John C. Loftin. Education. Employment History. Publications

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1 John C. Loftin Title and Address: Associate Professor Department of Mathematical & Computer Science Faculty of Arts & Sciences - Newark 101 Warren Street Newark, NJ Contact Information: Tel: loftin@rutgers.edu Education Highest Earned Degree Harvard University, Cambridge, MA. Ph.D. in Mathematics June, Dissertation Dissertation under the supervision of Prof. S.T. Yau: Applications of Affine Differential Geometry to Manifolds with Convex RP 2 Structure, April, Other Earned Degrees Harvard University, Cambridge, MA. A.M. in Mathematics, March, Stanford University, Stanford, CA. B.S. with distinction in Mathematics, June, A.B. in English, June, Employment History Positions Held 2009-ongoing Associate Professor Department of Mathematics and Computer Science, Rutgers University-Newark Assistant Professor Department of Mathematics and Computer Science, Rutgers University-Newark Ritt Assistant Professor Columbia University. Publications Articles in Refereed Journals J. Loftin and I. McIntosh, Equivariant Minimal Surfaces in CH 2 and Their Higgs Bundles, preprint, 35 pp., 2015, submitted. J. Loftin, Convex RP 2 Structures and Cubic Differentials Under Neck Separation, preprint, 62pp. 2015, submitted. I. Biswas, J. Loftin and M. Stemmler. Approximate Yang-Mills-Higgs Metrics on Flat Bundles over an Affine Manifold, Communications in Analysis and Geometry 22: 2014, I. Biswas, J. Loftin and M. Stemmler, The Vortex Equation on Affine Manifolds, Transactions of the American Mathematical Society 366(7): 2014,

2 I. Biswas, J. Loftin and M. Stemmler. Flat Bundles on Affine Manifolds, Arabian Journal of Mathematics 2(2): 2013, Z. Huang, J. Loftin and M. Lucia. Holomorphic Cubic Differentials and Minimal Lagrangian Surfaces in CH 2, Mathematical Research Letters 20(3): 2013, J. Loftin and I. McIntosh, Minimal Lagrangian Surfaces in CH 2 and Representations of Surface Groups into SU(2,1). Geometriae Dedicata 162 (2013), I. Biswas, J. Loftin, and M. Stemmler, Affine-Yang-Mills-Higgs Metrics, Journal of Symplectic Geometry 11(3): 2013, I. Biswas and J. Loftin. Hermitian-Einstein Connections on Principal Bundles over Flat Affine Manifolds, Int. J. Math. 23(4), 2012, 23pp. J. Loftin. Affine Hermitian-Einstein Metrics, Asian J. Math. 13(1): , J. Loftin and M.P. Tsui. Ancient Solutions of the Affine Normal Flow, J. Diff. Geom., 78(1): , J. Loftin. Flat Metrics, Cubic Differentials and Limits of Projective Holonomies, Geom. Dedicata 128: , J. Loftin. Singular Semi-Flat Calabi-Yau Metrics on S 2, Comm. Anal. Geom., 13(2): , J. Loftin, S.T. Yau and E. Zaslow. Affine Manifolds, SYZ Geometry and the "Y" Vertex, J. Diff. Geom., 71(1): , Erratum to Affine Manifolds, SYZ Geometry and the "Y" Vertex, 7 pp., J. Loftin. The Compactification of the Moduli Space of Convex RP 2 Surfaces, I, J. Diff. Geom., 68(2): , J. Loftin. Riemannian Metrics on Locally Projectively Flat Manifolds, Amer. Jour. Math., 124(3): , J. Loftin. Affine Spheres and Kähler-Einstein Metrics, Math. Res. Lett., 9(4): , J. Loftin. Affine Spheres and Convex RP n -Manifolds, Amer. Jour. Math., 123(2): , Published Conference Proceedings J. Loftin and M.P. Tsui. Limits of Solutions to a Parabolic Monge-Ampère Equation, in Recent Advances in Geometric Analysis, Advanced Lectures in Mathematics 11, Higher Education Press and International Press Beijing-Boston, 2009 (solicited but not refereed), (Proceedings of the International Conference on Geometric Analysis, NCTS Taipei, Taiwan, June, 2007), Chapters in Books or Monographs Reviews J. Loftin, I. McIntosh, to appear, Cubic Differentials in the Differential Geometry of Surfaces. in the Handbook of Teichmuller Theory, Vol 5, 47pp. J. Loftin, X.