minutes":"00","seconds":"00"},"timezone":"UTC+0","timezone_abbr":"UTC+0","cost":"","cost_details":{"currency_symbol":"","currency_position":"prefix","values":[]},"website":"","show_map":false,"show_map_link":false,"hide_from_listings":false,"sticky":false,"featured":false,"categories":[{"name":"An\u00e1lisis Matem\u00e1tico","slug":"analisis-matematico","term_group":0,"term_taxonomy_id":347,"taxonomy":"tribe_events_cat","description":"","parent":346,"count":86,"filter":"raw","id":347,"urls":{"self":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/347","collection":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories","up":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/346"}},{"name":"Destacado ULL","slug":"destacado-ull","term_group":0,"term_taxonomy_id":4,"taxonomy":"tribe_events_cat","description":"","parent":0,"count":4913,"filter":"raw","id":4,"urls":{"self":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/4","collection":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories"}},{"name":"Facultad de Ciencias","slug":"facultad-de-ciencias","term_group":0,"term_taxonomy_id":972,"taxonomy":"tribe_events_cat","description":"","parent":788,"count":409,"filter":"raw","id":972,"urls":{"self":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/972","collection":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories","up":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/788"}},{"name":"Instituto de Matem\u00e1ticas y Aplicaciones","slug":"instituto-matematicas-aplicaciones","term_group":0,"term_taxonomy_id":4399,"taxonomy":"tribe_events_cat","description":"","parent":0,"count":96,"filter":"raw","id":4399,"urls":{"self":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/4399","collection":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories"}},{"name":"Matem\u00e1ticas, Estad\u00edstica e Investigaci\u00f3n Operativa","slug":"matematicas-estadistica-e-investigacion-operativa","term_group":0,"term_taxonomy_id":559,"taxonomy":"tribe_events_cat","description":"","parent":346,"count":82,"filter":"raw","id":559,"urls":{"self":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/559","collection":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories","up":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/346"}},{"name":"Modelizaci\u00f3n e Investigaci\u00f3n Matem\u00e1tica. Estad\u00edstica y Computaci\u00f3n","slug":"modelizacion-e-investigacion-matematica-estadistica-computacion","term_group":0,"term_taxonomy_id":4655,"taxonomy":"tribe_events_cat","description":"","parent":4644,"count":69,"filter":"raw","id":4655,"urls":{"self":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/4655","collection":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories","up":"https:\/\/www.ull.es\/portal\/agenda\/wp-json\/tribe\/events\/v1\/categories\/4644"}}],"tags":[],"venue":{"id":40609,"author":"65","status":"publish","date":"2025-02-11 08:31:28","date_utc":"2025-02-11 08:31:28","modified":"2025-02-11 08:31:28","modified_utc":"2025-02-11 08:31:28","url":"https:\/\/www.ull.es\/portal\/agenda\/local\/aula-2-3-del-edificio-calabaza\/","venue":"Aula 2.3 del Edificio Calabaza","slug":"aula-2-3-del-edificio-calabaza","address":"Campus Anchieta","city":"San Crist\u00f3bal de La Laguna","province":"Santa Cruz de Tenerife","stateprovince":"Santa Cruz de Tenerife","json_ld":{"@type":"Place","name":"Aula 2.3 del Edificio Calabaza","description":"","url":"https:\/\/www.ull.es\/portal\/agenda\/local\/aula-2-3-del-edificio-calabaza\/","address":{"@type":"PostalAddress","streetAddress":"Campus Anchieta","addressLocality":"San Crist\u00f3bal de La Laguna","addressRegion":"Santa Cruz de Tenerife"},"telephone":"","sameAs":""},"show_map":true,"show_map_link":true,"global_id":"www.ull.es\/portal\/agenda?id=40609","global_id_lineage":["www.ull.es\/portal\/agenda?id=40609"]},"organizer":[{"id":18539,"author":"65","status":"publish","date":"2021-02-25 09:08:23","date_utc":"2021-02-25 09:08:23","modified":"2021-04-28 08:59:26","modified_utc":"2021-04-28 08:59:26","url":"https:\/\/www.ull.es\/portal\/agenda\/organizador\/instituto-de-matematicas-y-aplicaciones\/","organizer":"Instituto de Matem\u00e1ticas y Aplicaciones","slug":"instituto-de-matematicas-y-aplicaciones","json_ld":{"@type":"Person","name":"Instituto de Matem\u00e1ticas y Aplicaciones","description":"","url":"https:\/\/www.ull.es\/portal\/agenda\/organizador\/instituto-de-matematicas-y-aplicaciones\/","telephone":"","email":"","sameAs":""},"global_id":"www.ull.es\/portal\/agenda?id=18539","global_id_lineage":["www.ull.es\/portal\/agenda?id=18539"]},{"id":9915,"author":"51","status":"publish","date":"2019-01-13 22:23:18","date_utc":"2019-01-13 22:23:18","modified":"2021-02-25 09:02:57","modified_utc":"2021-02-25 09:02:57","url":"https:\/\/www.ull.es\/portal\/agenda\/organizador\/area-de-didactica-de-la-matematica-departamento-de-analisis-matematico-de-la-ull\/","organizer":"Departamento de An\u00e1lisis Matem\u00e1tico","slug":"area-de-didactica-de-la-matematica-departamento-de-analisis-matematico-de-la-ull","json_ld":{"@type":"Person","name":"Departamento de An\u00e1lisis Matem\u00e1tico","description":"","url":"https:\/\/www.ull.es\/portal\/agenda\/organizador\/area-de-didactica-de-la-matematica-departamento-de-analisis-matematico-de-la-ull\/","telephone":"","email":"","sameAs":""},"global_id":"www.ull.es\/portal\/agenda?id=9915","global_id_lineage":["www.ull.es\/portal\/agenda?id=9915"]}],"json_ld":{"@context":"http:\/\/schema.org","@type":"Event","name":"Seminario de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada 2026-2027","description":"<p>El Departamento de An\u00e1lisis Matem\u00e1tico y\u00a0 el Instituto de Matem\u00e1ticas y Aplicaciones de la Universidad de La Laguna organizan Seminarios de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada con car\u00e1cter semanal.Conferenciante: Marcus Vaktn\u00e4s\u00a0(Uppsala U., Suecia) Multiple orthogonal polynomials extend the notion of orthogonal polynomials, allowing broader applications to e.g. rational approximation, numerical integration, and random matrix theory....<\/p>\\n","image":"https:\/\/www.ull.es\/portal\/agenda\/wp-content\/uploads\/sites\/12\/2026\/09\/banner-eventos-.png","url":"https:\/\/www.ull.es\/portal\/agenda\/evento\/seminario-de-analisis-matematico-y-matematica-aplicada-2026-2027\/","startDate":"2026-10-14T15:00:00+00:00","endDate":"2026-10-14T16:00:00+00:00","location":{"@type":"Place","name":"Aula 2.3 del Edificio Calabaza","description":"","url":"https:\/\/www.ull.es\/portal\/agenda\/local\/aula-2-3-del-edificio-calabaza\/","address":{"@type":"PostalAddress","streetAddress":"Campus Anchieta","addressLocality":"San Crist\u00f3bal de La Laguna","addressRegion":"Santa Cruz de Tenerife"},"telephone":"","sameAs":""},"organizer":{"@type":"Person","name":"Instituto de Matem\u00e1ticas y Aplicaciones","description":"","url":"https:\/\/www.ull.es\/portal\/agenda\/organizador\/instituto-de-matematicas-y-aplicaciones\/","telephone":"","email":"","sameAs":""}}}