## 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

*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)**

Note on copyright issues: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holders.

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.

*L*_{p}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 L*_{p}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**L*-Minkowski problem,_{p}**Transactions of the AMS 356**(2004) 4359-4370.D. Hug, E. Lutwak, D. Yang, and G. Zhang,

*On the L*_{p}Minkowski problem for polytopes,**Discrete and Computational Geometry**(2005) 699-715.E. Lutwak, D. Yang, and G. Zhang,

*L*_{p}John ellipsoids,**Proceedings of the London Mathematical Society 90**(2005) 497-520.E. Lutwak, D. Yang, and G. Zhang,

*Volume inequalities for subspaces of L*_{p},**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**L*Minkowski Problem,_{p}**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) 5592-5599A. Cianchi, E. Lutwak, D. Yang, G. Zhang.

*A Unified Approach to CramÃ©r-Rao Inequalities,***IEEE Transactions in Information Theory**, to appear. DOI (identifier) 10.1109/TIT.2013.2284498.

## Publications

## Unpublished articles

D. Yang.

*Gunther's proof of Nash's isometric embedding theorem.*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