{"id":666,"date":"2022-02-08T15:33:34","date_gmt":"2022-02-08T15:33:34","guid":{"rendered":"https:\/\/pages.charlotte.edu\/colloquium\/?p=666"},"modified":"2022-02-08T15:33:34","modified_gmt":"2022-02-08T15:33:34","slug":"friday-february-11-2022-900-1000-via-zoom","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/colloquium\/blog\/2022\/02\/08\/friday-february-11-2022-900-1000-via-zoom\/","title":{"rendered":"Friday, February 11, 2022, 9:00-10:00 via Zoom"},"content":{"rendered":"\n<p><strong>Speaker:<\/strong>\u00a0Dr. Luo Ye from Xiamen University<\/p>\n\n\n\n<p><strong>Date and Time:<\/strong>\u00a0Friday, February 11, 2022, 9:00-10:00 via Zoom. Please contact\u00a0<a href=\"https:\/\/math.charlotte.edu\/directory\/william-brian\">Will Brian<\/a>\u00a0to obtain the Zoom link.<\/p>\n\n\n\n<p><strong>Title:<\/strong>\u00a0Tropical convexity analysis and some applications<\/p>\n\n\n\n<p><strong>Abstract:<\/strong>\u00a0 The tropical semiring is an idempotent semiring where \u00a0the usual operations of addition and multiplication are replaced by operations of minimum\/maximum and addition respectively. Tropical geometry is a theory of geometry over the tropical semiring which has rich combinatorial features and can be described as a degenerated version of algebraic geometry over the field of complex numbers under Maslov dequantization or over a non-archimedean field under the valuation map.\u00a0The \u00a0features of &#8220;linear combinations&#8221; in tropical geometry can be captured by the notion of tropical convexity. \u00a0 In this talk, I will introduce a general theory of tropical convexity analysis based on the so-called &#8220;B-pseudonorms\u201d on tropical projective spaces, and show some subsequent results, e.g., a tropical version of Mazur&#8217;s Theorem on closed tropical convex hulls and a fixed point theorem for tropical projections.\u00a0Two applications will also be presented. The first is to establish a connection between tropical projections and \u00a0reduced divisors on (metric) graphs, and the second is to construct \u00a0min-max-plus neural networks, a new type of artificial neural networks.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><\/h2>\n\n\n\n<p><a href=\"https:\/\/pages.charlotte.edu\/colloquium\/blog\/2022\/02\/01\/friday-february-4-2022-1100-1200-via-zoom\/#wp-toolbar\">Skip to toolbar<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker:\u00a0Dr. Luo Ye from Xiamen University Date and Time:\u00a0Friday, February 11, 2022, 9:00-10:00 via Zoom. Please contact\u00a0Will Brian\u00a0to obtain the Zoom link. Title:\u00a0Tropical convexity analysis and some applications Abstract:\u00a0 The tropical semiring is an idempotent semiring where \u00a0the usual operations of addition and multiplication are replaced by operations of minimum\/maximum and addition respectively. Tropical geometry [&hellip;]<\/p>\n","protected":false},"author":2373,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-666","post","type-post","status-publish","format-standard","hentry","category-spring-2022"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3kCtT-aK","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/666","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/users\/2373"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/comments?post=666"}],"version-history":[{"count":1,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/666\/revisions"}],"predecessor-version":[{"id":667,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/666\/revisions\/667"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/media?parent=666"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/categories?post=666"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/tags?post=666"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}