随机分析及其在微分几何与泛函分析等领域的应用。使用马氏过程Dirichlet型的泛函不等式刻画马氏半群的长时间行为和各种范数的估计,并刻画生成元的谱。使用随机分析研究(带边)Riemann流形的几何和分析性质,研究随机偏微分方程等。
主持国家杰出青年基金项目1项(2000-2004)、国际合作项目和博士点基金项目多项,参加973项目和项国家创新群体项目。在研项目包括两项国家重点项目和一项中俄合作项目。
1.F.-Y. Wang, On estimation of logarithmic Sobolev constant and gradient estimates of heat semigroups, Probability Theory Relat. Fields 108(1997), 87--101.
2.F.-Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemannian manifolds, Probability Theory Relat. Fields 109(1997), 417--424.
3.F.-Y. Wang, Functional inequalities for empty essential spectrum, J. Funct. Anal. 170(2000), 219--245.
4.M. R?ckner and F.-Y. Wang, Weak Poincar/'e inequalities and convergence rates of Markov semigroups, J. Funct. Anal. 185(2001), 564--603.
5.F.-Y. Wang, Probability distance inequalities on Riemannian manifolds and path spaces, J. Funct. Anal. 206 (2004), 167-190.
6.F.-Y. Wang, Harnack inequality and applications for stochastic generalized porous media equations, Annals of Probability 35(2007), 1333--1350.
7.F.-Y. Wang, From super Poincare to weighted log-Sobolev and entropy-cost inequalities, J. Mathematiques Pure Appl. 90(2008), 270--285.
8.F.-Y. Wang, Log-Sobolev inequality on non-convex manifolds, Adv. Math. 222(2009), 1503—1520.
9.F.-Y. Wang, Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on non-convex manifolds, Annals of Probab. 39(2011), 1449--1467.
10.F.-Y. Wang, Integration by parts formula and shift Harnack inequality for stochastic equations, Ann. Probab. 42(2014), 994—1019.
已培养12名博士、27名硕士,其中一人的博士论文入选2008年度“全国百篇优秀博士论文”并获中国数学会“钟家庆”奖。
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