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HTTP/1.1 200 OKConnection: keep-aliveContent-Length: 21453Server: GitHub.comContent-Type: text/html; charsetutf-8Last-Modified: Thu, 12 Sep 2024 21:55:39 GMTAccess-Control-Allow-Origin: *ETag: 66e3635b-53cdexpires: Sun, 15 Sep 2024 15:05:54 GMTCache-Control: max-age600x-proxy-cache: MISSX-GitHub-Request-Id: 8C9B:33BEA2:50CE0EA:52D7806:66E6F579Accept-Ranges: bytesAge: 0Date: Sun, 15 Sep 2024 14:55:54 GMTVia: 1.1 varnishX-Served-By: cache-bfi-krnt7300099-BFIX-Cache: MISSX-Cache-Hits: 0X-Timer: S1726412154.140633,VS0,VE69Vary: Accept-EncodingX-Fastly-Request-ID: 9fbe4da3b22e58bc3c00efc500607de1d2e0076a !DOCTYPE html>html langen> head> meta http-equivcache-control contentno-cache> meta http-equivexpires content0> meta http-equivpragma contentno-cache> meta http-equivContent-Type contenttext/html; charsetUTF-8/> meta nameviewport contentwidthdevice-width, initial-scale1, maximum-scale1.0/> title>Deane Yang/title> !-- CSS --> link hrefhttps://fonts.googleapis.com/icon?familyMaterial+Icons relstylesheet> link hrefcss/materialize.css typetext/css relstylesheet mediascreen,projection/> link hrefcss/style.css typetext/css relstylesheet mediascreen,projection/> !-- Favicon --> link relshortcut icon typeimage/png hrefimages/cropped-logo-favicon-150x150.png/> style> .tight-row { padding: 2px 5px; } /style> /head> body> div classcontainer>a idlogo-container hrefhttp://www.math.nyu.edu classbrand-logo>img classresponsive-img srcimages/math-django-header.png>/a> /div> div classcontainer> div classsection> div classrow> div classcol s9> !-- NAME --> h4>Deane Yang/h4> !-- TITLE --> h5 classlight>Professor of Mathematics/h5> !-- EMAIL, OFFICE, PHONE, etc. --> p>strong>email:/strong> a hrefmailto:deane.yang@nyu.edu>deane.yang@nyu.edu/a>/p> p>phone: +1 (212) 9983185 (Unused)/p> p>strong>pronouns:/strong> he/him/his/p> table classresponsive-table> tr> th classtight-row>Campus/th> th classtight-row>Location/th> th classtight-row>Office Hours/th> /tr> tr> td classtight-row>Manhattan/td> td classtight-row>Warren Weaver Hall 522/td> td classtight-row>(Fall 2024) Tuesdays 4-6pm, Fridays 2-4pm/td> /tr> tr> td classtight-row>Brooklyn/td> td classtight-row>2 Metrotech 864/td> td classtight-row>By appointment/td> /tr> tr> td classtight-row>Online/td> td classtight-row>Zoom/td> td classtight-row>By appointment/td> /tr> /table> /div> div classcol s3 right-align> div classcard> div classcard-image> !-- PHOTO --> img src./images/DeaneYangHeadshot.jpg> /div> /div> /div> /div> /div> !-- DIVIDER LINE BETWEEN SECTIONS --> div classdivider>/div> div classsection> !-- HEADER OF EACH SECTION --> h5>Teaching/h5> ul> li> Fall 2024 ul classbrowser-default> li> a hrefMATH-GA2450Fall2024/index.html>MATH-GA2450 Complex Variables I/a> /li> /ul> /li> /ul> /div> div classdivider>/div> div classsection> h5>a hrefhttps://deaneyang.github.io/blog/>A Cluttered Mind/a> (blog)/h5> /div> div classdivider>/div> div classsection> h5>Research/h5> p> I work with Erwin Lutwak and Gaoyong Zhang on affine and linearly invariant geometric and analytic inequalities. In the past I have worked on overdetermined systems of PDEs and convergence and collapsing theorems for Riemannian manifolds. /p> /div> div classdivider>/div> div classsection> h5>Academic profiles/h5> p> a hrefhttps://scholar.google.com/citations?userxNtFmOAAAAAJ&hlen>Google Scholar/a> /p> p> a hrefhttp://www.ams.org/mathscinet/search/author.html?mrauthid198075>Mathscinet/a> (requires university or individual subscription) /p> /div> div classdivider>/div> div classsection> h5>Professional history/h5> ul> li> 2017—present: i>Professor of Mathematics,/i> NYU Courant Institute of Mathematical Sciences /li> li> 