{"id":12738,"date":"2022-03-18T12:30:46","date_gmt":"2022-03-18T04:30:46","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=12738"},"modified":"2022-03-21T10:28:02","modified_gmt":"2022-03-21T02:28:02","slug":"001-53","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2022\/03\/18\/001-53\/","title":{"rendered":"[\u6578\u8ad6\u7814\u8a0e\u6703] <\/span>\u30103\u670825\u65e5\u3011\u4e8e\u9756 \u9662\u58eb Periods, Gamma values, and Algebraic Relations"},"content":{"rendered":"

Speaker\uff1a\u4e8e\u9756 \u9662\u58eb<\/a><\/span><\/p>\n

Job title\uff1a\u53f0\u7063\u5927\u5b78\u540d\u8b7d\u6559\u6388\u3001\u6e05\u83ef\u5927\u5b78\u69ae\u8b7d\u8b1b\u5ea7\u6559\u6388\u3001\u53f0\u7063\u5e2b\u7bc4\u5927\u5b78\u8b1b\u5ea7\u6559\u6388<\/p>\n

Title : Periods, Gamma values, and Algebraic Relations<\/p>\n

Abstract\uff1a
\nThis is a survey talk, leading to recent developments and open problems.
\nThe story started four centuries ago, with Euler, Gauss, Legendre, … The simplest\u00a0period is $2\\pi\\sqrt{-1}$, as every mathematics student\u00a0knows. We view periods as transcendental invariants attached to arithmetical objects via “analytic” means, e.g. arc length of the unit circle. We are interested in understanding these natural transcendental quantities,\u00a0or numbers. Facing the problem of finding all algebraic relations among the transcendental invariants.\u00a0If several numbers arise naturally, and no one knows any algebraic relations in between these numbers,\u00a0we wish to prove that they are actually algebraically independent. In the sense that verifying these, say N, numbers are not roots of any non-zero polynomial of N variables with coefficients from $\\mathbf Z$, when you substitute the N numbers for the N variables into polynomials, you never get\u00a0zero.
\nPeriods of arithmetical objects should be algebraically independent in\u00a0general, unless there are natural precious algebraic relations coming from the “geometry” behind the scene. This is the 20 century\u00a0philosophy leading to conjectures of Grothendieck, Deligne, Shimura, Lang-Rohrlich…. In the positive characteristic worlds, the global function fields over finite fields play roles as number\u00a0fields, natural arithmetic objects also abound.\u00a0 The algebraic dependence\/independence phenomena in Arithmetic Geometry here are a little more transparent. One can manage to prove more. I will give a very brief introduction\u00a0in the end of this talk on the algebraic independence of all coordinates of a non-zero period vector of a Hilbert-Blumenthal-Drinfeld module with complex multiplication, recent work of Brownawell-Chang-Papanikolas-Wei (extending a theorem of mine 30 years ago) .<\/p>\n

Time: 1:30 p.m., March 25(Fri.), 2022<\/p>\n

Place: Room 210, Department of Mathematics, NTNU<\/p>\n","protected":false},"excerpt":{"rendered":"

Speaker\uff1a\u4e8e\u9756 \u9662\u58eb Job title\uff1a\u53f0\u7063\u5927\u5b78\u540d\u8b7d\u6559\u6388\u3001\u6e05\u83ef\u5927\u5b78\u69ae\u8b7d\u8b1b\u5ea7\u6559\u6388\u3001\u53f0\u7063\u5e2b\u7bc4\u5927\u5b78\u8b1b\u5ea7\u6559\u6388 […]<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"off","ocean_gallery_id":[],"footnotes":""},"categories":[1,18,122,124],"tags":[],"class_list":["post-12738","post","type-post","status-publish","format-standard","hentry","category-news","category-events","category-gallery","category-speeches","entry"],"_links":{"self":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/12738","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=12738"}],"version-history":[{"count":7,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/12738\/revisions"}],"predecessor-version":[{"id":12754,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/12738\/revisions\/12754"}],"wp:attachment":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=12738"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=12738"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=12738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}