-J. Wang, and D. Yang, Cheng and Yau's Work on the Monge-Ampère Equation and Affine Geometry, in Geometry and Analysis, Vol. I, Higher Education Press and International Press, 2010, 17 pp. J. Loftin, Survey on Affine Spheres, in Handbook of Geometric Analysis, Vol. II, Higher Education Press and International Press, 2010, 31 pp. J. Loftin, Book review of Variational Principles for Discrete Surfaces: Theories and Algorithms, by F. Luo, X. D. Gu, and J. Dai, International Press, Somerville, MA, Mathematical Reviews, MR , 2010, 3pp. J. Loftin, Book review of The geometry of Hessian structures, by H. Shima, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, Mathematical Reviews, MR , 2008, 3pp. Conference Presentations, Lectures, Demonstrations

3 Invited Addresses Informal Geometric Analysis Seminar, Affine Spheres and the Real Monge-Ampère Equation, University of Maryland, College Park, November, Colloquium, An Extension of Teichmüller Theory, Howard University, Washington, DC, October, Geometry-Analysis Seminar, Minimal Surfaces in CH 2 and Their Higgs Bundles, Rice University, Houston, Texas, October, Geometry-Topology Seminar, Families of Projective Domains and Neck-Separating Degenerations of Convex RP 2 Surfaces, University of Maryland, College Park, Maryland, September, Topology, Arithmetic, and Dynamics Seminar, How To Pinch a Neck on a Convex RP 2 Surface, George Mason University, Fairfax, Virginia, September, Weekly Seminar, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, Laboratory of Algebraic Geometry and Its Applications, Faculty of Higher Mathematics, Higher School of Economics, Moscow, Russia, June, Geometry and Analysis of Surface Group Representations Seminar, part of Program on Dynamics on Moduli Spaces of Geometric Structures, Mathematical Sciences Research Institute, Berkeley, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, March, Complex Analysis and Dynamics Seminar, CUNY Graduate Center, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, February, Conference Speaker, Cubic Differentials, Differential Geometry of Surfaces, and Representations of Surface Groups into Real Forms of SL(3,C), Group Action Forum, Tsinghua Sanya International Mathematics Forum, Sanya, China, December, Conference Speaker, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, Workshop on Geometry of Moduli Spaces and Low Dimensional Manifolds, Research Institute for Mathematical Sciences, Kyoto University, December, Geometry and Topology Seminar, California Institute of Technology, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, November, Geometry-Analysis Seminar, Rice University, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, October, Speaker, Cubic Differentials and Limits of Convex RP 2 Structures under Neck Pinches, Concentration Period on Geometric Aspects of Higgs Bundles, in the program The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, Institute for Mathematical Sciences, National University of Singapore, August, Conference speaker, Some Projective Invariants of Convex Domains Coming from Differential Geometry, Conference on Geometry and Dynamics of Finsler Metrics, CIRM, Marseille, France, June, Colloquium, An Extension of Teichmüller Space, Lehigh University, March, Lecture at Second GEAR Retreat, Cubic Differentials in the Differential Geometry of Surfaces, University of Maryland, March, Special Seminar, Cubic Differentials and Limits of RP 2 Structures, Harvard University, March, Geometry and Topology Seminar, Minimal Lagrangian Surfaces in CH 2, University of Waterloo, Waterloo, Canada, March, Conference Speaker, Minimal Lagrangian Surfaces in CH 2, Conference on Advances in Teichmüller Theory, Erwin Schrodinger Institute, Vienna, Austria, February, Complex Analysis and Geometry Seminar, Minimal Lagrangian Surfaces in CH 2, Rutgers, New Brunswick, November, 2012.

