{"id":5,"date":"2017-12-06T14:11:58","date_gmt":"2017-12-06T14:11:58","guid":{"rendered":"http:\/\/sites.rutgers.edu\/professor-example\/?page_id=5"},"modified":"2022-09-10T05:26:04","modified_gmt":"2022-09-10T05:26:04","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/john-loftin\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<h2>Interests<\/h2>\n<p>Geometric Analysis; Affine and Projective Geometric Structures; Teichm\u00fcller Theory; Affine Differential Geometry<\/p>\n<h2>Research Articles<\/h2>\n<ul>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2022\/09\/Limits-of-Cubic-Differentials-and-Buildings.pdf\">Limits of Cubic Differentials and Buildings<\/a> (with Andrea Tamburelli and Michael Wolf), submitted, 2022.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2021\/05\/plumbing.pdf\">Coordinates on the Augmented Moduli Space of Convex RP<sup>2<\/sup> Structures<\/a> (with Tengren Zhang), Journal of the London Mathematical Society, 2021.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/minRH4.pdf\">The Moduli Spaces of Equivariant Minimal Surfaces in RH<sup>3<\/sup> and RH<sup>4<\/sup> via Higgs Bundles<\/a> (with Ian McIntosh), Geometriae Dedicata, 2019.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/arxiv_view_higgs_ch2.pdf\">Equivariant Minimal Surfaces in CH<sup>2<\/sup> and Their Higgs Bundles<\/a> (with Ian McIntosh), Asian Journal of Mathematics, 2019.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/neck-pinch-final7-19.pdf\">Convex RP<sup>2<\/sup> Structures and Cubic Differentials Under Neck Separation<\/a>, Journal of Differential Geometry, 2019.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/af-ymh.pdf\">Approximate Yang-Mills-Higgs Metrics on Flat Higgs Bundles over an Affine Manifold<\/a> (with Indranil Biswas and Matthias Stemmler), Communications in Analysis and Geometry, 2014.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/affine-vortex.pdf\">The Vortex Equations on Affine Manifolds<\/a> (with Indranil Biswas and Matthias Stemmler), Transactions of the AMS, 2014.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/mlag16.pdf\">Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH<sup>2<\/sup><\/a> (with Zheng Huang and Marcello Lucia), Mathematical Research Letters, 2013.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/affine-ymh.pdf\">Affine Yang-Mills-Higgs Metrics<\/a> (with Indranil Biswas and Matthias Stemmler), Journal of Symplectic Geometry, 2013.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/min-lag.pdf\">Minimal Lagrangian Surfaces in CH<sup>2<\/sup> and Representations of Surface Groups into SU(2,1)<\/a> (with Ian McIntosh), Geometriae Dedicata, 2013.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/affine.pdf\">Hermitian-Einstein Connections on Principal Bundles over Flat Affine Manifolds<\/a> (with Indranil Biswas), International Journal of Mathematics, 2012.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/10\/affine-he-revised-8-08.pdf\">Affine Hermitian-Einstein Metrics<\/a>, Asian Journal of Mathematics, 2009.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/ga2007-anf.pdf\">Limits of Solutions to a Parabolic Monge Amp\u00e8re Equation<\/a> (with Mao-Pei Tsui), in Proceeding of the International Conference on Geometric Analysis, NCTS (Taipei, Taiwan; June, 2007), 2009.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/anf.pdf\">Ancient Solutions of the Affine Normal Flow<\/a> (with Mao-Pei Tsui), Journal of Differential Geometry, 2008.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/comp2.pdf\">Flat Metrics, Cubic Differentials and Limits of Projective Holonomies<\/a>, Geometriae Dedicata, 2007.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/hess.pdf\">Affine Manifolds, SYZ Geometry and the &#8220;Y&#8221; Vertex<\/a> (with Shing-Tung Yau and Eric Zaslow), Journal of Differential Geometry, 2005, with <a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/hess-erratum.pdf\">erratum<\/a>, 2008.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/semiflat.pdf\">Singular Semi-Flat Calabi-Yau Metrics on S<sup>2<\/sup><\/a>, Communications in Analysis and Geometry, 2005.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/compactify.pdf\">The Compactification of the Moduli Space of Convex RP<sup>2<\/sup> Surfaces, I<\/a>, Journal of Differential Geometry, 2004.