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Professor Feng-Yu Wang

WIMCS Research Chair

Specialist Subjects: Stochastic analysis on manifolds, functional inequalities and spectral theory, particle systems, stochastic partial differential equations

Feng-Yu Wang was born in 1966 in Anhui, China. He graduated from Anhui Normal University in 1987 and received his Ph.D. in 1993 from Beijing Normal University, where he was appointed a Lecture and exceptionally promoted to Associated Professor and Professor in 1993, 1994 and 1995 respectively. He was appointed by the Educational Ministry of China in 2000 a Chang-Jiang Chair, and by WIMCS (Wales Institute of Mathematics and Computing Sciences) in 2007 as the Chair of Stochastic Processes.

Feng-Yu Wang's research work involves in several areas including probability theory, functional analysis, mathematical physics and Riemann geometry.

In the early 1990s he published a series papers on geometry analysis using probabilistic approaches. In particular, together with Mu-Fa Chen he established a general lower bound formula for the first eigenvalue (or spectral gap) of symmetric diffusion operators on manifolds, which extends or improves well-known results in the literature, and was regarded as a significant application of stochastic approaches to Riemannian geometry (Math. Rev. 2001m:60187).

In 1997 he established the dimension-free Harnack inequality for diffusion semigroups with curvature bounded below. This inequality has become a powerful tool in the study of log-Sobolev inequalities and related analysis. In particular, it was applied to derive dimension-free estimates on the log-Sobolev constant, explicit heat kernel estimates, and strong feller property of semigroups in infinite-dimensions. The inequality was called `Wang's Harnack inequality' in references.

From the end of 1990s, he started to develop general functional inequalities to describe various properties of Markov semigroups and spectral theory (partly joint with M. Rockner and F. Gong). In particular, he proved that under a reasonable regularity framework, the super Poincare inequality is equivalent to the empty of essential spectrum of the generator. Explicit estimates on higher order eigenvalues as well as various bounds on the associated semigroup are provided. These functional inequalities are also applied to the study on transportation cost inequalities and various ergodicity properties of Markov semigroups. For instance, its weak version (called the weak Poincare inequality) is very efficient in the study of general convergence rates of Markov semigroups. His first paper in this direction (J. Functional Analysis 2000) has entered the top 1% within its field according to Essential Science Indicators, Web of Science (ISI).

Besides general theory on functional inequalities and applications, recent work includes infinite dimensional stochastic analysis (analysis on Riemannian path spaces, particle systems, measure-valued processes), stochastic partial differential equations (various properties for stochastic generalized porous media equations), and stochastic analysis on Riemannian manifolds with curvature unbounded below.

 

Recent Publications

 

  1. F.-Y. Wang, A Generalization of Poincaré and log-Sobolev inequalities, Potential Analysis, 22(2005), 1-15.
  2. F.-Y. Wang, A character of the gradient estimate for diffusion semigroups, Proc. AMS. 133(2005), 827-834.
  3. S. Fang, F.-Y. Wang, Analysis on free Riemannian path spaces, Bull. Sci. Math. 129(2005), 339-355.
  4. F.-Y. Wang, Gradient estimates and the first Neumann eigenvalue on non-convex manifolds, Stochastic Processes and Applications 115(2005), 1475-1486.
  5. G. Da Prato, M. Röckner, B.L. Rozovskii, F.-Y. Wang, Strong solutions of Generalized porous media equations: existence, uniqueness and ergodicity, Comm. Part. Diff. Equ. 31 (2006), no. 1-3, 277-291.
  6. F.-Y. Wang, The stochastic order and critical phenomena for surperprocesses, Infinite Dimensional Analysis, Quantum Probability and Related Topics 9(2006), 107-128.
  7. M. Röckner, F.-Y. Wang, Functional inequalities for particle systems on Polish spaces, Potential Analysis 24(2006), 223-243.
  8. M. Arnaudon, A. Thalmaier, F.-Y. Wang, Harnack inequality and heat kernel estimate on manifolds with curvature unbounded below, Bull. Sci. Math. 130(2006), 223-233.
  9. E. Priola and F.-Y. Wang, Gradient estimates for diffusion semigroups with singular coefficients, J. Funct. Anal. 236(2006), 244-264.
  10. M. Röckner, F.-Y. Wang, L.-M. Wu, Large Deviations for Stochastic Generalized Porous Media Equations, Stochastic Processes and Applications 116(2006), 1677-1689.
  11. F.-Y. Wang, A Harnack-type inequality for Non-Symmetric Markov Semigroups, J. Funct. Anal . 239(2006), 297-309.
  12. X. Chen, F.-Y. Wang, Optimal integrability condition for the log-Sobolev inequality, Quart. J. Math. (Oxford) 58 (2007), 17-22.
  13. F.-Y. Wang, Estimates of the first Neumann eigenvalue and the log-Sobolev constant on Non-convex manifolds, Math. Nach. 280(2007),1431-1439.
  14. F.-Y. Wang, Ito type measure-valued stochastic differential equations, J. Math. Anal. Appl. 329(2007), 1102-1117.
  15. E. M. Ouhabaz, F.-Y. Wang, Sharp estimates for intrinsic ultracontractivity on $ C^{1,\alpha}$-domains, Manu. Math. 112(2007), 229-244.
  16. F.-Y. Wang, Harnack inequality and applications for stochastic generalized porous media equations, Annals of Probability 35(2007), 1333-1350.
  17. D. Bakry, M. Ledoux, F.-Y. Wang, Perturbations of functional inequalities using growth conditions, J. Math. Pures Appl. 87(2007), 394-407.
  18. J. Ren, M. Röckner, F.-Y. Wang, Stochastic generalized porous media and fast diffusion equations, J. Diff. Equ. 238 (2007), 118-156?
  19. M. Röckner, F.-Y. Wang, Concentration of invariant measures for stochastic generalized porous media equations, Inf. Dim. Anal. Quant. Probab. Relat. Topics. 10 2007 397-409

PhD

 

Mathematics

Swansea University

Tel: 01792 295087

Fax: 01792 295843

Email: f.y.wang@swansea.ac.uk

 

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