Published or accepted papers

  1. Rectifiability of optimal transportation plans, with Robert McCann and Micah Warren. Canad. J. Math. 64 (2012) 924-933.
  2. On the local structure of optimal measures in the multi-marginal optimal transportation problem. Calc. Var. and PDE. 43 (2012) 529-536. Currently available online at www.springerlink.com.
  3. Uniqueness and Monge solutions in the multi-marginal optimal transportation problem. SIAM J. Math. Anal. 43 (2011) 2758-2775.
  4. Regularity of optimal transportation between spaces with different dimensions. Math. Res. Lett. 19 (2012) 291-307.
  5. Convexity and multi-dimensional screening for spaces with different dimensions. J. Econom. Theory. 147 (2012) 2399-2418.
  6. Regularity properties of optimal transportation problems arising in hedonic pricing models. ESAIM: Control Optim. Calc. Var. 19 (2013) 668-678.
  7. Optimal transportation with infinitely many marginals. J. Funct. Anal. 264 (2013) 947–963.
  8. On a class of optimal transportation problems with infinitely many marginals. SIAM J. Math. Anal. 45 (2013) 2557-2575.
  9. Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutions. Discrete Contin. Dyn. Syst. 34 (2014) 1623-1639. (Special issue on "Optimal transport and applications.")
  10. Remarks on the semi-classical Hohenberg-Kohn functional. Nonlinearity 26 (2013) 2731-2744.
  11. Decoupling of DeGiorgi-type systems via multi-marginal optimal transport, with Nassif Ghoussoub. Comm. Partial Differential Equations. 39 (2014) 1032-1047.
  12. N-density representability and the optimal transport limit of the Hohenberg-Kohn functional, with Gero Friesecke, Christian B. Mendl, Codina Cotar and Claudia Klüppelberg. J. Chem. Phys. 139 (2013), 164109.
  13. A general condition for Monge solutions in the multi-marginal optimal transport problem, with Young-Heon Kim. SIAM J. Math. Anal. 46 (2014) 1538-1550.
  14. Multi-marginal optimal transport: theory and applications. ESAIM: Math. Model. Numer. Anal. 49 (2015) 1771-1790. (Special issue on "Optimal transport in applied mathematics.")
  15. Infinite-body optimal transport with Coulomb Cost, with Codina Cotar and Gero Friesecke. Calc. Var. Partial Differential Equations. 54 (2015) 717-742.
  16. Multi-marginal optimal transport on Riemannian manifolds, with Young-Heon Kim. Amer. J. Math. 137 (2015) 1045-1060.
  17. The multi-marginal optimal partial transport problem, with Jun Kitagawa. Forum Math. Sigma. 3 (2015), e17, 28pp.
  18. Solutions to multi-marginal optimal transport problems concentrated on several graphs, with Abbas Moameni. ESAIM: Control Optim. Calc. Var. 23 (2017) 551-567.
  19. Multi- to one-dimensional transportation, with Pierre-André Chiappori and Robert McCann. Comm. Pure Appl. Math. 70 (2017) 2405–2444.
  20. Wasserstein Barycenters over Riemannian manifolds, with Young-Heon Kim. Adv. Math. 307 (2017) 640-683.
  21. On Khinchine type inequalities for k-wise independent Rademacher random variables, with Susanna Spektor. Statist. Probab. Lett. 132 (2018) 35-39

Preprints

  1. Nonpositive curvature, the variance functional, and the Wasserstein barycenter, with Young-Heon Kim.
  2. Single Market Nonparametric Identification of Multi-Attribute Hedonic Equilibrium Models, with Victor Chernozhukov, Alfred Galichon and Marc Henry.
  3. Multidimensional matching, with Pierre-André Chiappori and Robert McCann.
  4. Interpolating between matching and hedonic pricing models.
  5. A canonical barycenter via Wasserstein regularization, with Young-Heon Kim.

Theses, notes, etc.

  1. The multi-marginal optimal transportation problem. Oberwolfach Reports, 31 (2010) 1843-1845.
  2. Structural results on optimal transportation plans. PhD Thesis at the University of Toronto. My advisor was Robert McCann.
  3. Optimal transport: From moving soil to same-sex marriage, with Nassif Ghoussoub. CMS Notes 45 (June 2013) 14-15,17.