4 Workshop Speaker, 4 50-minute talks on SYZ Conjecture and Affine Differential Geometry, Workshop on Integrable Systems and Geometric PDEs, Taida Institute for Mathematical Sciences, Taipei, Taiwan, October, Conference Speaker, Flat Bundles over Affine Manifolds, ICTS Meeting on Complex Analytic Geometry, Tata Institute, Bombay, India, March, Geometry Seminar, Minimal Lagrangian Surfaces in CH 2, Durham University, UK, February, Seminaire Analyse Complexe et Geometrie, Minimal Lagrangian Surfaces in CH 2, Institut de Mathematiques de Jussieu, Paris, France, February, Research Seminar Talk, Cubic Differentials and Limits of RP 2 Structures, Program on Geometry and Analysis of Surface Group Representations, Institut Henri Poincare, Paris, France, January, Special Session Lecture, Cubic Differentials and Limits of RP 2 Structures, AMS Special Session on the Geometry of Real Projective Structures, Joint Mathematics Meeting, Boston, January, Workshop Lecture, Minimal Lagrangian Surfaces in CH 2 and Representations into SU(2,1), Ahlfors-Bers Colloquium, Rice University, March, Complex Analysis Seminar, Minimal Lagrangian Surfaces in CH 2, CUNY Graduate Center, February, Special Seminar, Minimal Lagrangian Surfaces in CH 2, Harvard University, December, Geometry Seminar, Noncompact Affine Normal Flow, Ohio State University, November, Minicourse Speaker, Surfaces, SL(3), and an equation of Tzitzeica, Advanced School and Workshop on Discrete Groups in Complex Geometry, ICTP (Trieste, Italy), July, Conference Speaker, Towards a Compactification of the Moduli Space of Convex RP 2 Structures, Mini- Conference on Geometric Structures in 2 and 3 Dimensions, Autrans, France, January, Geometry/Topology Seminar, Surfaces, SL(3), and an equation of Tzitzeica, University of Maryland, November, Department Colloquium, Surfaces, SL(3), and an equation of Tzitzeica, University of Waterloo (Canada), October, Geometry Seminar, Surface Group Representations and Generalizations of Teichmuller Space, University of Waterloo (Canada), October, Workshop Lecture, Surfaces, SL(3), and an equation of Tzitzeica, Workshop on Global Differential Geometry, MFO (Oberwolfach, Germany), July, Conference Speaker, SL(3) Geometry, Special Lagrangians, and an Equation of Tzitzeica, International Conference on Several Complex Variables, Complex Geometry, and Partial Differential Equations, Wuhan University (Wuhan, China), July, Department Colloquium, Surfaces, SL(3), and an equation of Tzitzeica, University of Toledo (Toledo, Ohio), January, Special Session Lecture, Affine Hermitian-Einstein Metrics, Special Session on Complex Geometry and Partial Differential Equations, AMS Fall Eastern Section Meeting (Middletown, CT), October, Mathematical Physics Seminar, Two Dimensional Affine Spheres, University of York (UK), June, Conference Speaker, Two Dimensional Affine Spheres, Geometry, Integrability and Twistor Theory Conference, Cambridge University, June, Workshop Lecture, Real Projective Surfaces and Holomorphic Cubic Differentials, Ahlfors-Bers Colloquium, Rutgers Newark, May, Department Colloquium, Affine Hermitian-Einstein Metrics, Lehigh University, March, 2008.

