{"id":420,"date":"2019-08-05T00:55:03","date_gmt":"2019-08-05T00:55:03","guid":{"rendered":"http:\/\/sites.rutgers.edu\/xiaowei-wang\/?page_id=420"},"modified":"2026-02-03T22:22:07","modified_gmt":"2026-02-03T22:22:07","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/xiaowei-wang\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<h3><strong>Brief Resume<\/strong>:<\/h3>\n<ul>\n<li>Ph.D. 2002, Brandeis University (Supervised by Professor Shing-Tung Yau)<\/li>\n<li>Assistant Adjunct\/Hedrick Assistant Professor, 2002-2005, UCLA<\/li>\n<li>Assistant Professor (Tenure Track), 2005-2010, The Chinese University of Hong Kong<\/li>\n<li>Assistant, Associate Professor, Professor 2010-present, Rutgers University at Newark<\/li>\n<li><a href=\"https:\/\/orcid.org\/0000-0003-1935-1786\">https:\/\/orcid.org\/0000-0003-1935-1786<\/a><\/li>\n<\/ul>\n<h3><strong>Research Interest<\/strong>:<\/h3>\n<ul>\n<li>Differential Geometry<\/li>\n<li>Algebraic Geometry<\/li>\n<li>Symplectic Geometry<\/li>\n<\/ul>\n<h3><strong>Papers and Preprints<\/strong>:<\/h3>\n<h4>Algebraic Geometry (Geometric Invariant Theory and Moduli)<\/h4>\n<ul>\n<li>with Kenneth Ascher,\u00a0 Kristin\u00a0 DeVleming and\u00a0 Yuchen\u00a0 Liu, <em>Hassett&#8211;Keel Program in genus four,<\/em> (2025), <a href=\"https:\/\/arxiv.org\/abs\/2504.20312\">arXiv 2504.20312<\/a><\/li>\n<li>with Kenneth Ascher,\u00a0 Dori\u00a0 Bejleri,\u00a0 Harold\u00a0 Blum,\u00a0 Kristin\u00a0 DeVleming,\u00a0 Giovanni\u00a0 Inchiostro\u00a0 and\u00a0 Yuchen\u00a0 Liu,<br \/>\n<em>Moduli of boundary polarized Calabi-Yau pairs,<\/em> (2023), <a href=\"https:\/\/arxiv.org\/abs\/2307.06522\">arXiv 2307.06522<\/a><\/li>\n<li><em>GIT stability, K-stability and the moduli space of Fano varieties<\/em>.<span style=\"font-size: 1rem\">Moduli of K-stable varieties,\u00a0 Springer INdAM Ser., <\/span><strong style=\"font-size: 1rem\">31<\/strong><span style=\"font-size: 1rem\">, Springer, Cham, (2019), 153-181<\/span><\/li>\n<li>with Chi Li and\u00a0 Chenyang Xu,\u00a0\u00a0<a href=\"https:\/\/rutgers.box.com\/s\/x0mqjuesepqgtvr7i6mz01k38iy5bscn\"><em>Algebraicity of the Metric Tangent Cones and Equivariant K-stability<\/em><\/a>, <a href=\"https:\/\/arxiv.org\/abs\/1805.03393\">arXiv:1805.03393<\/a>. J. Amer. Math. Soc. <strong>34 <\/strong>(2021), no. 4, 1175-1214.<\/li>\n<li>with King-Leung Lee, Zhiyuan Li and Jacob Sturm,\u00a0<a href=\"https:\/\/rutgers.box.com\/s\/rwfykn55oc3g9xl1a9exsp1baumvsyve\"><i>Asymptotic Chow stability for toric Del Pezzo surfaces<\/i><\/a>,\u00a0<span style=\"font-size: 1rem\">Math. Res. Lett.<\/span>\u00a0 <strong style=\"font-size: 1rem\">26<\/strong><span style=\"font-size: 1rem\"> (2019), no. 6, 1759-1787, \u00a0<\/span><a style=\"font-size: 1rem\" href=\"https:\/\/arxiv.org\/abs\/1711.10099\">arXiv:1711.10099<\/a><\/li>\n<li>with Yuguang Zhang,\u00a0<em>\u00a0Balanced embedding of degenerating Abelian varieties<\/em>,\u00a0<a href=\"http:\/\/arxiv.org\/abs\/1605.01860.pdf\">arXiv:1605.01860<\/a><\/li>\n<li>with Chi Li and\u00a0 Chenyang Xu,\u00a0\u00a0<em>Quasi-projectivity fo the moduli space of smooth K\\&#8221;ahler-Einstein Fano manifolds<\/em>.. Ann. Sci. \\&#8217;Ecole Norm. Sup. (4)\u00a0<b>51<\/b> (2018) no. 3, 739-772, <a style=\"color: #0056b3\" href=\"http:\/\/arxiv.org\/abs\/1502.06532\">arXiv:1502.06532<\/a><\/li>\n<li>with Chi Li and\u00a0 Chenyang Xu,\u00a0 <em><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiTSon3MFhPm7fLSr?e=s9k8dv\">On the proper moduli spaces of smoothable K\\&#8221;ahler-Einstein Fano varieties<\/a>, <\/em><span style=\"font-size: 1rem\">Duke Math. J. <\/span><strong style=\"font-size: 1rem\">168<\/strong><span style=\"font-size: 1rem\">\u00a0(2019), no. 8, 1387-1459, <\/span><a style=\"font-size: 1rem;color: #0056b3\" href=\"http:\/\/arxiv.org\/abs\/1411.0761\">arXiv:1411.0761<\/a><\/li>\n<li>with Chenyang Xu,\u00a0<a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiSk30qFmD7Olwpia?e=3jHvxU\"><i>Nonexistence of asymptotic GIT compactification,<\/i><\/a> Duke Math. J.