2015—2017: i>Professor of Mathematics,/i> NYU Tandon School of Engineering /li> li> 2014—2015: i>Professor of Mathematics,/i> NYU Polytechnic School of Engineering /li> li> 2008—2014: i>Professor of Mathematics,/i> Polytechnic Institute of New York University/li> li> 1993—2008: i>Professor of Mathematics,/i> Polytechnic University /li> li> 1996—1997: i>Vice Provost for Academic Development,/i> Polytechnic University /li> li> 1993—1995: i>Department Head of Mathematics,/i> Polytechnic University /li> li> 1991—1993: i>Associate Professor,/i> Polytechnic University /li> li> 1989—1991: i>Visiting Associate Professor,/i> Columbia University /li> li> 1988—1990: i>Associate Professor,/i> Rice University /li> li> 1985—1988: i>Assistant Professor,/i> Rice University /li> li> 1983—1984: i>NSF Postdoctoral Fellow,/i> NYU Courant Institute of Mathematical Sciences /li> li> 1983: i>PhD in Mathematics,/i> Harvard University /li> li> 1979: i>BA in Mathematics and Physics,/i> University of Pennsylvania /ul> /div> div classdivider>/div> div classsection> h5>Survey papers/h5> ul> li> D. Yang, i>a hrefpapers/affine_survey.pdf>Affine Integral Geometry from a Differentiable Viewpoint/a>, /i> b>Handbook of Geometric Analysis vol. II,/b> International Press, 2010. /li> li> J. Loftin, X. J. Wang, D. Yang, i>a hrefpapers/cheng-yau.pdf> Cheng and Yaus work on the Monge-Ampère equation and affine geometry/a>, /i> b>Geometry and Analysis (Vol. I),/b> Higher Education Press and International Press, 2010. /li> li> D. Yang, i>a hrefpapers/on_blaschke.pdf> On Wilhelm Blaschkes Mathematical Work and Influence on S. S. Chern /a>/i> (a hrefpapers/on_blaschke_chinese.pdf>Chinese version/a>). /li> /ul> /div> div classdivider>/div> div classsection> h5>Selected refereed journal articles/h5> p> Note on copyright issues: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each authors copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holders. /p> !-- USE ol>.../ol> FOR NUMBERED LIST --> ol> li>E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/ellipsoid.pdf>A new ellipsoid associated with convex bodies/a>, /i> b>Duke Mathematical Journal 104/b> (2000) 375-390. /li> li>E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/jdg00.pdf>Lsub>p/sub> affine isoperimetric inequalities/a>, /i> b>Journal of Differential Geometry 56/b> (2000) 111-132. /li> li> E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/trans.pdf>A new affine invariant for polytopes and Schneiders projection problem. /a>/i> b>Transactions of the AMS 353/b> (2001) 1767-1779. /li> li> O. Guleryuz, E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/contoured.pdf>Information theoretic inequalities for contoured probability distributions/a>, /i> b>IEEE Transactions on Information Theory 48/b> (2002) 2377-2383. /li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/cramer_rao.pdf>The Cramer-Rao inequality for star bodies/a>, /i> b>Duke Mathematical Journal 112/b> (2002) 59-81. /li> li>E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/affine_sobolev.pdf>Sharp affine Lsub>p/sub> Sobolev Inequalities/a>, /i> b>Journal of Differential Geometry 62/b> (2002) 17-38. /li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/AOP222.pdf>Moment-entropy inequalities/a>, /i>b>Annals of Probability 32/b> (2004) 757-774. /li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/tams.pdf>On the i>Lsub>p/sub>/i>-Minkowski problem/a>, /i>b>Transactions of the AMS 356/b> (2004) 4359-4370. /li> li> D. Hug, E. Lutwak, D. Yang, and G. Zhang, a hrefpapers/discrete_minkowski.pdf>i>On the Lsub>p/sub> Minkowski problem for polytopes, /i>/a>b>Discrete and Computational Geometry/b> (2005) 699-715. /li> li> E. Lutwak, D. Yang, and G. Zhang, a