Analytic Torsion Forms and Eta Forms
Formes de torsion analytique et familles de submersions,I. Bull. Soc. Math. France 127 (1999), 541-621 [pdf],II. Asian J. Math. 4 (2000), 633-667 [pdf],announced in C. R. Acad. Sci. Paris Série I 324 (1997), 205-210.Submersions and equivariant Quillen metrics [pdf]Ann. Inst. Fourier (Grenoble) 50 (2000), 1539-1588.Flat vector bundles and analytic torsion forms [pdf],Séminaire de Théorie Spectrale et Géométrie, Vol. 19, Univ. Grenoble I, Saint, 2001, 25-40.Functoriality of real analytic torsion forms [pdf],Israel J. Math. 131 (2002), 1-50.With J.-M. BismutHolomorphic immersions and equivariant torsion forms [pdf],J. Reine Angew. Math. 575 (2004), 189-235.announced in C. R. Math. Acad. Sci. Paris 334 (2002), 893-897.With J. BrüningAn anomaly formula for Ray-Singer metrics on manifolds with boundary [pdf],Geom. Funct. Anal. 16 (2006), 767-837.announced in C. R. Math. Acad. Sci. Paris 335 (2002), 603-608.Formes de torsion analytique et fibrations singulières [pdf],Nonlinear hyperbolic equations, spectral theory, and wavelet transformations,Oper. Theory Adv. Appl., vol. 145, Birkhäuser, Basel (2003), 395-418.With U. BunkeIndex and secondary index theory for flat bundles with duality [pdf],Aspects of boundary problems in analysis and geometry, Oper. Theory Adv. Appl., vol. 151, Birkhäuser, Basel (2004), 265-341.Orbifolds and analytic torsions [pdf],Trans. Amer. Math. Soc. 357 (2005), 2205--2233.With H. FengTransversal holomorphic section and localization of analytic torsions [pdf],Pacific J. Math. 219 (2005), 255-271.With W. ZhangEta-invariants, torsion forms and flat vector bundles [pdf],Math. Annalen. 340 (2008), 569-624. With W. ZhangEta-invariant and flat vector bundles [pdf],Chinese Ann. Math. Ser. B. 27 (2006), 67-72. With W. ZhangAn anomaly formula for L^2-analytic torsions on manifolds with boundary [pdf], Analysis, Geometry and Topology of Elliptic Operators:Papers in Honor of Krzysztof P Wojciechowski. Eds. B. Booss-Bavnbek, S. Klimek, M. Lesch and W. Zhang, World Scientific (2006), 235--262.With W. ZhangEta-invariant and flat vector bundles II [pdf], Inspired by S. S. Chern. Ed. P. A. Griffiths, Nankai Tracts in Mathematics. Vol. 11. World Scientific, 2006, 335-350.With J. BrüningOn the gluing formula for the analytic torsion [pdf],Math. Z. 273 (2013), 1085-1117.With J.-M. Bismut and W. ZhangAsymptotic torsion and Toeplitz operators [pdf],Journal of the Institute of Mathematics of Jussieu 16 (2017), 223-349.announced in Opérateurs de Toeplitz et torsion analytique asymptotique [pdf],C. R. Math. Acad. Sci. Paris 349 (2011), 977-981.With B. Liu Differential K-theory, $/eta$-invariant and localization [pdf],C. R. Math. Acad. Sci. Paris 357 (2019), 803-813.Remarks on the equivariant analytic torsion forms and the immersion formula [pdf], Proceedings of the London Mathematical Society 122 (2021), 425-431. Appendix of 'an arithmetic Lefschetz–Riemann–Roch theorem, by Shun Tang, 377-433, 2021.With B. Liu Comparison of two equivariant eta-forms [pdf],Adv. Math. 404 (2022), Paper No. 108163. 76pp.With B. LiuDifferential K-theory and localization formula for $/eta$-invariants [pdf], Invent. Math. 222 (2020), 545--613.Orbifold submersion and analytic torsions [pdf],Arithmetic L-functions and differential geometric methods, 141-177, Progr. Math., 338, Birkhäuser/Springer, 2021. Quillen metrics and branched coverings [pdf], International Mathematics Research Notices. (2024), 6606-6631.Elliptic Genera
