Xiang Dong LI  Maître de Conférences  à l'Institut de Mathématiques de Toulouse

Dipl\^ome d'Habilitation à Diriger des Recherches, soutenu le 12 décembre 2007 à l'Université Paul Sabatier, mention "Très honorable"

Thèse d'HDR: Transformées de Riesz, théorie de Hodge $L^p$, estimation $L^p$ de $d$ et $\bar\partial$ sur les variétés riemanniennes et kaehleriennes complètes

PhD (Grade A) 1999  AMSS, Academia Sinica , and University of Lisbon

Thesis: Stochastic Analysis and Geometry on Path and Loop Spaces  [PhD.ps]  [PhD.pdf]

Supervisors:   Prof. Zhi-Ming Ma (Beijing), Prof. P. Malliavin  (Paris)  and Prof. A. B. Cruzeiro (Lisbon)

July  1998--Sept 1999     3rd year of PhD at the University of Lisbon

Oct  1997--June 1998      2nd year of PhD at the University Paris VI

Mar 1994--Sept 1997      MA and 1st year of PhD at Academia Sinica, Beijing

Sept 1985--June 1990      BA, Sino-French Center of Mathematics, Wuhan University

Special Prize of the President Scholarship of the Chinese Academy of Sciences, 1999

Prize of Excellent PhD Thesis awarded by the Chinese Ministry of Education, 2002

Prize Anastacio da Cunhua awarded by the Portuguese Mathematical Society, 2002

Sept  2003 -- Now               Maître de Conférences , Université Paul Sabatier (Toulouse III)

August 1-15, 2007              Junior Research Fellow, Institute of Mathematical Research, University of Hong Kong

Sept  2005 -- June 2006     Délégation au CNRS à  l'Université Paris-Sud

June 2004 -- Aug 2004      Visiting Institute of Applied Mathematics, Chinese Academy of Sciences

Oct.  2000 --  Sept 2003     Postdoctoral Research Fellow (Grade: RS1A) , University of Oxford

Apr.  2000 -- June 2000      Visiting Department of Mathematics, University of California, San Diego

Oct.  1999 -- Sept  2000      Postdoctoral Research Fellow, University of Lisbon

July   1990 -- Feb.  1994      Research Assistant, Institute of Electromechanics-Astronautics in ChongQing

$L^p$-estimates of $\bar\partial$ and $L^p$-cohomology on complete K\"ahler manifolds

Liouville theorems and uniqueness theorems of heat equations on complete Riemannian manifolds

Stochastic analysis and differential geometry on path and loop spaces

Differential equations on rough  path spaces and its applications

Undergraduate teaching at University Toulouse III,  Sept. 2003- PRESENT

Graduate Lectures in Stochastic Differential Geometry,  The 10th Chinese National Graduate Summer School in Mathematics,
Organized by Univ. Sun Yat-Sen, August 2005.

Several Undergraduate Lectures in Martingale Theory and Stochastic Processes,  University of Oxford, Hilary Term, Academic year 2001-2002.

Graduate Lectures in Stochastic Analysis, University of Oxford,  Michaelmas Term, Academic year 2001-2002. [postscript]

Graduate Lectures in Malliavin Calculus and Stochastic Differential Geometry, Mathematical Institute, Oxford, Academic year 2000-2001.

Graduate Lectures in Stochastic Analysis and Geometry on Path and Loop Spaces , Institute of Applied Mathematics, Academia Sinica, July-August 1999.

2. The de Rham-Hodge semigroup on the path space: existence and L^2-contractivity. C.R. Acad. Sci. Paris Ser. I Math. 328 (1999), no. 2, 161--166. [posscript]

3. Existence and uniqueness of geodesics on path spaces. J. Funct. Anal.173 (2000),no. 1, 182--202. [postscript]

4. Sobolev spaces and capacities theory on path spaces over a compact Riemannian manifold,  Probability Theory and Related Fields,   125 (2003),  96--134. [pdf]

5. (with T. Coulhon and X. T. Duong)  Littlewood-Paley-Stein functions on complete Riemannian manifolds for $1\leq p\leq 2$, Studia Math., 154 (1), 2003, 37--57.  [postscript]

6. Asymptotic behavior of divergences and Cameron-Martin theorem on loop spaces,  Annals of Probability  [pdf] , 32(2004), No3B, 2409-2445.

7. Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds, J. Math. Pure Appl.,  84(2005), 1295-1361.[pdf]

8. Riesz transforms for symmetric diffusion operators on complete Riemannian manifolds, Revista Mat. Iberoamerican,  22(2006), 591-648. [pdf]

9. (joint with T. Lyons)   Smoothness of Ito maps and diffusion processes on  path spaces (I), [pdf], Ann. Sci. ENS.  Paris,  4 Series, t. 39(2006), 649-677.