hrefpapers/plms.pdf>i>Lsub>p/sub> John ellipsoids, /i>/a>b>Proceedings of the London Mathematical Society 90/b> (2005) 497-520. /li> li> E. Lutwak, D. Yang, and G. Zhang, a hrefpapers/lp_subspaces.pdf>i>Volume inequalities for subspaces of Lsub>p/sub>, /i>/a>b>Journal of Differential Geometry 68/b> (2004) 159-184. /li> li> W. Chen, R. Howard, E. Lutwak, D. Yang, and G. Zhang, a hrefpapers/affine_inequality2d.html>i>A generalized affine isoperimetric inequality, /i>/a>b>Journal of Geometric Analysis 14/b> (2004) 597-612. /li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/renyi1d.pdf>Cramer-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information/a>, /i>b>IEEE Transactions on Information Theory 51/b> (2005) 473-478. /li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/IMRN_final.pdf>Optimal Sobolev Norms and the i>Lsub>p/sub>/i> Minkowski Problem/a>, /i>b>International Mathematical Research Notices/b> (2006) 1-21./li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/ajm.pdf>Volume Inequalities for Isotropic Measures/a>, /i>b>American Journal of Mathematics 129/b> (2007) 1711-1723./li> li>E. Lutwak, D. Yang, G. Zhang. i>a hrefpapers/moment_matrix.pdf>Moment-entropy inequalities for a random vector/a>, /i>b>IEEE Transactions on Information Theory 53/b> (2007) 1603-1607./li> li>A. Cianchi, E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/clyz_CV_rev.pdf>Affine Moser-Trudinger and Morrey-Sobolev inequalities, /a>/i>b>Calculus of Variations and PDE's 36/b> (2009) 419-436./li> li> E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/orlicz_projection_body.pdf>Orlicz projection bodies,/a>/i> b> Advances in Mathematics 223/b> (2010) 220-242. /li> li> C. Haberl, E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/orlicz_minkowski_problem.pdf>The even Orlicz Minkowski problem,/a>/i> b> Advances in Mathematics 224/b> (2010) 2485-2510. /li> li> E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/bb3_jdg.pdf> A volume inequality for polar bodies,/a>/i> b> Journal of Differential Geometry 84/b> (2010) 163-178. /li> li> E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/orlicz_centroid.pdf> Orlicz centroid bodies,/a>/i> b> Journal of Differential Geometry 84/b> (2010) 365-387. /li> li> G. Bianchi, D. Klain, E. Lutwak, D. Yang, G. Zhang. i> A countable set of directions is sufficient for Steiner symmetrization,/i> b> Advances in Applied Mathematics 47/b> (2011) 869-873. /li> li> E. Lutwak, D. Yang, G. Zhang. i> The Brunn-Minkowski-Firey inequality for nonconvex sets,/i> b> Advances in Applied Mathematics 48/b> (2012) 407-413. /li> li> E. Lutwak, S. Lv, D. Yang, G. Zhang. i> a hrefpapers/fisher_info.pdf>Extensions of Fisher information and Stams inequality,/a>/i> b> IEEE Transactions in Information Theory/b> (2012) 1319-1327. /li> li> K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/LBMI.pdf>The log-Brunn-Minkowski inequality,/a>/i> b> Advances in Mathematics 231/b> (2012) 1974-1997. /li> li> K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/LMP.pdf>The logarithmic Minkowski problem,/a>/i> b> Journal of the American Mathematics Society 26/b> (2013) 831-852. /li> li> E. Lutwak, S Lv, D. Yang, G. Zhang. i> a hrefpapers/affine_moment.pdf>Affine moments of a random vector,/a>/i> b>IEEE Transactions in Information Theory 59/b> (2013) 5592-5599 /li> li> A. Cianchi, E. Lutwak, D. Yang, G. Zhang. i> a hrefpapers/unified_cramer_rao.pdf>A Unified Approach to Cramér-Rao Inequalities,/a>/i> b>IEEE Transactions in Information Theory 60/b>, (2014) 643--650. /li> li> K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang. i>a hrefhttps://projecteuclid.org/euclid.jdg/1424880981>Affine images of isotropic measures,/a>/i> b>Journal of Differential Geometry 