Yanir A. Rubinstein

Videos   Books   Meetings   Postdocs   Students   REU   Minicourses & Lecture Notes   Publications   Seminars   Teaching   Past Seminars   Contact Info  




2019: My email address changed!

Please click here to see my updated contact info. Unfortunately, I can no longer access my old email address, very sorry if I missed your message! :)


As seen on TV

  • Mathematics on the Golf Channel (AIM, 2011)
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  • Ricci flow and the completion of the space of Kahler metrics (SCGP, 2011)

  • Einstein metrics on Kahler manifolds (Duke University, 2012)

  • Tian's properness conjectures (MSRI, 2016)

    Books

  • Y.A. Rubinstein, B. Shiffman, Eds., Advances in Complex Geometry, American Mathematical Society, 2019.

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


    Meetings

  • 34th Geometry Festival - University of Maryland, April 5-7, 2019.

  • Metro Area Differential Geometry Seminar (MADGuyS) - Howard University, April 27, 2019.

  • UMD Geometry Week - University of Maryland, March 12-16, 2018.

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

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


    Postdocs

  • Jakob Hultgren

  • Tamás Darvas

  • Jesus Martinez Garcia


    Students

  • Yuxiang Ji

  • Mirna Pinsky

  • Kewei Zhang

  • Matthew Dellatorre

  • Ryan Hunter

  • Michael Lindsey

  • Frederick Tsz-Ho Fong


    Research Experience for Undergraduates (REU)

  • 2016: Co-edited the book Directions for Mathematics Research Experience for Undergraduates. The book has been reviewed in Notices of the American Mathematical Society and in The Mathematical Gazette.

  • 2016: Co-authored an article on new models for REUs and the culture of Mathematics.

  • 2013: Co-organized the conference New Directions for Mathematics Research Experiences for Undergraduates at Mt. Holyoke College. Here is an article summarizing the conference.

  • 2012: Co-founded SURIM and led an REU on Optimal Transportation, resulting in a theorem, a senior thesis project, and the Kennedy Honors Thesis Prize and the SIAM Student Paper prize for my student Michael Lindsey.
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    Minicourses & Lecture notes

  • An introduction to Kahler geometry: Tian's properness conjectures - SCGAS Winter School - UC Irvine, January 25-29, 2016. Here are the lecture notes.

  • Solutions to an equation that do not solve the equation - Getting Started with PDEs - IIAS, Hebrew University, September 3-9, 2015.

  • Smooth and singular Kahler-Einstein metrics - Advanced School on PDEs in Geometry and Physics - Hefei, China, June 30-July 11, 2014. Here are the lecture notes.


    Publications

  • High-dimensional convex sets arising in algebraic geometry, preprint, 2019, arxiv:1906.07929.
  • (with K. Zhang) Small angle limits of Hamilton's footballs, Bull. London Math. Soc. 52 (2020) 189-199.
  • (with T. Buttsworth, A. Pulemotov, W. Ziller) On the Ricci iteration for homogeneous metrics on spheres and projective spaces, preprint, 2018, arxiv:1811.01724.
  • (with I.A. Cheltsov, K. Zhang) Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces, Selecta Math. 25 (2019), 1-36.
  • Tian's properness conjectures: an introduction to Kahler geometry, preprint, 2018, arxiv:1807.00928.
  • (with T. Darvas, C.H. Lu) Quantization in geometric pluripotential theory, preprint, 2018, arxiv:1806.03800. Comm. Pure Appl. Math., to appear.
  • (with T. Darvas) Convergence of the Kahler-Ricci iteration, Analysis and PDE 12 (2019), 721-735.
  • (with B. Berndtsson, D. Cordero-Erausquin, B. Klartag) Complex Legendre duality, preprint, 2016, arxiv:1608.05541. Amer. J. Math., to appear.
  • (with B. Berndtsson, D. Cordero-Erausquin, B. Klartag) Complex interpolation of R-norms, duality and foliations, J. Eur. Math. Soc. (JEMS) 22 (2020), 477-–505.
  • (with T. Darvas) A minimum principle for Lagrangian graphs, Comm. Anal. Geom. 27 (2019), 857-876.
  • (with A. Pulemotov) Ricci iteration on homogeneous spaces, Trans. Amer. Math. Soc. 371 (2019), 6257-6287.
  • (with M. Lindsey) Optimal transport via a Monge-Ampère optimization problem , SIAM J. Math. Anal. 49 (2017), 3073-3124.
  • (with I.A. Cheltsov) On flops and canonical metrics, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018), 283-–311.
  • (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 (2017), 133-156.
  • (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