{"id":50,"date":"2018-05-30T22:28:24","date_gmt":"2018-05-30T22:28:24","guid":{"rendered":"http:\/\/blog.metu.edu.tr\/burakk\/?page_id=50"},"modified":"2021-08-18T10:55:03","modified_gmt":"2021-08-18T10:55:03","slug":"research-interests","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/burakk\/research-interests\/","title":{"rendered":"Research interests"},"content":{"rendered":"<p align=\"justify\">I have been trained as a <a href=\"https:\/\/www.wikiwand.com\/en\/Mathematical_logic\">mathematical logic<\/a>ian, with focus in\u00a0<a href=\"https:\/\/www.wikiwand.com\/en\/Set_theory\">set theory<\/a>. My research interests currently lie in\u00a0<a href=\"https:\/\/www.wikiwand.com\/en\/Descriptive_set_theory\">descriptive set theory<\/a>\u00a0and its applications to other fields of mathematics such as <a href=\"https:\/\/www.wikiwand.com\/en\/Topological_dynamics\">topological dynamics<\/a> and <a href=\"https:\/\/www.wikiwand.com\/en\/Group_theory\">group theory<\/a>. That said, I am also interested in various questions of more pure set-theoretic nature.<\/p>\n<p align=\"justify\">In the broadest sense, descriptive set theory is the study of \u201cdefinable\u201d subsets of <a href=\"https:\/\/en.wikipedia.org\/wiki\/Polish_space\">Polish spaces<\/a>. For a detailed discussion of how <a href=\"https:\/\/link.springer.com\/book\/10.1007%2F978-1-4612-4190-4\">classical descriptive set theory<\/a> came into existence, you can read\u00a0<a href=\"http:\/\/math.bu.edu\/people\/aki\/2.pdf\">this excellent article<\/a>\u00a0by Akihiro Kanamori.<\/p>\n<p align=\"justify\">As it is the case with any other field of mathematics, descriptive set theory has evolved over time. One of the major research areas of contemporary descriptive set theory is the study\u00a0of <a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-1-4020-5764-9_5\">Borel equivalence relations<\/a>. Although\u00a0the study of Borel equivalence relations\u00a0is important on its own and has its own motivations, it also provides a mathematical framework to analyze the relative complexity of classification problems from diverse areas of mathematics.<\/p>\n<p align=\"justify\">My <a href=\"https:\/\/rucore.libraries.rutgers.edu\/rutgers-lib\/50019\/\">PhD dissertation<\/a> was about the analysis of some classification problems from topological dynamics. More specifically, I analyzed the Borel complexity of the topological conjugacy relation on various Cantor minimal systems, including certain symbolic systems.<\/p>\n<p align=\"justify\">Since then, I have been working on some problems in Ramsey theory of countable ordinals, descriptive graph combinatorics, definability of various geometric constructions and some problems in group theory of model-theoretic nature.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have been trained as a mathematical logician, with focus in\u00a0set theory. My research interests currently lie in\u00a0descriptive set theory\u00a0and its applications to other fields of mathematics such as topological dynamics and group theory. That said, I am also interested in various questions of more pure set-theoretic nature. In the broadest sense, descriptive set theory [&hellip;]<\/p>\n","protected":false},"author":4571,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-50","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/pages\/50","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/users\/4571"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/comments?post=50"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/pages\/50\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/burakk\/wp-json\/wp\/v2\/media?parent=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}