{"id":14955,"date":"2026-11-02T14:46:41","date_gmt":"2026-11-02T10:46:41","guid":{"rendered":"https:\/\/bte.iliauni.edu.ge\/?p=14955"},"modified":"2026-11-02T14:46:41","modified_gmt":"2026-11-02T10:46:41","slug":"professor-giorgi-khimshiashvili-s-seminar-analytically-solvable-pursuit-problems-with-geometric-constraints","status":"publish","type":"post","link":"https:\/\/bte.iliauni.edu.ge\/en\/professor-giorgi-khimshiashvili-s-seminar-analytically-solvable-pursuit-problems-with-geometric-constraints\/","title":{"rendered":"Professor Giorgi Khimshiashvili\u2019s Seminar \u201cAnalytically solvable pursuit problems with geometric constraints\u201d"},"content":{"rendered":"<p>Institute for Fundamental and Interdisciplinary Mathematical Research Seminar:<\/p>\n<p>Speaker: Prof. Giorgi Khimshiashvili<\/p>\n<p>\u201cAnalytically solvable pursuit problems with geometric constraints\u201d<\/p>\n<p>Planar pursuit problems with geometric constraints of the lifeline type and non-zero capture radius type will be considered. It will be shown that an analytic solution to the Apollonius pursuit problem with non-zero capture can be given in terms of the so-called Cartesian ovals of the fourth degree. Specifically, the minimal pursuit time can be expressed as the minimal positive root of a certain quartic polynomial, which implies that the optimal direction of pursuit can also be expressed by an explicit formula. In the Apollonius setting with a lifeline we\u2019ll compute the optimal pursuit direction for a given direction of escape, which will yield the direction of escape with the maximal capture time. Several open problems for further exploration will also be presented.<\/p>\n<p>Time: November 3, 17:00-19:00<\/p>\n<div>\n<div>\n<div>\n<p>Location: Ilia State University, Room T302, 45 Ilia Chavchavadze Avenue.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Institute for Fundamental and Interdisciplinary Mathematical Research Seminar: Speaker: Prof. Giorgi Khimshiashvili \u201cAnalytically solvable pursuit problems with geometric constraints\u201d Planar pursuit problems with geometric constraints of the lifeline type and non-zero capture radius type will be considered. It will be shown that an analytic solution to the Apollonius pursuit problem with non-zero capture can be&#8230;<\/p>\n","protected":false},"author":7,"featured_media":14957,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[172],"tags":[],"class_list":["post-14955","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-new-blog"],"acf":[],"_links":{"self":[{"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/posts\/14955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/comments?post=14955"}],"version-history":[{"count":0,"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/posts\/14955\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/media\/14957"}],"wp:attachment":[{"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/media?parent=14955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/categories?post=14955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bte.iliauni.edu.ge\/en\/wp-json\/wp\/v2\/tags?post=14955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}