1. Unimodular hunting II (with B. Allombert, in preparation).
-- (29/09/20) We classify the rank 29 unimodular integral lattices without roots: a list of these 10092 lattices.
An associated gp scripts file, including an automatized proof that our list is complete (tutorial).
-- (13/11/20) We classify the rank 28 unimodular integral lattices: there are 374062 such lattices, see this notice.
A full list of lattices with no norm 1 vectors (47.1 MB), and the same list split as explained in the notice:
i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20, i21, i24, i28.
An associated gp scripts file, including an automatized proof that our list is complete (tutorial).

2. (14/07/20) Unimodular hunting (in preparation).
We classify the unimodular integral lattices of rank 26 and 27: a list of these 2566 (in rank 26) and 17059 (in rank 27) lattices.
See also this companion file for a few helpful gp scripts to play with this (PARI/GP readable) list,
including an automatized proof that it is indeed complete (tutorial).


Beware that the published versions may differ from the ones below or from those on arXiv.

30. Statistics for Kneser p-neighbors (pdf, with an appendix by O. Taïbi),
To appear in Bulletin SMF, 46 p.

29. Siegel modular forms of weight 13 and the Leech lattice (with O. Taïbi, pdf),
L'Enseignement Mathématique 68 no 1-2, 61-98 (2022).

28. The characteristic masses of Niemeier lattices (pdf),
Journal de Théorie des Nombres de Bordeaux 32, 545-583 (2020).
A website with more data and the source code of our algorithms.

27. Sur les minima des formes hamiltoniennes binaires définies positives (with F. Paulin, pdf),
Publ. Math. Besançon, Alg. & Th. des Nombres, 5-25 (2020).

26. Discrete series multiplicities for classical groups over Z and level 1 algebraic cusp forms (with O. Taïbi, pdf),
Publ. Math. I.H.É.S. 131, 261-323 (2020),
An associated homepage containing many tables, auxiliary data, and the source code of our algorithms.

25. An automorphic generalization of the Hermite-Minkowski theorem (pdf),
Duke Math. Journal 169, 1039-175 (2020).

24. Une application des variétés de Hecke des groupes unitaires (pdf),
Chapter 10 of the book Shimura Varieties, edited by T. Haines & M. Harris,
London Math. Soc. Lecture Note Series 457, Cambridge, 266-296 (2020).

23. Automorphic forms and even unimodular lattices (with Jean Lannes),
Ergebnisse der Mathematik und ihrer Grenzgebiete 69, Springer Verlag, xxi + 417 pp. (2019).
Some associated PARI programs, and a list of corrections (last update 11/03/2020).

22. Subgroups of Spin(7) or SO(7) with each element conjugate to some element of G_2, and applications to automorphic forms (pdf),
Documenta Math. 24, 95-161 (2019).
(In the final version, 11 examples of compatible systems of l-adic Galois representations of type G_2, over Q and with good reduction everywhere, have been added.)

21. Two appendices (8 p.) in the paper On vector-valued Siegel modular forms of degree 2 and weight (j,2) by Fabien Cléry and Gerard van der Geer (pdf),
Documenta Math. 23, 1129-1156 (2018).

20. Level one algebraic cuspforms of classical groups of small rank (with D. Renard),
Memoirs of the A.M.S. 1121, vol. 237, 128 p. (2015) (pdf)
Some tables relative to this paper are available at: Level one algebraic cuspforms of classical groups.
Some corrections, remarks and updates.

19. The p-adic analytic space of pseudocharacters of a profinite group, and pseudorepresentations over arbitrary rings,
London Math. Soc. Lecture Notes Series 414, Proceedings of the LMS Durham Symposium 2011,
Automorphic forms and Galois representations vol. 1, 221-285 (2014) (pdf).

18. Sous-groupes de GL(2) et arbres (with. J. Bellaïche),
Journal of Algebra 410, 501-525 (2014).

17. Construction of automorphic Galois representations II (with M. Harris),
Cambridge Math. Journal 1, 53-73 (2013) (pdf).

16. Sur la densité des représentations cristallines du groupe de Galois absolu de Q_p,
Math. Annalen 335, 1469-1525 (2013) (pdf).

15. On the infinite fern of Galois representations of unitary type,
Annales Scientifiques de l'E.N.S. 44, 963-1019 (2011) (pdf).

