Teaching

Research

I work with Erwin Lutwak and Gaoyong Zhang on affine and linearly invariant geometric and analytic inequalities. In the past I have worked on overdetermined systems of PDE's and convergence and collapsing theorems for Riemannian manifolds.

 I also work with Andy Kalotay on modeling fixed income securities, including bonds, callable bonds, floaters, mortgage-backed securities.

Recent talks

Recent survey papers

Recently published refereed journal articles

(updated February 25, 2013)

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  1. E. Lutwak, D. Yang, G. Zhang. A new ellipsoid associated with convex bodies, Duke Mathematical Journal 104 (2000) 375-390.

  2. E. Lutwak, D. Yang, G. Zhang. Lp affine isoperimetric inequalities, Journal of Differential Geometry 56 (2000) 111-132.

  3. E. Lutwak, D. Yang, G. Zhang. A new affine invariant for polytopes and Schneider's projection problem. Transactions of the AMS 353 (2001) 1767-1779.

  4. O. Guleryuz, E. Lutwak, D. Yang, G. Zhang. Information theoretic inequalities for contoured probability distributions, IEEE Transactions on Information Theory 48 (2002) 2377-2383.

  5. E. Lutwak, D. Yang, G. Zhang. The Cramer-Rao inequality for star bodies, Duke Mathematical Journal 112 (2002) 59-81.

  6. E. Lutwak, D. Yang, G. Zhang. Sharp affine Lp Sobolev Inequalities, Journal of Differential Geometry 62 (2002) 17-38.

  7. E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities, Annals of Probability 32 (2004) 757-774.

  8. E. Lutwak, D. Yang, G. Zhang. On the Lp-Minkowski problem, Transactions of the AMS 356 (2004) 4359-4370.

  9. D. Hug, E. Lutwak, D. Yang, and G. Zhang, On the Lp Minkowski problem for polytopes, Discrete and Computational Geometry (2005) 699-715.

  10. E. Lutwak, D. Yang, and G. Zhang, Lp John ellipsoids, Proceedings of the London Mathematical Society 90 (2005) 497-520.

  11. E. Lutwak, D. Yang, and G. Zhang, Volume inequalities for subspaces of Lp, Journal of Differential Geometry 68 (2004) 159-184.

  12. W. Chen, R. Howard, E. Lutwak, D. Yang, and G. Zhang, A generalized affine isoperimetric inequality, Journal of Geometric Analysis 14 (2004) 597-612.

  13. E. Lutwak, D. Yang, G. Zhang. Cramer-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information, IEEE Transactions on Information Theory 51 (2005) 473-478.

  14. E. Lutwak, D. Yang, G. Zhang. Optimal Sobolev Norms and the Lp Minkowski Problem, International Mathematical Research Notices (2006) 1-21.

  15. E. Lutwak, D. Yang, G. Zhang. Volume Inequalities for Isotropic Measures, American Journal of Mathematics 129 (2007) 1711-1723.

  16. E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities for a random vector, IEEE Transactions on Information Theory 53 (2007) 1603-1607.

  17. A. Cianchi, E. Lutwak, D. Yang, G. Zhang. Affine Moser-Trudinger and Morrey-Sobolev inequalities, Calculus of Variations and PDE's 36 (2009) 419-436.

  18. E. Lutwak, D. Yang, G. Zhang. Orlicz projection bodies, Advances in Mathematics 223 (2010) 220-242.

  19. C. Haberl, E. Lutwak, D. Yang, G. Zhang. The even Orlicz Minkowski problem, Advances in Mathematics 224 (2010) 2485-2510.

  20. E. Lutwak, D. Yang, G. Zhang. A volume inequality for polar bodies, Journal of Differential Geometry 84 (2010) 163-178.

  21. E. Lutwak, D. Yang, G. Zhang. Orlicz centroid bodies, Journal of Differential Geometry 84 (2010) 365-387.

  22. G. Bianchi, D. Klain, E. Lutwak, D. Yang, G. Zhang. A countable set of directions is sufficient for Steiner symmetrization, Advances in Applied Mathematics 47 (2011) 869-873.

  23. E. Lutwak, D. Yang, G. Zhang. The Brunn-Minkowski-Firey inequality for nonconvex sets, Advances in Applied Mathematics 48 (2012) 407-413.

  24. E. Lutwak, S. Lv, D. Yang, G. Zhang. Extensions of Fisher information and Stam's inequality, IEEE Transactions in Information Theory (2012) 1319-1327.

  25. K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. The log-Brunn-Minkowski inequality, Advances in Mathematics 231 (2012) 1974-1997.

  26. K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. The logarithmic Minkowski problem, Journal of the American Mathematics Society 26 (2013) 831-852.

  27. E. Lutwak, S Lv, D. Yang, G. Zhang. Affine moments of a random vector, IEEE Transactions in Information Theory 59 (2013) 5592-5599

  28. A. Cianchi, E. Lutwak, D. Yang, G. Zhang. A Unified Approach to Cramér-Rao Inequalities, IEEE Transactions in Information Theory, to appear. DOI (identifier) 10.1109/TIT.2013.2284498.

Publications

Unpublished articles

  1. D. Yang. Gunther's proof of Nash's isometric embedding theorem.

  2. J. Goodman and D. Yang. Local solvability of nonlinear partial differential equations of real principal type.

  3. C. T. Yang (as told to D. Yang). Memories of Chern

Books I enjoyed reading

  • Beg, Borrow, Steal and Hurry Down Sunshine by Michael Greenberg
  • Interpreter of Maladies, Unaccustomed Earth, and The Namesake by Jhumpa Lahiri
  • In the Pond and The Bridegroom by Ha Jin
  • Monkey King, Sour Sweet, An Insular Possession, all by Timothy Mo (I haven't tried to read any of his more recent books)
  • Incompleteness: The Proof and Paradox of Kurt Godel, by Rebecca Goldstein
  • The Russian Debutante Handbook, by Gary Shteyngart

Photos

Food