{"id":12701,"date":"2022-02-14T16:48:31","date_gmt":"2022-02-14T21:48:31","guid":{"rendered":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12701"},"modified":"2022-02-19T20:08:48","modified_gmt":"2022-02-20T01:08:48","slug":"seminar-talk-on-euclidean-twistor-unification-and-the-twistor-p1","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12701","title":{"rendered":"Seminar talk on Euclidean Twistor Unification and the Twistor P<sup>1<\/sup>"},"content":{"rendered":"<p>Today I gave a talk via Zoom at the <a href=\"https:\/\/www.furey.space\/\">Algebra, Particles and Quantum Theory seminar series<\/a> organized by Nichol Furey.  The slides from the talk are <a href=\"https:\/\/www.math.columbia.edu\/~woit\/twistorunification\/algpartqm.pdf\">here<\/a> (I gather the talk was recorded and video might be available at some point).<\/p>\n<p>This talk emphasized explaining the twistor geometry, integrating some of what I&#8217;ve learned over the last few months thinking about the &#8220;twistor $P^1$&#8221; (see <a href=\"https:\/\/arxiv.org\/abs\/2202.02657\">here<\/a>).  For instance, one way to think of the basic object of Euclidean twistor theory is as $\\mathbf {CP}^3$, together with a different real structure (the twistor real structure) than the usual one given by conjugation of complex coordinates.   One thing that struck me while writing up these slides is that the Euclidean twistor story gets a lot of mileage out of identifying $\\mathbf C^2$ and $\\mathbf H$, together with taking as fundamental $\\mathbf H^2$.  It has always seemed possible that the octonions might have a role to play here; one way into that might be to think about identifying $\\mathbf H^2$ with $\\mathbf O$ in some analogous way to the $\\mathbf C,\\mathbf H$ story.<\/p>\n<p>There&#8217;s nothing new here about any of the many open questions of how to use this geometrical framework to get a fully worked out dynamics that would include the Standard Model and gravity.  After a detour into number theory and hyper-K&auml;hler geometry for several months, I&#8217;m now getting back to thinking about those questions.<\/p>\n<p><strong>Update<\/strong>: Video of the talk is now available <a href=\"https:\/\/www.youtube.com\/watch?v=qxq4ZuA1q4E\">here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today I gave a talk via Zoom at the Algebra, Particles and Quantum Theory seminar series organized by Nichol Furey. The slides from the talk are here (I gather the talk was recorded and video might be available at some &hellip; <a href=\"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=12701\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_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_post_was_ever_published":false},"categories":[31],"tags":[],"class_list":["post-12701","post","type-post","status-publish","format-standard","hentry","category-twistor-unification"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12701","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12701"}],"version-history":[{"count":11,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12701\/revisions"}],"predecessor-version":[{"id":12716,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/12701\/revisions\/12716"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12701"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12701"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}