{"id":2338,"date":"2022-03-24T17:22:07","date_gmt":"2022-03-24T15:22:07","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2338"},"modified":"2022-04-07T10:41:02","modified_gmt":"2022-04-07T07:41:02","slug":"colloquium-tuesday-march-29-2022-speaker-speaker-christopher-voll-bielefeld-title-zeta-functions-of-groups-rings-and-modules","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2338","title":{"rendered":"Colloquium: Tuesday, March 29, 2022. Speaker:  Speaker: Christopher Voll\u00a0(Bielefeld). Title: &#8220;Zeta functions of groups, rings, and modules&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><br>The zoom link for our meetings is:<br><a rel=\"noreferrer noopener\" href=\"https:\/\/us02web.zoom.us\/j\/83337601824\" target=\"_blank\">https:\/\/us02web.zoom.us\/j\/83337601824<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract: Zeta functions are ubiquitous in mathematics. In algebra and geometry, they often have an enumerative interpretation, prominent examples being the Dedekind zeta function of a number field and the (Weil) zeta&nbsp;function of an algebraic variety over a finite field.<br>Over the last few decades, zeta functions have become powerful tools&nbsp;also in the study of asymptotic invariants of infinite groups and&nbsp;modules,&nbsp;notably in the study of their subgroup and submodule growth, viz. the&nbsp;distribution of their finite index subgroups resp. submodules.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Under favourable conditions, zeta functions of groups, rings, and&nbsp;modules&nbsp;share key features with their more classical predecessors in algebra and&nbsp;geometry &#8212; such as Eulerian products with rational factors, local and&nbsp;(sometimes) global functional equations, analytic continuation etc. &#8212;&nbsp;while retaining a distinct flavour.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In my talk, I will survey some recent developments in the theory of&nbsp;these zeta functions. I will concentrate on the phenomenon of local&nbsp;functional equations, combining delicate combinatorial arguments with&nbsp;consequences of the &#8220;Weil conjectures&#8221;, deep results on the numbers of&nbsp;rational points on algebraic varieties over finite fields.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The zoom link for our meetings is:https:\/\/us02web.zoom.us\/j\/83337601824 Abstract: Zeta functions are ubiquitous in mathematics. In algebra and geometry, they often have an enumerative interpretation, prominent examples being the Dedekind zeta function of a number field and the (Weil) zeta&nbsp;function of&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2338\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-2338","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2338"}],"version-history":[{"count":2,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2338\/revisions"}],"predecessor-version":[{"id":2368,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2338\/revisions\/2368"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}