Yanir A. Rubinstein

Outreach   Wide audience   Editorial   Videos   Books   Meetings   Postdocs   Students   REU   Minicourses & Lecture Notes   Publications   Seminars   Teaching   Past Seminars   Contact  



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(unfortunately, I can no longer access my old email address, very sorry if I missed your message! :) )

Outreach

  • Grand Challenges: Increasing Participation of Minorities and Women In STEM Through Sports Performance Analytics Research

  • Mobile Math: Connecting Students to STEM Through Sports

  • Outreach through the Curriculum and Experiential Learning

    Wide audience

  • (with R.J. Berman) Less is More: 30-minutes talks, Notices of the Amer. Math. Soc., December 2024.

    Editorial

  • Advances in Mathematics

    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)

  • Yau-Tian-Donaldson pour les nuls (Centre de recherches mathématiques - CRM, 2021)

    Books

  • V. Mastrantonis, Y.A. Rubinstein, An introduction to convex, complex, and differential geoemtry via the Mahler conjectures, in preparation.

  • R.J. Berman, Y.A. Rubinstein, Eds., Convex and Complex: Perspectives on Positivity in Geometry, American Mathematical Society, 2025.

  • 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

  • Frontiers of Geometric Analysis - In honor of Gang Tian's 65th birthday, Santa Cruz, June 3-7, 2024.

  • Convex and Complex: Perspectives on Positivity in Geometry - In honor of Bo Berndtsson's 70th birthday, Cetraro, October 31-November 4, 2022.

  • 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

  • Robert Shorb

  • Vasanth Pidaparthy

  • Vlasios Mastrantonis

  • Chenzi Jin

  • 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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    REU students

  • Vishesh Jain

  • Michael Lindsey

  • Lyuboslav Panchev
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  • 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.

    Minicourses & Lecture notes

  • A crash course to large deviation principles and optimal transport - UMD graduate course on Topics in Geometric Analysis Fall 2017. Here are the lecture notes . (Published version in: Birational Geometry, Kahler-Einstein Metrics and Degenerations (I. Cheltsov et al., Eds), Springer Proceedings in Mathematics & Statistics 409, Springer, 2023, pp. 795-837.)

  • An introduction to Kahler geometry: Tian's properness conjectures - SCGAS Winter School - UC Irvine, January 25-29, 2016. Here are the lecture notes. (Published version in: Geometric Analysis (J. Chen et al., Eds.), Progress in Mathematics, Vol. 333, Birkhauser, 2020, pp. 381-443.)

  • 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. (Published version in: Geometric and Spectral Analysis (P. Albin et al., Eds.), Contemp. Math. 630, AMS and Centre Recherches Mathematiques, 2014, pp. 45-138.)

    Publications

  • Convex meets complex, preprint, 2024, arxiv:2410.23500.

  • (with C. Jin, G. Tian) Asymptotics of discrete Okounkov bodies and thresholds, preprint, 2024, arxiv:2410.20694.

  • (with C. Jin) Asymptotics of quantized barycenters of lattice polytopes with applications to algebraic geometry, preprint, 2024, arxiv:2406.18969.

  • (with C. Jin) Tian's stabilization problem for toric Fanos, preprint, 2024, arxiv:2403.17262.

  • (with V. Mastrantonis) Two-dimensional Blocki, L^p-Mahler, and Bourgain conjectures, preprint, 2024, arxiv:2401.10992. To appear in Indiana Univ. Math. J.

  • (with B. Berndtsson, V. Mastrantonis) L^p-polarity, Mahler volumes, and the isotropic constant, Analysis & PDE 17 (2024), 2179-2245.

  • (with C. Jin) Chebyshev potentials, Fubini-Study metrics, and geometry of the space of Kahler metrics, Bull. London Math. Soc. (2023).

  • (with V. Mastrantonis) The Nazarov proof of the non-symmetric Bourgain-Milman inequality , Indiana Univ. Math. J. 73 (2024), 911-953.

  • On large deviation principles and the Monge-Ampère equation (following Berman, Hultgren) , in: Birational Geometry, Kahler-Einstein Metrics and Degenerations (I. Cheltsov et al., Eds), Springer Proceedings in Mathematics & Statistics 409, Springer, 2023, pp. 795-837.

  • (with Y. Ji, K. Zhang) Eguchi-Hanson metrics arising from Kahler-Einstein edge metrics , J. Topology & Analysis (2024).

  • (with K. Zhang) Angle deformation of Kahler-Einstein edge metrics on Hirzebruch surfaces, Pure Appl. Math. Quart. 18, special issue in honor of Bernard Shiffman (2022), 343-366.

  • (with G. Tian, K. Zhang) Basis divisors and balanced metrics, Crelle J. 778 (2021), 171-218.

  • (with P. Cascini, J. Martinez-Garcia) On the body of ample angles of asymptotically log Fano varieties, Rendiconti Circolo Mat. Palermo (2022).

  • Classification of strongly asymptotically log del Pezzo flags and surfaces, Int. J. Math. 33 (2022).

  • High-dimensional convex sets arising in algebraic geometry, in: Geometric Aspects of Functional Analysis (B. Klartag, E. Milman, Eds.), Lecture Notes in Mathematics 2266 (2020), pp. 301--323.

  • (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, Transformation Groups 26 (2021), 145--164.

  • (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, in: Geometric Analysis (J. Chen et al., Eds.), Progress in Mathematics, Vol. 333, Birkhauser, 2020, pp. 381-443.

  • (with T. Darvas, C.H. Lu) Quantization in geometric pluripotential theory, Comm. Pure Appl. Math. 73 (2020), 1100-1138.

  • (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, Amer. J. Math. 142 (2020), 323-339.

  • (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