With K. LiuOn family rigidity theorems. I [pdf],Duke Math. J. 102 (2000), 451-474.With K. LiuOn family rigidity theorems for Spin^c manifolds [pdf],Mirror symmetry, IV (Montreal, QC, 2000), AMS/IP Stud. Adv. Math. vol. 33,Amer. Math. Soc., Providence, RI (2002), 343-360.With K. Liu and W. ZhangRigidity and vanishing theorems in K-theory [pdf],Comm. Anal. Geom. 11 (2003), 121-180.announced in C. R. Acad. Sci. Paris Série I 330 (2000), 301-305.With K. Liu and W. ZhangSpin^c manifolds and rigidity theorems in K-theory [pdf],Asian J. Math. 4 (2000), 933-959.With K. Liu and W. ZhangOn elliptic genera and foliations [pdf],Math. Res. Lett. 8 (2001), 361-376.With C. Dong and K. LiuOn orbifold elliptic genus [pdf],Orbifolds in mathematics and physics (Madison, WI, 2001),Contemp. Math., vol. 310, Amer. Math. Soc., Providence, RI (2002), 87-105.With C. Dong and K. LiuElliptic genus and vertex operator algebras [pdf],Pure and Applied Mathematics Quarterly. 1 (2005), 791-815.With C. Dong, K. Liu and J. ZhouK-theory associated to vertex operator algebras [pdf],Math. Res. Lett. 11 (2004), 629-647.Bergman Kernels and Geometric quantization
With G. MarinescuThe Spin^c Dirac operator on high tensor powers of a line bundle [pdf],Math. Z. 240 (2002), 651-664.With X. Dai and K. LiuOn the asymptotic expansion of Bergman kernel [pdf],J. Differential Geom. 72 (2006), 1-41. announced in C. R. Math. Acad. Sci. Paris 339 (2004), 193-198.With G. MarinescuGeneralized Bergman kernels on symplectic manifolds [pdf],Adv. Math. 217 (2008), 1756-1815.announced in C. R. Math. Acad. Sci. Paris 339 (2004), 493-498.With G. MarinescuToeplitz operators on symplectic manifolds, [pdf], J. Geom. Anal. 18 (2008), 565-611.With G. MarinescuThe first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator [pdf], Internat. J. Math. 17 (2006), 737--759. With W. ZhangBergman kernels and symplectic reduction [pdf],Astérisque 318 (2008), 154 pp.announced in C. R. Math. Acad. Sci. Paris 341 (2005), 297-302.With W. ZhangToeplitz quantization and symplectic reduction [pdf],Differential Geometry and Physics. Eds. M.-L. Ge and W. Zhang, Nankai Tracts in Mathematics Vol. 10, World Scientific, 2006, 343-349.With K. LiuA remark on 'Some numerical results in complex differential geometry' [pdf].Math. Res. Lett. 14 (2007), 165-171.With W. ZhangSuperconnection and family Bergman kernels [pdf],announced in C. R. Math. Acad. Sci. Paris 344 (2007), 41-44.Math. Annalen. 386 (2023), 2207-2253.With K. LiuAsymptotic of the operators Q_k [pdf], Appendix to "Calabi flow and projective embeddings" by J. Fine, J. Differential Geom. 84 (2010), 489-523.With W. ZhangGeometric quantization for proper moment maps: the Vergne conjecture [pdf], Acta Mathematica 212 (2014), 11-57.announced in Geometric quantization for proper moment maps [pdf],C. R. Math. Acad. Sci. Paris 247 (2009), 389-394.With W. ZhangTransversal index and $L^2$-index for manifolds with boundary [pdf],Metric and Differential Geometry, a volume in honor of Jeff Cheeger for his 65th birthday. Edited by X. Dai and X. Rong. Progress in Mathematics 297, Birkhäuser Boston, Inc., Boston, MA. 2012, 299-316.With G. MarinescuBerezin-Toeplitz quantization of Kahler manifolds [pdf], J. Reine Angew. Math. 662 (2012), 1-58.Geometric quantization on Kahler and symplectic manifolds [pdf], Proceedings of the International Congress of Mathematicians.Volume II, 785--810, Hindustan Book Agency, New Delhi, 2010.With G. MarinescuBerezin-Toeplitz quantization and its kernel expansion [pdf], the Proceedings of GEOQUANT school 2009 (Luxembourg).Travaux mathématiques 19 (2011), 125-166.With X. Dai and K. LiuA remark on weighted Bergman kernels on orbifolds [pdf],Math. Res. Lett. 19 (2012), 143-148.With G. MarinescuRemark on the off-diagonal expansion of the Bergman kernel on compact Kahler manifolds [pdf],Communications in Mathematics and Statistics. 1 (2013), 37-41. With J. DanielCharacteristic Laplacian in sub-Riemannian geometry [pdf]. International Mathematics Research Notices. 24 (2015), 13290-13323.With T. Barron, G. Marinescu and M. PinsonnaultSemi-classical properties of Berezin--Toeplitz operators with C^k symbol [pdf],Journal of Mathematical Physics 55 (2014), no.4, 042108, 25pp. With G. MarinescuExponential Estimate for the asymptotics of Bergman kernels [pdf],Math. Annalen. 