{"id":71075,"date":"2019-04-26T14:53:55","date_gmt":"2019-04-26T14:53:55","guid":{"rendered":"https:\/\/raed.academy\/?p=71075"},"modified":"2019-05-22T15:01:16","modified_gmt":"2019-05-22T15:01:16","slug":"on-some-results-and-conjectures-in-the-theory-of-automorphic-forms","status":"publish","type":"post","link":"https:\/\/raed.academy\/en\/on-some-results-and-conjectures-in-the-theory-of-automorphic-forms\/","title":{"rendered":"The rolle in mathematics of automorphic forms"},"content":{"rendered":"<h2>Pilar Bayer stars in the last colloquium of the Institute of Mathematical Sciences in Madrid<\/h2>\n<div id=\"attachment_70926\" style=\"width: 319px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-70926\" class=\"jetpack-lazy-image jetpack-lazy-image--handled wp-image-70926\" src=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Pilar-Bayer-Isant.jpg\" alt=\"Dra. Pilar Bayer Isant\" width=\"309\" height=\"189\" aria-describedby=\"caption-attachment-70926\" data-attachment-id=\"70926\" data-permalink=\"https:\/\/raed.academy\/resultados-conjeturas-teoria-formas-automorfas\/pilar-bayer-isant-4\/\" data-orig-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Pilar-Bayer-Isant.jpg\" data-orig-size=\"450,275\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Dra. Pilar Bayer Isant\" data-image-description=\"\" data-medium-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Pilar-Bayer-Isant.jpg\" data-large-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Pilar-Bayer-Isant.jpg\" data-lazy-loaded=\"1\" \/><p id=\"caption-attachment-70926\" class=\"wp-caption-text\">Dr Pilar Bayer<\/p><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-full wp-image-70989 jetpack-lazy-image jetpack-lazy-image--handled\" src=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/coloquio_UAM-ICMAT.jpg\" alt=\"\" width=\"390\" height=\"564\" data-attachment-id=\"70989\" data-permalink=\"https:\/\/raed.academy\/valoracion-y-compraventa-de-empresas-oriol-amat\/coloquio_uam-icmat\/\" data-orig-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/coloquio_UAM-ICMAT.jpg\" data-orig-size=\"390,564\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"coloquio_UAM-ICMAT\" data-image-description=\"\" data-medium-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/coloquio_UAM-ICMAT.jpg\" data-large-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/coloquio_UAM-ICMAT.jpg\" data-lazy-loaded=\"1\" \/><a href=\"https:\/\/raed.academy\/en\/academicians\/dr-pilar-bayer-isant\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Pilar Bayer<\/strong><\/a> presented some of her results at the Colloquium of the Institute of Mathematical Sciences, in Madrid the last April 12th. <a href=\"https:\/\/raed.academy\/en\/academicians\/dr-pilar-bayer-isant\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Pilar Bayer<\/strong><\/a> is an emeritus professor of the <a href=\"http:\/\/ub.edu\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universitat de Barcelona<\/strong><\/a>, full academician of the Royal European Academy of Doctors-Barcelona 1914 (RAED) and secretary of its Experimental Sciences Section. At the <a href=\"https:\/\/www.uam.es\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universidad Aut\u00f3noma de Madrid<\/strong><\/a>, she held the lecture entitled \u201cOn some results and conjectures in the theory of automorphic forms\u201d. The event was scheduled in the cycle of colloquia organized by the <a href=\"https:\/\/www.icmat.es\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Instituto de Ciencias Matem\u00e1ticas<\/strong><\/a> (ICMAT), a mathematical research center supported by the Spanish Consejo Superior de Investigaciones Cient\u00edficas (CSIC), the <a href=\"https:\/\/www.uam.es\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universidad Aut\u00f3noma de Madrid<\/strong><\/a>, the <a href=\"https:\/\/www.uc3m.es\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universidad Carlos III<\/strong><\/a> and the <a href=\"http:\/\/www.ucm.es\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universidad Complutense de Madrid<\/strong><\/a>.<\/p>\n<p>The talk of <a href=\"https:\/\/raed.academy\/en\/academicians\/dr-pilar-bayer-isant\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Bayer<\/strong><\/a> was focused in new results and conjectures in the theory automorphic forms. Automorphic forms are a generalization of periodic functions and play an important rolle in modern number theory. From this concept, it derives an extensive network of results and conjectures, some of them included in the famous <strong>Langlands<\/strong> Program. The conjectures relate representations of the absolute <strong>Galois<\/strong> group of a number field with representations of some algebraic groups, playing the automorphic forms an important next of union. An example of this situation can be found in <strong>Wiles<\/strong>&#8216; modularity theorem, which was one of the conjectures of the <strong>Langlands<\/strong> program and became a key piece in the proof of <strong>Fermat<\/strong>&#8216;s Last Theorem. The quotation \u201cthere are five fundamental operations in mathematics: addition, subtraction, multiplication, division and modular forms\u201d, attributed to the German mathematician Martin Eichler, has been subscribed on numerous occasions by other mathematicians as well, to indicate the relevance of such forms.