## 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
Differential K-theory, $\eta$-invariant and localization [pdf],
C. R. Math. Acad. Sci. Paris 357 (2019), 803--813.

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],
Invent. Math. 222 (2020), 545--613.

Orbifold submersion and analytic torsions [pdf], 33pp.

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],
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 mathématiques 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 W. Lu and G. Marinescu
Donaldson's $Q$-operators for symplectic manifolds[pdf]
SCIENCE CHINA Mathematics.  60 (2017), 1047-1056.

With H. Auvray and G. Marinescu
Bergman 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 manifolds
of bounded geometry[pdf]
Comm. Partial Differential Equations. 44 (2019), 1037--1071.

With W. Lu and G. Marinescu
Optimal 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 eigenstates
of 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]
47pp. arXiv:1906.05627

From local index theory to Bergman kernel: a heat kernel approach,
[pdf]
Progress in Mathematics, Vol. 333 (2020), 265-286.

With H. Auvray and G. Marinescu
Quotient of Bergman kernels on punctured Riemann surfaces [pdf]

Talks
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. 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.