\u00a0<strong>163<\/strong>\u00a0(2014),\u00a0no. 12, 2217-2241, <a style=\"color: #0056b3\" href=\"http:\/\/arxiv.org\/abs\/1212.0173\">arXiv:1212.0173<\/a><\/li>\n<li>with Jun Li,\u00a0\u00a0<a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiXFmZQnCd-PAFs8o?e=J3RHOn\"><i>Hilbert Mumford criterion for nodal curves<\/i><\/a>, Compos. Math.\u00a0<b>151<\/b> (2015), no. 11, 2076-2130, <a href=\"http:\/\/arxiv.org\/abs\/1108.1727\">arXiv:1108.1727<\/a><\/li>\n<li><i><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiST4r0C9sIHsBWRu?e=3MyY9a\">Height and GIT weight<\/a><\/i>. Math. Res. Lett.\u00a0<b>19\u00a0<\/b>(2012), no. 4,\u00a0 909&#8211;926<\/li>\n<li>with Hok-Pun Yu,\u00a0<em><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiSrcibc4gS3ZLzli?e=vsmgvY\">Theta function and Bergman metric on Abelian varieites<\/a>,<\/em>\u00a0New York J. Math.\u00a0<strong>15<\/strong> (2009), 19-35<\/li>\n<li><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiSMZdyomcb0I5-QV?e=UZyYEp\"><em>Balance point and stability of vector bundle over a projective manifold<\/em><\/a>, Math. Res. Lett.\u00a0<strong>9<\/strong> (2002), no. 2-3, 393-411<\/li>\n<\/ul>\n<h4>Differential Geometry (Einstein metric, G2 Geometry and Isometric Embedding)<\/h4>\n<ul>\n<li>with Jian Song and Jacob Sturm, <em>An analytic proof of stable reduction theorem,<\/em> (2020), <a href=\"https:\/\/arxiv.org\/pdf\/2009.13596.pdf\">arXiv:2009.13596<\/a> , Math. Ann. <strong>390 <\/strong>(2024), no. 3, 4245\u20134263.<\/li>\n<li>with Jian Song and Jacob Sturm, <em>Continuity of Weil-Petersson potential,\u00a0<\/em>(2020), <a href=\"https:\/\/arxiv.org\/pdf\/2008.11215.pdf\">arXiv:2008.11215<\/a><\/li>\n<li>with Jian Song and Jacob Sturm,\u00a0<em>Riemannian geometry of K\\&#8221;ahler-Einstein currents III: compactness of K\\&#8221;ahler-Einstein manifolds of negative scalar curvature<\/em><em>,\u00a0<\/em>(2020),\u00a0\u00a0<a href=\"http:\/\/arxiv.org\/abs\/2003.04709\">arXiv:2003.04709<\/a><\/li>\n<li>with\u00a0<span style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, 'Helvetica Neue', Arial, sans-serif;font-size: 1rem\">Duong H. Phong, Jian Song and \u00a0Jacob Sturm,\u00a0<\/span><span style=\"font-size: 1rem\"><em>The Ricci flow on the sphere with marked points<\/em>. J. Differential Geom. <\/span><strong style=\"font-size: 1rem\">114<\/strong><span style=\"font-size: 1rem\"> (2020), no. 1, 117-170.<\/span><\/li>\n<li>with\u00a0 Ved Datar, Bin Guo and Jian Song,\u00a0\u00a0<em>Connecting toric manifolds by conical Kahler-Einstein metrics.<\/em>\u00a0Adv. Math.\u00a0\u00a0<b>323\u00a0<\/b>(2018) 38-83, <a href=\"http:\/\/arxiv.org\/abs\/1308.6781\">arXiv:1308.6781<\/a><span style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, 'Helvetica Neue', Arial, sans-serif\">\u00a0<\/span><\/li>\n<li>with Ke Zhu,\u00a0<em>Isometric embeddings via heat kernel<\/em>. J. Differential Geom.