dyang.at.poly - Deane Yang, Professor of Mathematics

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 mortgages and 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,

Recent articles

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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. 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_p-Minkowski problem.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_p Minkowski Problem,International Mathematical Research Notices (2006) 1-21.
E. Lutwak, D. Yang, G. Zhang. Volume Inequalities for Isotropic Measures,American Journal of Mathematics, to appear.
E. Lutwak, D. Yang, G. Zhang. Moment-entropy inequalities for a random vector,IEEE Transactions on Information Theory 53 (2007) 1603-1607.

Publications

As listed in Mathscinet

Unpublished articles

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

Books I enjoyed reading

Anything written by Jhumpa Lahiri (unfortunately, there are only two so far)
Anything written 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

Deane Yang, Professor of Mathematics