{"id":623,"date":"2016-10-27T17:52:40","date_gmt":"2016-10-27T14:52:40","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=623"},"modified":"2016-11-06T19:23:31","modified_gmt":"2016-11-06T17:23:31","slug":"colloquium-tuesday-november-1-2-pm-speaker-eitan-sayag-ben-gurion-title-spherical-functions-spherical-distributions-and-their-applications","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=623","title":{"rendered":"Colloquium: Tuesday, November 1, 2 pm. Speaker: Eitan Sayag (Ben Gurion). Title: &#8220;Spherical functions, spherical distributions and their applications&#8221;."},"content":{"rendered":"<p>Periods of automorphic forms provides an important tool to classify automorphic representations and arise time and time again in problems with arithmetic origin.<\/p>\n<p>Motivated by that, I shall describe some of our investigation of local counterparts of these periods that involve representation theory and invariant harmonic analysis on p-adic and real spherical spaces. The results I plan to report on include:<\/p>\n<p>&nbsp;<\/p>\n<p>* Quantitative generalizations of Howe-Moore phenomena regarding decay of generalized matrix coefficients in the real case.<\/p>\n<p>* Qualitative generalizations of Howe\/Harish-Chandra character expansions in the p-adic case.<\/p>\n<p>&nbsp;<\/p>\n<p>I shall explain how to use the results on generalized matrix coefficients to obtain new results on counting lattice points in the realm of real Spherical spaces.<\/p>\n<p>If time permits I will explain the role of Bernstein center in studying distributions in the p-adic case allowing tight control on the singularities of generalized characters on p-adic Spherical spaces.<\/p>\n<p>&nbsp;<\/p>\n<p>My lecture will be based on joint works with B. Kr\\&#8221;{o}tz, F. Knop and H. Schlichtkrull regarding decay of functions and on a joint work with Avraham Aizenbud and Dmitry Gourevitch regarding the regularity of certain distributions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Periods of automorphic forms provides an important tool to classify automorphic representations and arise time and time again in problems with arithmetic origin. Motivated by that, I shall describe some of our investigation of local counterparts of these periods that&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=623\">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-623","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\/623","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=623"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/623\/revisions"}],"predecessor-version":[{"id":624,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/623\/revisions\/624"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}