5 Differential Geometry Seminar, Affine Hermitian-Einstein Metrics, Harvard University, March, Workshop Lecture, Affine Hermitian-Einstein Metrics, Workshop on Special Structures in Riemannian Geometry, BIRS (Banff, Canada), February, Geometry Seminar, Affine Differential Geometry and the SYZ Conjecture, National Taiwan University, June, Conference Speaker, Affine Normal Flow of Noncompact Hypersurfaces, International Conference on Geometric Analysis, NCTS (Taipei, Taiwan), June, Department Colloquium, The Affine Normal Flow, Yeshiva University, New York, March, Geometry/Topology Seminar, Real Projective Surfaces and Holomorphic Cubic Differentials, Rutgers University (New Brunswick), February, Special Session Lecture, Ancient Solutions of the Affine Normal Flow, Joint Special Session on Nonlinear Analysis and Nonlinear Geometric PDEs, AMS Fall Eastern Section Meeting (Storrs, CT), October, Summer Geometry and Topology Seminar, Affine Geometry and Singular RP 2 Surfaces, University of Maryland, July, Nonlinear Analysis Seminar, Ancient Solutions of the Affine Normal Flow, Rutgers University (New Brunswick), April, Department Colloquium, Projective Invariants of Convex Domains, University of Toledo (Toledo, Ohio), November, Workshop Lecture, Singular Semi-Flat Calabi-Yau Metrics on S n, Workshop on Global Differential Geometry, MFO (Oberwolfach, Germany), August, Speaker, Singular Semi-Flat Calabi-Yau Metrics on S n, International Conference on Complex Analysis, Differential Geometry, and Partial Differential Equations, in honor of Masatake Kuranishi's 80th birthday, Columbia University, May, Speaker, Singular Semi-Flat Calabi-Yau Metrics on S n, Workshop on Geometry and Topology, University of Minnesota, March, Nonlinear Analysis Seminar, Singular Semi-Flat Calabi-Yau Metrics on S n, Rutgers University (New Brunswick), February, Geometry Seminar, Singular Semi-Flat Calabi-Yau Metrics on S n, McMaster University (Hamilton, Ontario), January, Geometry and Analysis Seminar, Singular Semi-Flat Calabi-Yau Metrics on S n, Columbia University, September, Speaker, Singular Semi-Flat Calabi-Yau Metrics on S 2, Mirror Symmetry Conference, NCTS (Hsinchu, Taiwan), July, Differential Geometry and Analysis Seminar, Singular Semi-Flat Calabi-Yau Metrics on S 2, CUNY Graduate Center, March, Nonlinear Analysis Seminar, Singular Semi-Flat Calabi-Yau Metrics on S 2, Rutgers (New Brunswick), February, Geometric Analysis Seminar, Singular Semi-Flat Calabi-Yau Metrics on S 2, University of Wisconsin, February, Speaker, Singular Semi-Flat Calabi-Yau Metrics on S 2, Workshop on Geometric Analysis, MSRI (Berkeley, California), December, Geometry Seminar, Singular Semi-Flat Calabi-Yau Metrics on S 2, Northwestern University (Evanston, Illinois), November, 2003.

6 Speaker, Singular Semi-Flat Calabi-Yau Metrics on S 2, Short Programme on Analysis and Resolution of Singularities, CRM (Montreal), August, Nonlinear Analysis Seminar, Monge-Ampère Equations and Projective Quotients of Convex Domains, Rutgers (New Brunswick), April, Geometry and Analysis Seminar, Families of Degenerating Real Projective Surfaces, Columbia University, October, Special Session Lecture, Toward a Compactification of the Moduli Space of Convex RP 2 Surfaces, AMS Sectional Meeting, Special Session on Flat Structures, Moduli Spaces, and Minimal Surfaces: Portland, Oregon, June, Department Colloquium, Differential Geometric Invariants of Convex Cones, Polytechnic University (Brooklyn, New York), February, Geometry and Analysis Seminar, Toward a Compactification of the Moduli Space of Convex RP 2 Surfaces, Columbia University, October, Special Session Lecture, Affine Spheres and Kähler-Einstein Metrics, AMS Sectional Meeting, Special Session on Ricci Curvature and Related Topics: Hoboken, New Jersey, April, Geometry Seminar, Affine Spheres and Kahler-Einstein Metrics, UC Irvine, April, Differential Geometry Seminar, Riemannian Metrics on Projectively Flat Manifolds, CUNY Graduate Center, February, Six-hour Lecture Series, Affine Differential Geometry and RP n -Manifolds, Seoul National University, March, Geometry and Analysis Seminar, Riemannian Metrics on Locally Projectively Flat Manifolds, Columbia University, February, Valley Geometry Seminar, Affine Spheres and Convex