Yanir A. Rubinstein

Mailing address:
University of Maryland
Department of Mathematics
4176 Campus Drive
College Park, MD 20742-4015, USA

Office: Mathematics Building, room 4403.

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Mathematics on the Golf Channel

Books

M.A. Peterson, Y.A. Rubinstein, Eds., Directions for Mathematics Research Experience for Undergraduates, World Scientific, 2016. (book review in The Mathematical Gazette)

Meetings

  • Maryland Analysis and Geometry Atelier - University of Maryland, 21-25 August 2017.

  • Pacific Rim Workshop on Geometric Analysis - University of British Columbia, July 24-28, 2017.

  • Metro Area Differential Geometry Seminar (MADGuyS) - Johns Hopkins University, April 22, 2017.

  • New Directions for Mathematics Research Experiences for Undergraduates - Mt. Holyoke College, June 21-22, 2013.

  • 28th Geometry Festival: Calabifest - In celebration of the 90th birthday of Eugenio Calabi, University of Maryland, April 12-14, 2013.

  • Complex Geometry and Microlocal Analysis - special session at the AMS Eastern Spring meeting, Boston College, April 6-7, 2013.

  • Bay Area Differential Geometry Seminar (BADG) - Stanford, June 2, 2012.

    Minicourses

  • SCGAS Winter School - UC Irvine, January 25-29, 2016.

  • Getting Started with PDEs - IIAS, Hebrew University, September 3-9, 2015.

  • Advanced School on PDEs in Geometry and Physics - Hefei, China, June 30-July 11, 2014.

    Seminars

  • JHU-UMD Complex Geometry Seminar

  • Informal Geometric Analysis Seminar

  • Seminars in the Department.

    Teaching

    2016-2017

  • Differential Equations for Scientists and Engineers (honors) (course 246H, Spring 2017): TuTh 12:30pm, MATH 1308.
  • Differential Equations for Scientists and Engineers (honors) (course 246H, Fall 2016): TuTh 12:30pm, MATH 0304.
  • 2015-2016

  • Differential Equations for Scientists and Engineers (honors) (course 246H, Fall 2015): MWF 10am, MATH 1311.
  • Topics in fully nonlinear PDE (course 858Y, Fall 2015): MWF 12 noon, MATH 1313.
  • 2014-2015

  • Geometric Analysis (course 742, Fall 2014): TTh 9:30am, MATH 0104.
  • Topics in Complex Analysis: Kahler Manifolds (course 868K, Fall 2014): TTh 12:30am, EGR 3114.
  • 2013-2014

  • Geometric Analysis (course 742, Fall 2013): TTh 11am, MATH 1308.
  • Differential Geometry of Curves and Surfaces I (course 436, Fall 2013): TTh 2pm, MATH B0421.
  • 2012-2013

  • Topics in Geometric Analysis: The Yamabe Problem (course 748F, Spring 2013): TTh 2pm.
  • Geometry (course 430, Fall 2012): TTh 2pm.
  • 2011-2012
  • Undergraduate research project: Optimal Transportation (SURIM, Summer 2012).

  • Introduction to Optimal Transportation (course 287, Winter 2012, at Stanford): MWF 11am.

  • Linear Algebra and Differential Calculus of Several Variables (course 51, Autumn 2011, at Stanford): MWF 11am and 1:15pm.
  • 2009-2010
  • Partial Differential Equations (course 256A, Spring 2010, at Stanford): MWF 2:15pm.
  • Complex Analysis, Geometry, and Topology (course 215A, Autumn 2009, at Stanford): TTh 2:15pm.
  • 2008-2009

  • Riemannian Geometry (course 110.645, Fall 2008, at JHU).

  • Past Seminars

    2009-2012 (Stanford):

  • Geometry Seminar.

  • 2008-2009 (JHU):

  • Complex Geometry Seminar.
  • Informal graduate student seminar on Kahler geometry through examples.

  • 2005-2006 (MIT):

  • Graduate Student Seminar on Geometric Stability in Differential Geometry.