\u00a0<strong>99 <\/strong>(2015), no. 3, 497-538, <a style=\"color: #0056b3\" href=\"http:\/\/arxiv.org\/abs\/1305.5613\">arXiv:1305.5613<\/a><\/li>\n<li>with Naichung Conan Leung and Ke Zhu,\u00a0<em>Instantons in G_2 manifolds from J-holomorphic curves in coassociative submanifolds<\/em>.. Proceedings of Gokova Geometry-Topology Conference 2012, 89-111, <a style=\"color: #0056b3\" href=\"http:\/\/arxiv.org\/abs\/1303.6728\">arXiv:1303.6728<\/a><\/li>\n<li>with Jian Song,\u00a0<i><i><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiTY5f4F4LpjtNmy0?e=1DbjiA\">The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality<\/a>,\u00a0<\/i><\/i><span style=\"font-size: 1rem\">Geom. Topol. <\/span><strong style=\"font-size: 1rem\">20<\/strong><span style=\"font-size: 1rem\"> (2016), no. 1, 49-102, <\/span><a style=\"font-size: 1rem\" href=\"http:\/\/arxiv.org\/abs\/1207.4839\">arXiv:1207.4839<\/a><\/li>\n<li>\u00a0with Naichung Conan Leung and Ke Zhu,\u00a0<i>Thin instantons in G2-manifolds and Seiberg-Witten invariants.<\/i>\u00a0J. Differential Geom.\u00a0<strong>95<\/strong> (2013), no. 3, \u00a0419-483,<i>\u00a0<\/i><a style=\"color: #0056b3\" href=\"http:\/\/arxiv.org\/abs\/1107.1947\">arXiv:1107.1947<\/a><span style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, 'Helvetica Neue', Arial, sans-serif\">\u00a0<\/span><\/li>\n<li><em><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiSd1OjbkTUm16Ctl?e=Vfs1h1\">Canonical metrics on stable vector bundles.<\/a><\/em>\u00a0Comm. Anal. Geom.\u00a0<strong>13<\/strong>, no. 2, (2005), 253-285<\/li>\n<\/ul>\n<h4>Symplectic Geometry(Moment Map and Symplectic Quotient)<\/h4>\n<ul>\n<li>with Ruadha\u00ed Dervan, Thomas Murphy, Julius Ross, Lars Martin Sektnan, <em>Twisted scalar curvature as a moment map, <\/em><a href=\"https:\/\/arxiv.org\/abs\/2601.18141\">arXiv:2601.18141<\/a>.<span style=\"font-size: 1rem\">\u00a0<\/span><\/li>\n<li>with King-Leung Lee and Jacob Sturm, <a href=\"https:\/\/rutgersconnect-my.sharepoint.com\/:b:\/r\/personal\/xiaowwan_newark_rutgers_edu\/Documents\/Andromeda\/Research\/Moment-Convex.pdf?csf=1&amp;web=1&amp;e=VdSrPz\"><em>Moment map, convex function<\/em><\/a>, <a href=\"https:\/\/arxiv.org\/pdf\/2208.03724.pdf\">a<\/a><a href=\"https:\/\/arxiv.org\/pdf\/2208.03724.pdf\">rXiv:2208.03724<\/a>. J. Symplectic Geom., 23(4):951\u2013994, 2025.<\/li>\n<li>with Naichung Conan Leung,<em>\u00a0<a href=\"https:\/\/1drv.ms\/u\/s!AlJqSZJ3i3DQiTGTfTnLlcdCkpu2?e=AE1HAu\">A quadratic inequality for sum of co-adjoint orbits.<\/a><\/em>\u00a0Comm. Anal. Geom.\u00a0<strong>17<\/strong>\u00a0 (2009),\u00a0no.2, 265-282<\/li>\n<li><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiSx65txt63_UimNR\"><em>Riemannian moment map<\/em><\/a><em>.<\/em> Comm. Anal. Geom.\u00a0<strong>16<\/strong>\u00a0(2008), no. 4, 837-863<\/li>\n<li><em><a href=\"https:\/\/1drv.ms\/b\/s!AlJqSZJ3i3DQiSgWxa6urq7R98av?e=CYMnDt\">Moment map, Futaki invariant and stability of projective manifold.<\/a>\u00a0<\/em> Comm. Anal. Geom.\u00a0<strong>12<\/strong>\u00a0(2004), no. 5,\u00a0 1009-1037<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Brief Resume: Ph.D. 2002, Brandeis University (Supervised by Professor Shing-Tung Yau) Assistant Adjunct\/Hedrick Assistant Professor, 2002-2005, UCLA Assistant Professor (Tenure Track), 2005-2010, The Chinese University of Hong Kong Assistant, Associate &hellip; <a href=\"https:\/\/sites.rutgers.edu\/xiaowei-wang\/research\/\" class=\"\">Read More<\/a><\/p>\n","protected":false},"author":344,"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-420","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 - Xiaowei Wang<\/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\/xiaowei-wang\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - Xiaowei Wang\" \/>\n<meta property=\"og:description\" content=\"Brief Resume: Ph.D. 2002, Brandeis University (Supervised by Professor Shing-Tung Yau) Assistant Adjunct\/Hedrick Assistant Professor, 2002-2005, UCLA Assistant Professor (Tenure Track), 2005-2010, The Chinese University of Hong Kong Assistant, Associate &hellip; 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