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
  22. A canonical barycenter via Wasserstein regularization, with Young-Heon Kim. SIAM J. Math. Anal. 50 (2018) 1817–1828.
  23. Interpolating between matching and hedonic pricing models. To appear in Econom. Theory

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. Transition to nestedness in multi- to one-dimensional optimal transport, with Pierre-André Chiappori and Robert McCann.
  5. Optimal transportation between unequal dimensions, with Robert McCann.

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.