362 (2015), 1327-1347.With G. Marinescu and S. ZelditchScaling asymptotics of heat kernels of line bundles [pdf],Contemp. Math. 644 (2015), 275-202, volume in honor of Phong for his 60th birthday (Paul Feehand, ed.).With Tien-Cuong Dinh and G. MarinescuEquidistribution and convergence speed of zeros of holomorphic sections of singular Hermitian line bundles [pdf],Journal of Functional Analysis 271 (2016), no.11, 3082-3110.With D. Coman and G. MarinescuEquidistribution for sequences of line bundles on normal Kahler spaces [pdf],Geom. Topol. 21 (2017), 923-962.With Tien-Cuong Dinh and Viet-Anh Nguyen,Equidistribution speed for Fekete points associated with an ample line bundle [pdf],Ann. Sci. Ec. Norm. Super. (4) 50 (2017), 545-578.With Semyon Klevtsov, G. Marinescu and Paul WiegmannQuantum Hall effect and Quillen metric [pdf]Comm. Math. Phys. 349, (2017), 819-855.With Tien-Cuong Dinh and Viet-Anh Nguyen,On the asymptotic behavior of Bergman kernels for positive line bundles [pdf]Pacific Journal of Math. 289 (2017), 71-89.With W. Lu and G. MarinescuDonaldson's $Q$-operators for symplectic manifolds [pdf] SCIENCE CHINA Mathematics. 60 (2017), 1047-1056.With H. Auvray and G. MarinescuBergman kernels on punctured Riemann surfaces [pdf] Math. Annalen announced in C. R. Math. Acad. Sci. Paris 354 (2016),1018-1022[pdf].With Y. Kordyukov and G. Marinescu Generalized Bergman kernels on symplectic manifoldsof bounded geometry[pdf] Comm. Partial Differential Equations. 44 (2019), 1037--1071.With W. Lu and G. MarinescuOptimal convergence speed of Bergman metrics on symplectic manifolds [pdf] Journal of Symplectic Geometry. 18 (2020), 1091--1126.With L. Ioos, W. Lu and G. Marinescu Berezin-Toeplitz quantization for eigenstatesof the Bochner-Laplacian on symplectic manifolds [pdf] arXiv:1703.06420, J. Geom. Anal. 30 (2020), 2615--2646.With Chin-Yu Hsiao and G. Marinescu Geometric quantization on CR manifolds [pdf] Commun. Contemp. Math. 25 (2023), Paper No. 2250074, 73pp.From local index theory to Bergman kernel: a heat kernel approach [pdf] Progress in Mathematics, Vol. 333 (2020), 265-286.Quantization Commutes with Reduction, a Survey [pdf] Acta Math. Sci. Ser. B (Engl. Ed.), 41 (2021), 1859-1872.Remarks on the equivariant analytic torsion forms and the immersion formula [pdf] Proceedings of the London Mathematical Society 425-431. Appendix of 'an arithmetic Lefschetz-Riemann-Roch theorem', by Shun Tang, 122 (2021), 377-433.With H. Auvray and G. MarinescuQuotient of Bergman kernels on punctured Riemann surfaces [pdf] Math. Z. 301 (2022), 2339-2367.With D. Coman, W. Lu and G. MarinescuBergman kernels and equidistribution for sequences of line bundles on Kahler manifolds [pdf], Adv. Math. 414 (2023), Paper No. 108854, 34ppTalks
Séminaire Bourbaki, Exp. No. 1130, 11 mars 2017: Geometric hypoelliptic Laplacian and orbital integrals, [after Bismut, Lebeau and Shen] [pdf]Astérisque 407 (2019), 333-389.Books
With G. MarinescuHolomorphic Morse inequalities and Bergman kernels,Progress in Mathematics 254, Birkhäuser Boston, Inc., Boston, MA. 2007, 422 pp.Award winning monograph of the 2006 Ferran Sunyer i Balaguer Prize.With W. ZhangBergman kernels and symplectic reduction[pdf],Astérisque 318 (2008), 154 pp.Editor with X. Dai, R. Léandre and W. Zhang From Probability to Geometry (I),Volume in honor of the 60th birthday of Jean-Michel Bismut.Astérisque 327 (2009), xxxvii+424 pp.Editor with X. Dai, R. Léandre and W. Zhang From Probability to Geometry (II),Volume in honor of the 60th birthday of Jean-Michel Bismut.Astérisque 328 (2009), x+393 pp.Editor with Jean-Benoit Bost, Helmut Hofer, Francois Labourie, Yves Le Jan, Weiping Zhang,Geometry, analysis and probability-in honor of Jean-Michel Bismut, Progress in Mathematics 310,Birkhäuser Boston, Inc., Boston, MA. 2017, 365 pp.Translation to chinese
With Y.Yao Opérateurs pseudo-différentiels et théorème de Nash-Moser(English: Pseudo-differential Operators and the Nash-Moser Theorem)(Chinese version)by Serge Alinhac and Patrick GérardMémoire
Théorie de l'indice local et applications [pdf],Habilitation à diriger des recherches, Paris-Sud, le 25 mai, 2005.
Last modified: 16/11/2005