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-70923 jetpack-lazy-image jetpack-lazy-image--handled alignleft\" src=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Instituto-Ciencias-Matematicas-Madrid-ICMAT-edificio-dstNtc.jpg\" alt=\"Instituto de Ciencias Matem\u00e1ticas de Madrid (ICMAT)\" width=\"390\" height=\"259\" aria-describedby=\"caption-attachment-70923\" data-attachment-id=\"70923\" data-permalink=\"https:\/\/raed.academy\/resultados-conjeturas-teoria-formas-automorfas\/instituto-ciencias-matematicas-madrid-icmat-edificio-dstntc\/\" data-orig-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Instituto-Ciencias-Matematicas-Madrid-ICMAT-edificio-dstNtc.jpg\" data-orig-size=\"600,398\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Instituto-Ciencias-Matematicas-Madrid-ICMAT-edificio-dstNtc\" data-image-description=\"\" data-medium-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Instituto-Ciencias-Matematicas-Madrid-ICMAT-edificio-dstNtc.jpg\" data-large-file=\"https:\/\/raed.academy\/wp-content\/uploads\/2019\/04\/Instituto-Ciencias-Matematicas-Madrid-ICMAT-edificio-dstNtc.jpg\" data-lazy-loaded=\"1\" \/><a href=\"https:\/\/raed.academy\/en\/academicians\/dr-pilar-bayer-isant\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Pilar Bayer<\/strong><\/a> has developed her career as mathematical researcher and professor at institutions such as the <a href=\"https:\/\/www.uni-regensburg.de\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>University of Regensburg<\/strong><\/a> (Germany), where she consolidated her training in number theory, the <strong><a href=\"https:\/\/web.unican.es\" target=\"_blank\" rel=\"noopener noreferrer\">Universidad de Cantabria<\/a><\/strong>, the\u00a0<a href=\"https:\/\/www.uab.cat\/es\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universitat Aut\u00f2noma de Barcelona<\/strong><\/a> and the University of Barcelona, where she has served as full professor of algebra in the Department of Algebra and Geometry from 1982 until her retirement in 2016.<\/p>\n<p><a href=\"https:\/\/raed.academy\/en\/academicians\/dr-pilar-bayer-isant\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Bayer<\/strong><\/a> has been working on topics related to automorphic forms very early in her career. Among her publications, the article <strong>\u201cOn automorphic forms and Hodge theory\u201d<\/strong>, jointly with <strong>J\u00fcrgen Neukirch<\/strong> and published in 1981 in <strong>\u201cMathematische Annalen\u201d<\/strong>, yields an example of it. Her areas of expertise include zeta functions, the inverse problem of <strong>Galois<\/strong> theory, diophantine equations and <strong>Shimura<\/strong> curves. One of her contributions has been the creation in 1986 of the <strong>Barcelona Number Theory Seminar<\/strong>, an international reference in\u00a0 research in number theory, coordinated at present by the University of Barcelona, the <a href=\"https:\/\/www.uab.cat\/es\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universitat Aut\u00f2noma de Barcelona<\/strong><\/a> and the <a href=\"http:\/\/www.upc.edu\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Universitat Polit\u00e8cnica de Catalunya<\/strong><\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pilar Bayer stars in the last colloquium of the Institute of Mathematical Sciences in Madrid Pilar Bayer presented some of her results at the Colloquium of the Institute of Mathematical Sciences, in Madrid the last April 12th. Pilar Bayer is an emeritus professor of the Universitat de Barcelona, full academician of the Royal European Academy [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":70925,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[67],"tags":[],"class_list":["post-71075","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized-6","et-has-post-format-content","et_post_format-et-post-format-standard"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The rolle in mathematics of automorphic forms - Royal European Academy of Doctors<\/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:\/\/raed.academy\/en\/on-some-results-and-conjectures-in-the-theory-of-automorphic-forms\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The rolle in mathematics of automorphic forms - Royal European Academy of Doctors\" \/>\n<meta property=\"og:description\" content=\"Pilar Bayer stars in the last colloquium of the Institute of Mathematical Sciences in Madrid Pilar Bayer presented some of her results at the Colloquium of the Institute of Mathematical Sciences, in Madrid the last April 12th. 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