    Publications

  • (with B. Berndtsson, D. Cordero-Erausquin, B. Klartag) Complex Legendre duality, preprint, 2016, arxiv:1608.05541.
  • (with B. Berndtsson, D. Cordero-Erausquin, B. Klartag) Complex interpolation of R-norms, duality and foliations, preprint, 2016, arxiv:1607.06306.
  • (with T. Darvas) A minimum principle for Lagrangian graphs, preprint, 2016, arxiv:1606.08818.
  • (with A. Pulemotov) Ricci iteration on homogeneous spaces, preprint, 2016, arxiv:1606.05064.
  • (with M. Lindsey) Optimal transport via a Monge-Ampère optimization problem , preprint, 2016, arxiv:1603.07435.
  • (with I.A. Cheltsov) On flops and canonical metrics, preprint, 2015, arxiv:1508.04634.
  • (with J.P. Solomon) The degenerate special Lagrangian equation, Adv. Math. 310 (2017), 889-939.
  • (with T. Darvas) Tian's properness conjectures and Finsler geometry of the space of Kahler metrics, J. Amer. Math. Soc. 30 (2017), 347-387.
  • (with R. Vakil) REUs with limited faculty involvement, "underrepresented" subjects in the undergraduate curriculum, and the culture of Mathematics, in: Directions for Mathematics Research Experience for Undergraduates (M.A. Peterson, Y.A. Rubinstein, Eds.), World Scientific, 2016, pp. 53-72.
  • (with T. Darvas) Kiselman's principle, the Dirichlet problem for the Monge-Ampere equation, and rooftop obstacle problems (alternative link), J. Math. Soc. Japan 68 (2016), 773--–796.
  • Smooth and singular Kahler-Einstein metrics in: Geometric and Spectral Analysis (P. Albin et al., Eds.), Contemp. Math. 630, AMS and Centre Recherches Mathematiques, 2014, pp. 45-138.
  • (with A. Carlotto and O. Chodosh) Slowly converging Yamabe flows, Geom. & Top. 19 (2015), 1523-1568.
  • (with O. Chodosh, V. Jain, M. Lindsey, and L. Panchev) On discontinuity of planar optimal transport maps , J. Topology & Analysis 7 (2015), 239-260.
  • (with S. Artstein-Avidan) Differential analysis of polarity: Polar Hamilton-Jacobi, conservation laws, and Monge Ampère equations, J. d'Analyse Math. 132, 133-–15 (2017).
  • (with I.A. Cheltsov) Asymptotically log Fano varieties, Adv. Math. 285 (2015), 1241-1300.
  • (with R. Mazzeo and N. Sesum) Ricci flow on surfaces with conic singularities, Analysis and PDE 8 (2015), 839-882.
  • (with R. Mazzeo) The Ricci continuity method for the complex Monge-Ampere equation, with applications to Kahler-Einstein edge metrics, C. R. Math. Acad. Sci. Paris 350 (2012), 693-697.
  • (with S. Zelditch) The Cauchy problem for the homogeneous Monge-Ampere equation, III. Lifespan, Crelle's J. 724 (2017), 105-143.
  • (with R. Mazzeo and T. Jeffres) Kahler-Einstein metrics with edge singularities, (with an appendix by C. Li and Y.A. Rubinstein), Annals of Math. 183 (2016), 95-176.
  • (with B. Clarke) Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics, Ann. IHP Anal. Non Lineaire 30 (2013), 251-274.
  • (with B. Clarke) Ricci flow and the metric completion of the space of Kahler metrics, Amer. J. Math. 135 (2013), 1477-1505.
  • (with S. Zelditch) The Cauchy problem for the homogeneous Monge-Ampere equation, II. Legendre transform, Adv. Math. 228 (2011), 2989-3025.
  • (with S. Zelditch) The Cauchy problem for the homogeneous Monge-Ampere equation, I. Toeplitz quantization, J. Differential Geom. 90 (2012), 303-327.
  • (with I. Rodnianski and G. Staffilani) On the global well-posedness of the one-dimensional Schrodinger map flow, Analysis and PDE 2 (2009), 187-209.
  • (with S. Zelditch) Bergman approximations of harmonic maps into the space of Kahler metrics on toric varieties, J. Symp. Geom. 8 (2010), 239-265.
  • Geometric quantization and dynamical constructions on the space of Kahler metrics, Ph.D. Thesis, Massachusetts Institute of Technology, 2008.
  • Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, Adv. Math. 218 (2008), 1526-1565.
  • On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow, Trans. Amer. Math. Soc. 361 (2009), 5839-5850.
  • The Ricci iteration and its applications, C. R. Acad. Sci. Paris 345 (2007), 445-448.
  • On energy functionals, Kahler-Einstein metrics, and the Moser-Trudinger-Onofri neighborhood, J. Funct. Anal. 255, special issue dedicated to Paul Malliavin (2008), 2641-2660.
  • (with M. Peterson) Turbulence on a desktop, Comp. Sci. Eng. 3 (2001), 86-94.
  • (with S. Gueron) The minimal reversible coagulation-fragmentation process having no factorized coagulation and fragmentation rates, Markov Process. Related Fields 6 (2000), 257-264.
  • (with H. Bailey) A Variety of Triangle Inequalities, College Math. J. 31 (2000), 350-355.
  • Errata list for my articles