Papers and Preprints of Xiaonan MA

    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. Bismut Holomorphic 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. Brüning An 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. Bunke Index 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. Feng Transversal holomorphic section and localization of analytic torsions [pdf], Pacific J. Math. 219 (2005), 255-271.
  • With W. Zhang Eta-invariants, torsion forms and flat vector bundles [pdf], Math. Annalen. 340 (2008), 569-624.
  • With W. Zhang Eta-invariant and flat vector bundles [pdf], Chinese Ann. Math. Ser. B. 27 (2006), 67-72.
  • With W. Zhang An 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. Zhang Eta-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. Brüning On the gluing formula for the analytic torsion [pdf], Math. Z. 273 (2013), 1085-1117.
  • With J.-M. Bismut and W. Zhang Asymptotic 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 Comparison of two equivariant eta-forms [pdf], 56pp. arXiv:1808.04044
  • With B. Liu Differential K-theory and localization formula for eta-invariants [pdf], 44pp. arXiv:1808.03428

    Elliptic Genera

  • With K. Liu On family rigidity theorems. I [pdf], Duke Math. J. 102 (2000), 451-474.
  • With K. Liu On 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. Zhang Rigidity 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. Zhang Spin^c manifolds and rigidity theorems in K-theory [pdf], Asian J. Math. 4 (2000), 933-959.
  • With K. Liu and W. Zhang On elliptic genera and foliations [pdf], Math. Res. Lett. 8 (2001), 361-376.
  • With C. Dong and K. Liu On 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. Liu Elliptic genus and vertex operator algebras [pdf], Pure and Applied Mathematics Quarterly. 1 (2005), 791-815.
  • With C. Dong, K. Liu and J. Zhou K-theory associated to vertex operator algebras [pdf], Math. Res. Lett. 11 (2004), 629-647.

    Bergman Kernels and Geometric quantization

  • With G. Marinescu The Spin^c Dirac operator on high tensor powers of a line bundle [pdf], Math. Z. 240 (2002), 651-664.
  • With X. Dai and K. Liu On 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. Marinescu Generalized 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. Marinescu Toeplitz operators on symplectic manifolds, [pdf], J. Geom. Anal. 18 (2008), 565-611.
  • With G. Marinescu The 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. Zhang Bergman kernels and symplectic reduction [pdf], Astérisque 318 (2008), 154 pp. announced in C. R. Math. Acad. Sci. Paris 341 (2005), 297-302.
  • With W. Zhang Toeplitz 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. Liu A remark on 'Some numerical results in complex differential geometry' [pdf]. Math. Res. Lett. 14 (2007), 165-171.
  • With W. Zhang Superconnection and family Bergman kernels [pdf], announced in C. R. Math. Acad. Sci. Paris 344 (2007), 41-44.
  • With K. Liu Asymptotic 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. Zhang Geometric 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. Zhang Transversal 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. Marinescu Berezin-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. Marinescu Berezin-Toeplitz quantization and its kernel expansion [pdf], the Proceedings of GEOQUANT school 2009 (Luxembourg). Travaux mathÈmatiques 19 (2011), 125-166.
  • With X. Dai and K. Liu A remark on weighted Bergman kernels on orbifolds [pdf], Math. Res. Lett. 19 (2012), 143-148.
  • With G. Marinescu Remark 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. Daniel Characteristic Laplacian in sub-Riemannian geometry [pdf]. International Mathematics Research Notices. 24 (2015), 13290-13323.
  • With T. Barron, G. Marinescu and M. Pinsonnault Semi-classical properties of Berezin--Toeplitz operators with C^k symbol [pdf], Journal of Mathematical Physics 55 (2014), no.4, 042108, 25pp.
  • With G. Marinescu Exponential Estimate for the asymptotics of Bergman kernels [pdf], Math. Annalen. 362 (2015), 1327-1347.
  • With G. Marinescu and S. Zelditch Scaling 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. Marinescu Equidistribution 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. Marinescu Equidistribution 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 Wiegmann Quantum 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 H. Auvray and G. Marinescu Bergman kernels on punctured Riemann surfaces [pdf] announced in C. R. Math. Acad. Sci. Paris 354 (2016),1018-1022[pdf].
  • With W. Lu and G. Marinescu Optimal convergence speed of Bergman metrics on symplectic manifolds [pdf] arXiv:1702.00974
  • With W. Lu and G. Marinescu Donaldson's $Q$-operators for symplectic manifolds[pdf] SCIENCE CHINA Mathematics. 60 (2017), 1047-1056.
  • With Y. Kordyukov and G. Marinescu Generalized Bergman kernels on symplectic manifolds of bounded geometry, [pdf] 33pp. arXiv:1806.06401

    Talks

    Séminaire Bourbaki - 11 mars 2017: Geometric hypoelliptic Laplacian and orbital integrals, [after Bismut, Lebeau and Shen] [pdf]

    Books

  • With G. Marinescu Holomorphic 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. Zhang Bergman 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 Gérard

    Mémoire

  • Théorie de l'indice local et applications [pdf], Habilitation à diriger des recherches, Paris-Sud, le 25 mai, 2005.

Last modified: 16/11/2005