Teaching

• Spring 2024
  • MATH-GA1002 Multivariable Analysis
  • MATH-GA2120 Linear Algebra II

A Cluttered Mind (blog)

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.

Academic profiles

Google Scholar

Mathscinet (requires university or individual subscription)

Professional history

• 2017—present: Professor of Mathematics, NYU Courant Institute of Mathematical Sciences
• 2015—2017: Professor of Mathematics, NYU Tandon School of Engineering
• 2014—2015: Professor of Mathematics, NYU Polytechnic School of Engineering
• 2008—2014: Professor of Mathematics, Polytechnic Institute of New York University
• 1993—2008: Professor of Mathematics, Polytechnic University
• 1996—1997: Vice Provost for Academic Development, Polytechnic University
• 1993—1995: Department Head of Mathematics, Polytechnic University
• 1991—1993: Associate Professor, Polytechnic University
• 1989—1991: Visiting Associate Professor, Columbia University
• 1988—1990: Associate Professor, Rice University
• 1985—1988: Assistant Professor, Rice University
• 1983—1984: NSF Postdoctoral Fellow, NYU Courant Institute of Mathematical Sciences
• 1983: PhD in Mathematics, Harvard University
• 1979: BA in Mathematics and Physics, University of Pennsylvania

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).

Selected refereed journal articles

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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. L_p 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 L_p 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 L_p-Minkowski problem, Transactions of the AMS 356 (2004) 4359-4370.
9. D. Hug, E. Lutwak, D. Yang, and G. Zhang, On the L_p Minkowski problem for polytopes, Discrete and Computational Geometry (2005) 699-715.
10. E. Lutwak, D. Yang, and G. Zhang, L_p 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 L_p, 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 L_p 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 60, (2014) 643--650.
29. K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang. Affine images of isotropic measures, Journal of Differential Geometry 99 (2015) 407--442.
30. Y. Huang, E. Lutwak, D. Yang, G. Zhang. Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems, Acta Mathematica 216 (2016) 325-388.
31. E. Lutwak, D. Yang, G. Zhang. L_p dual curvature measures, Advances in Mathematics 329 (2018) 85-132.
32. K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang, Y. Zhao. The dual Minkowski problem for symmetric convex bodies, Advances in Mathematics 356 (2019).
33. K. J. Böröczky, E. Lutwak, D. Yang, G. Zhang, Y. Zhao. The Gauss Image Problem, Communications in Pure and Applied Mathematics (2020).

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
4. C. T. Yang. Equivalence of the Alexander-Kolmogorff and Čech Cohomology Theories. Dissertation, Tulane University, 1952.

Mathematical Fragments

1. A simple way to discover the Riemann curvature
2. DeTurck's trick for the prescribed Ricci equation
3. A simple proof of the Theorema Egregium of Gauss
4. Gromov's approach to solving underdetermined ODE's
5. Gunther's proof of Nash's isometric embedding theorem.
6. Holonomy equals curvature.
7. The exterior derivative via Stokes's theorem
8. The Lie derivative of a differential form
9. A simple proof of Heron's formula for the area of a triangle
10. The pullback of a connection on a vector bundle
11. The dot product via length and orthogonality
12. Fundamental concepts of calculus

Good advice on how to email a professor (not just me)

Front page of New York Times, 2/23/2017

• Lead article by my brother Kenneth Chang on newly discovered planets outside the solar system
• Photo by my son Stephen Yang of Native American protesters setting fire to their camp in Cannon Ball, North Dakota

My mathematical ancestry

Produced by the Mathematical Genealogy Project