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/affke.pdf\">Affine Spheres and K\u00e4hler-Einstein Metrics<\/a>, Mathematical Research Letters, 2002.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/met.pdf\">Riemannian Metrics on Locally Projectively Flat Manifolds<\/a>, American Journal of Mathematics, 2002.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/rpn.pdf\">Affine Spheres and Convex RP<sup>n<\/sup> Manifolds<\/a>, American Journal of Mathematics, 2001.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/thesis.pdf\">Dissertation<\/a>, Harvard University, 1999.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h2>Survey Articles<\/h2>\n<ul>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/yau-birthday-2018.pdf\">On the Donaldson-Uhlenbeck-Yau Correspondence<\/a>, Notices of the International Congress of Chinese Mathematicians, 2019.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/cubic-survey.pdf\">Cubic Differentials in the Differential Geometry of Surfaces<\/a> (with Ian McIntosh), in Handbook of Teichm\u00fcller Theory (Vol. 6), 2016.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/affine-survey.pdf\">Flat Bundles on Affine Manifolds<\/a> (with Indranil Biswas and Matthias Stemmler), Arabian Journal of Mathematics, 2013.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/cheng-yau.pdf\">Cheng and Yau&#8217;s Work on the Monge-Amp\u00e8re Equation and Affine Geometry<\/a> (with Xu-Jia Wang and Deane Yang), in Geometry and Analysis (Vol. I), 2010.<\/li>\n<li><a href=\"http:\/\/sites.rutgers.edu\/john-loftin\/wp-content\/uploads\/sites\/229\/2019\/08\/as-survey.pdf\">Survey on Affine Spheres<\/a>, in Handbook of Geometric Analysis (Vol. II), 2010.<\/li>\n<li style=\"list-style-type: none\"><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Interests Geometric Analysis; Affine and Projective Geometric Structures; Teichm\u00fcller Theory; Affine Differential Geometry Research Articles Limits of Cubic Differentials and Buildings (with Andrea Tamburelli and Michael Wolf), submitted, 2022. Coordinates &hellip; <a href=\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/\" class=\"\">Read More<\/a><\/p>\n","protected":false},"author":11,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-custom.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-5","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Research - John Loftin<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - John Loftin\" \/>\n<meta property=\"og:description\" content=\"Interests Geometric Analysis; Affine and Projective Geometric Structures; Teichm\u00fcller Theory; Affine Differential Geometry Research Articles Limits of Cubic Differentials and Buildings (with Andrea Tamburelli and Michael Wolf), submitted, 2022. Coordinates &hellip; Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/\" \/>\n<meta property=\"og:site_name\" content=\"John Loftin\" \/>\n<meta property=\"article:modified_time\" content=\"2022-09-10T05:26:04+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/\",\"url\":\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/\",\"name\":\"Research - John Loftin\",\"isPartOf\":{\"@id\":\"https:\/\/sites.rutgers.edu\/john-loftin\/#website\"},\"datePublished\":\"2017-12-06T14:11:58+00:00\",\"dateModified\":\"2022-09-10T05:26:04+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/sites.rutgers.edu\/john-loftin\/research\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/sites.rutgers.edu\/john-loftin\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Research\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/sites.rutgers.edu\/john-loftin\/#website\",\"url\":\"https:\/\/sites.rutgers.edu\/john-loftin\/\",\"name\":\"John Loftin\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/sites.rutgers.edu\/john-loftin\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Research - John Loftin","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sites.rutgers.edu\/john-loftin\/research\/","og_locale":"en_US","og_type":"article","og_title":"Research - John Loftin","og_description":"Interests Geometric Analysis; Affine and Projective Geometric Structures; Teichm\u00fcller Theory; Affine Differential Geometry Research Articles Limits of Cubic Differentials and Buildings (with Andrea Tamburelli and Michael Wolf), submitted, 2022. 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