99/b> (2015) 407--442. /li> li> Y. Huang, E. Lutwak, D. Yang, G. Zhang. i>a hrefhttps://projecteuclid.org/euclid.acta/1485802481> Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems,/a>/i> b>Acta Mathematica 216/b> (2016) 325-388. /li> li> E. Lutwak, D. Yang, G. Zhang. i>a hrefhttps://doi.org/10.1016/j.aim.2018.02.011> Lsub>p/sub> dual curvature measures,/a>/i> b>Advances in Mathematics 329/b> (2018) 85-132. /li> li> K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang, Y. Zhao. i>a hrefhttps://doi.org/10.1016/j.aim.2019.106805> The dual Minkowski problem for symmetric convex bodies,/a>/i> b>Advances in Mathematics 356/b> (2019). /li> li> K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang, Y. Zhao. i>a hrefhttps://doi.org/10.1002/cpa.21898> The Gauss Image Problem,/a>/i> b>Communications in Pure and Applied Mathematics/b> (2020). /li> /ol> /div> div classdivider>/div> div classsection> h5>Unpublished articles/h5> ol> li>D. Yang. i>a hrefpapers/gunther.pdf>Gunthers proof of Nashs isometric embedding theorem./a>/i>/li> li>J. Goodman and D. Yang. i>a hrefpapers/goodman-yang.pdf>Local solvability of nonlinear partial differential equations of real principal type./a>/i>/li> li>C. T. Yang (as told to D. Yang). i>a hrefmemories_of_chern.htm>Memories of Chern/a>/i>/li> li>C. T. Yang. i>a hrefpapers/DissertationChungTaoYang.pdf>Equivalence of the Alexander-Kolmogorff and Čech Cohomology Theories/a>/i>. Dissertation, Tulane University, 1952./li> /ol> /div> div classdivider>/div> div classsection> a namefragments>/a> h5 idfragments>Mathematical Fragments/h5> ol> li> i>a hrefpapers/riemann.pdf> A simple way to discover the Riemann curvature/a>/i>/li> li> i>a hrefpapers/deturck_trick.pdf> DeTurcks trick for the prescribed Ricci equation/a>/i>/li> li> i>a hrefpapers/gauss.pdf> A simple proof of the Theorema Egregium of Gauss/a>/i>/li> li> i>a hrefpapers/underdetermined_ode.pdf> Gromovs approach to solving underdetermined ODEs/a>/i>/li> li> i>a hrefpapers/gunther.pdf>Gunthers proof of Nashs isometric embedding theorem./a>/i>/li> li> i>a hrefpapers/holonomy.pdf>Holonomy equals curvature./a>/i>/li> li> i>a hrefpapers/exterior_derivative.pdf>The exterior derivative via Stokess theorem/a>/i> /li> li> i>a hrefpapers/LieDerivative.pdf>The Lie derivative of a differential form/a>/i> /li> li> i>a hrefpapers/heron.pdf>A simple proof of Herons formula for the area of a triangle/a>/i> /li> li> i>a hrefpapers/PullbackConnection.pdf> The pullback of a connection on a vector bundle/a>/i> /li> li> i> a hrefpapers/Orthogonal.pdf> The dot product via length and orthogonality /a> /i> /li> li> i> a hrefpapers/CalculusConcepts.pdf> Fundamental concepts of calculus /a> /i> /li> /ol> /div> !-- DIVIDER LINE BETWEEN SECTIONS --> div classdivider>/div> div classsection> h6>a hrefhttp://www.math.ubc.ca/~ilaba/teaching/email.html>Good advice on how to email a professor (not just me)/a> /h6> /div> div classdivider>/div> div classsection> h5> a hrefimages/NewYorkTimes20170223.pdf>Front page of New York Times, 2/23/2017/a> /h5> ul> li> Lead article by my brother Kenneth Chang on newly discovered planets outside the solar system /li> li> Photo by my son Stephen Yang of Native American protesters setting fire to their camp in Cannon Ball, North Dakota /li> /div> div classdivider>/div> div classsection> h5> a hrefpapers/DeaneYangMathGenealogy.pdf>My mathematical ancestry/a> /h5> h6> Produced by the a hrefhttps://www.mathgenealogy.org/>Mathematical Genealogy Project/a> /h6> /div> /div> !-- Scripts--> script srchttps://code.jquery.com/jquery-2.1.1.min.js>/script> script srcjs/materialize.js>/script> script srcjs/init.js>/script> /body>/html>
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