Laboratoire de mathématiques d'Orsay

Team Analyse Harmonique

Martin Puchol

Research Interests

I work differential geometry, and in particular complex and Kälerian geometry, as well as on local index theory, analysis on manifolds and quantization. The central objects in my work are the Laplacian, the heat kernel and the Bergman kernel.

Documents

Some mathematical documents that I wrote:

• Matser thesis (french), Une démonstration analytique de la conjecture de Guillemin-Sternberg. Pdf file
• PhD. Thesis, inégalités de Morse holomorphes G-invariantes et formes de torsion asymptotiques (G-invariant holomorphique Morse inequalities and asymptotic torsion forms). Pdf file
• Talk during the conference Index theory and Singular Structures (Mai 2017, Toulouse, France)
  Title : The asymptotics of the holomorphic torsion forms Pdf file
• Talk during the conference Geometric quantization and applications (April 2018, Banff, Canada)
  Title : G-invariant holomorphic Morse inequalities Pdf file
• Talk during the Conference on Index Theory and Related Topics (August 2021, Singapour)
  Title : A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion Pdf file

Publications

• With Yeping Zhang and Jialin Zhu : Scattering matrices and analytic torsions. Anal. PDE 14 (2021), no. 1, 77–134. DOI: 10.2140/apde.2021.14.77 Fichier pdf
  Announced in: C. R. Math. Acad. Sci. Paris 355 (2017), no. 10, 1089–1093. DOI: 10.1016/j.crma.2017.09.018 Fichier pdf
• With Thomas Letendre, Variance of the volume of random real algebraic submanifolds II. Indiana Univ. Math. J. 68 (2019), no. 6, 1649–1720. DOI: 10.1512/iumj.2019.68.7830 Fichier pdf
• Holomorphic Morse inequalities for orbifolds. Math. Z. 289 (2018), no. 3-4, 1237–1260. DOI: 10.1007/s00209-017-1996-7. Fichier pdf
• G-invariant holomorphic Morse inequalites.  J. Differential Geom. 106(3): 507-558, 2017. DOI: 10.4310/jdg/1500084025. Fichier pdf
  Announced in: C. R. Math. Acad. Sci. Paris 354 (2016), no. 5, 526–531. DOI: 10.1016/j.crma.2015.12.010. Fichier pdf

• The asymptotics of the holomorphic analytic torsion forms. J. London Math. Soc. to appear. Fichier pdf
  Announced in: C. R. Math. Acad. Sci. Paris 354 (2016), no. 3, 301–306. DOI: 10.1016/j.crma.2015.11.004. Fichier pdf
• Avec J. Zhu, The first terms in the expansion of the Bergman kernel in higher degrees. Pacific J. Math. 274 (2015), no. 2, 373–403. DOI 10.2140/pjm.2015.274.373. Fichier pdf

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