14. The sign of Galois representations attached to automorphic forms for unitary groups (with J. Bellaïche),
Compositio Math. 147, 1337-1352 (2011) (pdf).

13. Représentations potentiellement triangulines de dimension 2 (with L. Berger),
Journal de théorie des nombres de Bordeaux Vol 22 no 3, 557-574 (2010) (pdf).

12. On the vanishing of some non semisimple orbital integrals (with D. Renard),
Expositiones Math. 28, 276-289 (2010) (pdf).

11. Families of Galois representations and Selmer groups (with J. Bellaïche),
Astérisque 324, Soc. Math. France, 314 p. (2009)

10. Corps de nombres peu ramifiés et formes automorphes autoduales (with L. Clozel),
Journal of the A.M.S. 22 Vol 2, 467-519 (2009) (pdf).

9. Characters of Speh representations and Lewis Carroll identity (with D. Renard),
Represent. Theory 12, 447-452 (2008) (pdf).

8. Quelques courbes de Hecke se plongent dans l'espace de Colmez,
Journal of Number Theory 128 no 8, 2430-2449 (2008) (pdf).

7. On number fields with given ramification,
Compositio Mathematica 143 no 6, 1359-1373 (2007) (pdf, short version: pdf).

6. Graphs having no quantum symmetry (with T. Banica and J. Bichon),
Ann. Inst. Fourier 57, 955-971 (2007).

5. Lissité de la courbe de Hecke de GL(2) aux points Eisenstein critiques (with J. Bellaïche),
Journal Inst. Math. Jussieu vol. 5.2, 333-349 (2006) (pdf).

4. Converging sequences of p-adic Galois representations and density theorems (with J. Bellaïche, C. Khare and M. Larsen),
Int. Math. Research Notices 59, 3691-3720 (2005) (pdf).

3. Une correspondance de Jacquet-Langlands p-adique,
Duke Math. Journal 126 no1, 161-194 (2005). ( Erratum ).

2. Formes non tempérées pour U(3) et conjectures de Bloch-Kato (with J.Bellaïche),
Annales scientifiques de l'E.N.S. 37/4, 611-662 (2004) (pdf ).

1. Familles p-adiques de formes automorphes pour GL(n)
Journal fur die reine und angewandte Mathematik 570, 143-217 (2004) (pdf).

Non-refereed publications :

3. Kneser neighbours and orthogonal Galois representations in dimensions 16 and 24 (pdf, avec J. Lannes),
Algebraic Number Theory, Oberwolfach Report 31/2011.

2. The infinite fern of Galois representations of type U(3) (pdf),
Algebraic Number Theory, Oberwolfach Report (2009).

1. On number fields with given ramification,
Algebraic Number Theory, Oberwolfach Rep. 2, No. 2, Report 28, p. 1554 (2005).

Unpublished :

6. Sur un énoncé de la lettre de Galois à Chevalier, (pdf)
NEW (15/02/22) 7 p. in French.

5. On restrictions and extensions of cusp forms, (pdf)

4. Représentations galoisiennes automorphes et conséquences arithmétiques des conjectures de Langlands et Arthur, (pdf, defense)
Habilitation thesis, defended on March 29th, 2013 (Paris XI), 122 p. in French.

3. Déterminants et représentations de dimension 2, (pdf)
(03/2012) Letter to J.-P. Serre, 6 p. in French.

2. Sur la variété des caractères p-adique du groupe de Galois absolu de Q_p (pdf),
Preprint of 2009 that I gave to a few people at the time, and that I intended to complete.
I finally decided to put it on line (2/07/2011).

1. Familles p-adiques de formes automorphes et applications aux conjectures de Bloch-Kato ( pdf , résumé ).
Ph. D. thesis, defended on June 13th, 2003 (Paris VII, under the supervision of M.Harris), 192 p.
The appendix has not been published.

Miscellaneous :

Coauthors (Erdos N.<=4):

- Bill Allombert,
- Teodor Banica,
- Joel Bellaïche (5),
- Laurent Berger,
- Julien Bichon,
- Fabien Cléry,
- Laurent Clozel,
- Gerard van der Geer,
- Michael Harris,
- Chandrashekhar Khare,
- Jean Lannes,
- Michael Larsen,
- Frédéric Paulin,
- David Renard (3),
- Olivier Taïbi (2).

Links to mathscinet , arXiv .