RP n -Manifolds, Amherst, Massachusetts, November, Geometry and Topology Seminar, Applications of Affine Differential Geometry to RP 2 Surfaces, University of Maryland, March, Geometry and Analysis Seminar, Applications of Affine Differential Geometry to RP 2 Surfaces, Columbia University, March, Papers, Abstracts, and Lectures Discussion Section Co-Leader, AIM (Palo Alto, California), Workshop on Representations of Surface Groups, March, Contributed Talk, PDEs on Projectively Flat Manifolds, EDGE Summer School and Conference (Edinburgh, Scotland), July, Abstracts (Unpublished Papers) J. Loftin. Convex RP 2 Structures and Cubic Differentials under Neck Separation: Let S be a closed oriented surface of genus at least two. Labourie and the author have independently used the theory of hyperbolic affine spheres to find a natural correspondence between convex RP 2 structures on S and pairs (Σ,U) consisting of a Riemann surface Σ and a holomorphic cubic differential U over Σ. We consider geometric families of convex RP 2 degenerates only along a set of simple, non-intersecting, non-homotopic loops c. We classify the resulting RP 2 structures on S-c and call them regular convex RP 2 structures. We put a natural topology on the moduli space of all regular convex RP 2 structures on S and show that this space is naturally homeomorphic to the total space of the vector bundle over the Deligne-Mumford compactification of the moduli space of Riemann surfaces whose fibers over a noded Riemann surface are spaces of regular cubic differentials. The proof relies on previous techniques of the author, Benoist-Hulin,

7 and Dumas-Wolf, as well as some details due to Wolpert of the geometry of hyperbolic metrics on conformal surfaces in the Deligne-Mumford compactification. Funding Externally-Funded Research and/or Training Grants 06/2013-ongoing (Grant Amount: $5,000,000) Rutgers-Newark PI, Northern NJ Information and Professional Scientific and Technical Services ("STEM") Career Development Grant, a training grant from the US Department of Labor to retrain STEM workers by providing tuition for taking relevant classes. This grant is administered through NJIT, but includes Rutgers Newark. As the local PI, I have advised students on courses to take in our department and the department of Management Science and Information Systems in the Rutgers Business Schools, and I have worked with Carmen Pardo to help sign them up for our courses. The only funds paid to Rutgers out the grant are tuition. PI's: Judith Sheft and Gale Spak (NJIT) ongoing (Grant Amount: $5,000,000) Founding member, GEAR Network, GEometric structures And Representation varieties. The GEAR Network brings together researchers from 46 nodes in the U.S., Canada, Europe, and Asia. Its goal is to promote research interactions between network members, to facilitate cross-pollination of ideas between different research communities, and to train students and researchers to cross traditional mathematical boundaries. PI: Steven Bradlow (UIUC). Each university is considered a node of the GEAR network if it houses a GEAR faculty member. (Loftin is one of two GEAR faculty members at Rutgers Newark.) Faculty members, as well as graduate students and postdocs, of nodes can apply to GEAR for funding to visit other nodes of the network and to attend conferences and programs sponsored through the network. The GEAR Network is administered through three hubs, at Illinois, Maryland, and Stanford. Below are a few selected long-term research programs Loftin has attended based on GEAR sponsorship. o o o University of Maryland, September 1 November 30, 2015, to visit Prof. Goldman during a sabbatical, travel and housing support through the GEAR Network. IMS (Singapore), The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, July 31 August 13, 2014, travel support through the GEAR Network. IHP (Paris), Program on Geometry and Analysis of Surface Group Representations, January 11 - March 25, 2012, full support through the GEAR Network. 07/2011-ongoing (Grant Amount: $35,000) Principal investigator, Simons Foundation Collaboration Grant for Mathematicians, Canonical Structures in Geometry and Topology (Grant Amount: $107,973) NSF Grant DMS Monge-Ampère Equations and Geometric Structures on Manifolds.