10. Martingale transforms and $L^p$-norm estimates on complete Riemannian manifolds [pdf], Probab. Theory and Related Fields, 2008.

2. Littlewood-Paley-Stein inequalities and Riesz transforms on complete Riemannian manifolds, Proceeding of the First Sino-German Conference in Stochastic Analysis, Beijing,  29 August - 3 Sept., 2002.

2. On the $L^p$-Hodge theory and the $L^{p}$-cohomology over complete Riemannian manifolds, 2007. This paper is still in revision for submission. If you need it, send an email to me.

3. On the Weak $L^p$-Hodge decomposition theorem over complete Riemannian manifolds [pdf], submitted, 2008.

4. Sobolev inequalities on forms and $L^{p, q}$-cohomology on complete Riemannian manifolds [pdf], submitted, 2008.

5. Riesz transforms on forms and $L^p$-Hodge decomposition over complete Riemannian manifolds [pdf], submitted, 2008.

6. (with F. Fang and Z.-L. Zhang) Two generalizations of the Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature [pdf], submitted, 2007. Also avalaible on ArXiv.0707.0526.

7. (with B. Driver) On the equivalence of the heat kernel measure and the pinned Wiener measure on the loop group over a compact Lie group,  2000.

8. Connections, geodesics and Wiener measures on path and loop spaces,  Lecture Note at the Quantum Fields Theory Seminar, University of Oxford, February 12,  2002.

On the $L^p$-Hodge theory over complete Riemannian manifolds, International Workshop on Stochastic calculus on manifolds, graphes, and random structures, Hausdroff Institute of Mathematics, Bonn, 8-12 Oct 2007.

On the $L^p$-Hodge theory over complete Riemannian manifolds, Institute of Mathematical Sciences, Chinese University of Hong Kong, September 2007.

Poincar\'e inequalities and Sobolev inequalities on forms over complete Riemannian manifolds, Inst. Appl. Math., Chinese Academy of Sciences, July, 2007.

Riesz transforms, Poincar\'e inequalities and $L^p$-Hodge theory over complete Riemannian manifolds, International Workshop on Markov Processes and Related Topics, Beijing Normal Univ., July 2007.

On the $L^p$-estimates and existence theorem of the $\bar\partial$-operator over complete K\"ahler manifolds, Lab. Emile Picard, Univ. Paul Sabatier, March 29, 2007.

On the $L^p$-Hodge theory and the $L^{p, q}$-cohomology over complete Riemannian manifolds, Univ. Cergy-Pontoise, March 19, 2007.

On the $L^{p, q}$-cohomology over complete Riemannian manifolds, Univ. Paris-Sud, March 9, 2007.

Riesz transforms and Hodge decomposition on complete Riemannian manifolds,  Univ. Zhejiang, Dec. 2005;  Univ. Sun Yat-Sen, July, 2006;  Univ.  Hong Kong,  Aug.  2006;  Univ. Nankai, Sept. 2006.

Liouville theorems for diffusion operators on complete Riemannian manifolds, Institute de Fourier, Université Grenoble I, Feb. 2006.

Liouville theorems and Riesz transforms on complete Riemannian manifolds, The First Sino-French Congres in Mathematics,  Zhuhai, December 12--17,  2005.

Liouville theorems and Feller property for diffusion operators on complete Riemannian manifolds, International Workshop on Markov Processes and Related Topics,  Beijing Normal University, August 10--14, 2004.

Riesz transforms and Schr\"odinger operators on non-compact Riemannian manifolds with negative Ricci curvature,  Satellite Conference of ICM2002 Beijing in Stochastic Analysis, Beijing, 29 August--3 September 2002.

Littlewood-Paley inequalities and Riesz transforms on complete Riemannian manifolds, International conference of Stochastic Processes and its Applications, University of Cambridge, 10-15, July, 2001.

Littlewood-Paley functions and Riesz transforms on complete Riemannian manifolds, International conference of Stochastic Analysis and Financial Mathematics, University Humboldt Berlin, 3-9, July, 2001.

Equivalence of the heat kernel measure and the pinned Wiener measure on loop group, International conference of Stochastic Analysis and Mathematical Physics, University of Lisbon, 25-30, October, 2000.

Existence and uniqueness of geodesics on path spaces, International conference on Analysis on Path Space and Related Topics, University of Warwick, 22-29, July, 2000.

Sobolev spaces and capacities on path spaces, International conference in Probability and Geometry, University Nancy I, 19-25, September 1999.