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,
- An application of fully nonlinear PDE's, Workshop on fully nonlinear PDE's and their applications, Neil Trudinger and Xu-Jia Wang, organizers, Center for Mathematical Sciences, Zhejiang University, Hangzhou, China, June 2005.
- An Option-Theoretic Model for the Valuation of Mortgage-Backed Securities,
Colloquium, Department of Mathematics, Polytechnic University,
Brooklyn, New York, March 2007.
- Affine Integral Geometry From A Differentiable Viewpoint,
New Directions in Exterior Differential Systems:
A conference in honor of Robert Bryant's 60th birthday, Estes Park, Colorado, July 2013
Recent survey papers
- D. Yang, Affine Integral Geometry from a Differentiable Viewpoint, Handbook of Geometric Analysis vol. II, International Press, 2010.
- J. Loftin, X. J. Wang, D. Yang, Cheng and Yau's work on the Monge-Ampère equation and affine geometry, Geometry and Analysis (Vol. I), Higher Education Press and International Press, 2010.
- D. Yang, On Wilhelm Blaschke's Mathematical Work and Influence on S. S. Chern (Chinese version).
Recently published refereed journal articles(updated February 25, 2013)
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E. Lutwak, D. Yang, G. Zhang. A new ellipsoid associated with convex bodies, Duke Mathematical Journal 104 (2000) 375-390.
E. Lutwak, D. Yang, G. Zhang. Lp affine isoperimetric inequalities, Journal of Differential Geometry 56 (2000) 111-132.
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.
O. Guleryuz, E. Lutwak, D. Yang, G. Zhang. Information theoretic inequalities for contoured probability distributions, IEEE Transactions on Information Theory 48 (2002) 2377-2383.
E. Lutwak, D. Yang, G. Zhang. The Cramer-Rao inequality for star bodies, Duke Mathematical Journal 112 (2002) 59-81.
E. Lutwak, D. Yang, G. Zhang. Sharp affine Lp Sobolev Inequalities, Journal of Differential Geometry 62 (2002) 17-38.
E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities, Annals of Probability 32 (2004) 757-774.
E. Lutwak, D. Yang, G. Zhang. On the Lp-Minkowski problem, Transactions of the AMS 356 (2004) 4359-4370.
D. Hug, E. Lutwak, D. Yang, and G. Zhang, On the Lp Minkowski problem for polytopes, Discrete and Computational Geometry (2005) 699-715.
E. Lutwak, D. Yang, and G. Zhang, Lp John ellipsoids, Proceedings of the London Mathematical Society 90 (2005) 497-520.
E. Lutwak, D. Yang, and G. Zhang, Volume inequalities for subspaces of Lp, Journal of Differential Geometry 68 (2004) 159-184.
W. Chen, R. Howard, E. Lutwak, D. Yang, and G. Zhang, A generalized affine isoperimetric inequality, Journal of Geometric Analysis 14 (2004) 597-612.
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.
E. Lutwak, D. Yang, G. Zhang. Optimal Sobolev Norms and the Lp Minkowski Problem, International Mathematical Research Notices (2006) 1-21.
E. Lutwak, D. Yang, G. Zhang. Volume Inequalities for Isotropic Measures, American Journal of Mathematics 129 (2007) 1711-1723.
E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities for a random vector, IEEE Transactions on Information Theory 53 (2007) 1603-1607.
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.
E. Lutwak, D. Yang, G. Zhang. Orlicz projection bodies, Advances in Mathematics 223 (2010) 220-242.
C. Haberl, E. Lutwak, D. Yang, G. Zhang. The even Orlicz Minkowski problem, Advances in Mathematics 224 (2010) 2485-2510.
E. Lutwak, D. Yang, G. Zhang. A volume inequality for polar bodies, Journal of Differential Geometry 84 (2010) 163-178.
E. Lutwak, D. Yang, G. Zhang. Orlicz centroid bodies, Journal of Differential Geometry 84 (2010) 365-387.
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.
E. Lutwak, D. Yang, G. Zhang. The Brunn-Minkowski-Firey inequality for nonconvex sets, Advances in Applied Mathematics 48 (2012) 407-413.
E. Lutwak, S. Lv, D. Yang, G. Zhang. Extensions of Fisher information and Stam's inequality, IEEE Transactions in Information Theory (2012) 1319-1327.
K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. The log-Brunn-Minkowski inequality, Advances in Mathematics 231 (2012) 1974-1997.
K. J. Böröczky, Jr., E. Lutwak, D. Yang, G. Zhang. The logarithmic Minkowski problem, Journal of the American Mathematics Society 26 (2013) 831-852.
E. Lutwak, S Lv, D. Yang, G. Zhang. Affine moments of a random vector, IEEE Transactions in Information Theory 59 (2013) 5592-5599
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.
J. Goodman and D. Yang. Local solvability of nonlinear partial differential equations of real principal type.
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