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Abdelmalek Abdesselam, Publications and Preprints


Preprints :

- A. A., B. Heim, and M. Neuhauser, "On a mod 3 property of ℓ-tuples of pairwise commuting permutations", arXiv:2403.01441[math.CO].

- A. A., and A. Thomas, "Structure constants for simple Lie algebras from principal sl2-triple", arXiv:2309.08213[math.RT].

- A. A., "Log-concavity with respect to the number of orbits for infinite tuples of commuting permutations", arXiv:2309.07358[math.CO].

- A. A., "Non-Abelian correlation inequalities and stable determinantal polynomials", arXiv:2207.07603[math-ph].

- A. A., G. W. Anderson, and A. R. Miller, "Tridiagonalized GUE matrices are a matrix model for labeled mobiles", arXiv:1404.7415[math.PR].

- A. A., A. Chandra, and G. Guadagni, "Rigorous quantum field theory functional integrals over the p-adics I: anomalous dimensions", arXiv:1302.5971[math.PR].

- A. A., A. Chandra, and G. Guadagni, "Rigorous quantum field theory functional integrals over the p-adics: research announcement", arXiv:1210.7717[math.PR].

- A. A., and G. W. Anderson, "Counting colored planar maps free-probabilistically", arXiv:1203.3185v2[math.PR].

- A. A., and D. C. Brydges, "Cramer's rule and loop ensembles", preliminary version, Oct 2006, (.pdf) . This is a review of a result of G. X. Viennot which we think is important for statistical mechanics.


Published articles :

  1. A. A., P. Brunialti, T. Doan, and P. Velie, "A bijection for tuples of commuting permutations and a log-concavity conjecture". Res. Number Theory 10 (2024), no. 2, 45. Preprint version. Published version.

  2. A. A., "A local injective proof of log-concavity for increasing spanning forests". Discrete Math. 346 (2023), no. 12, Paper No. 113651. Preprint version. Published version.

  3. A. A., "QFT, RG, and all that, for mathematicians". In: "Advances in Non-Archimedean Analysis and Applications, The p-adic Methodology in STEAM-H", Eds.: W. A. Zuniga-Galindo and Bourama Toni, pp. 167--183, Springer, 2021. Preprint version. Published version.

  4. A. A., "A second-quantized Kolmogorov-Chentsov Theorem via the operator product expansion", Comm. Math. Phys. 376 (2020), no. 1, 555--608. Preprint version. Published version.

  5. A. A., "An algebraic independence result related to a conjecture of Dixmier on binary form invariants", Res. Math. Sci. 6 (2019), no. 3, Paper No. 26, 17 pp. Preprint version. Published version.

  6. A. A., "The weakly dependent strong law of large numbers revisited", Grad. J. Math. 3 (2018), no. 2, 94--97. Preprint version. Published version.

  7. A. A., "Towards three-dimensional conformal probability", p-Adic Numbers Ultrametric Anal. Appl. 10 (2018), no. 4, 233--252. Preprint version. Published version.

  8. A. A., and J. Chipalkatti, "On the reconstruction problem for Pascal lines", Discrete Comput. Geom. 60 (2018), no. 2, 381--405. Preprint version. Published version.

  9. A. A., C. Ikenmeyer, and G. Royle, "16,051 formulas for Ottaviani's invariant of cubic threefolds", J. Algebra (Computational Algebra) 447 (2016), 649--663. Preprint version. Published version.

  10. A. A., and J. Chipalkatti, "On Hilbert covariants". Canadian J. Math. 66 (2014), no 1, 3--30. Preprint version. Published version.

  11. A. A., and J. Chipalkatti, "Quadratic involutions on binary forms". Michigan Math. J. 61 (2012), no. 2, 279--296. Preprint version. Published version.

  12. A. A., "On the volume conjecture for classical spin networks". J. Knot Theory Ramifications 21 (2012), no. 3, 1250022 (62 pages). Preprint version. Published version.

  13. A. A., and D. Hasler, "Analyticity of the ground state energy for massless Nelson models". Comm. Math. Phys. 310 (2012), no. 2, 511--536. Preprint version. Published version.

  14. A. A., "A massless quantum field theory over the p-adics", contribution to the Oberwolfach Report or the 2011 meeting "The Renormalization Group" organized by: M. Disertori, J. Feldman and M. Salmhofer. Oberwolfach Rep. 8 (2011), no. 1, pp. 785--788. Published version. Oberwolfach version. Preprint version.

  15. A. A., "The ground state energy of the massless spin-Boson model". Ann. Henri Poincaré 12 (2011), no. 7, 1321--1347. Preprint version. Published version.

  16. A. A., "Renormalization group trajectories between two fixed points". In: "XVIth International Congress on Mathematical Physics, Prague, Czech Republic, 3 -- 8 August 2009", Ed.: Pavel Exner, 346--351, World Scientific, Singapore, 2010. Preprint version. Published version.

  17. A. A., and J. Chipalkatti, "The Higher Transvectants are Redundant". Ann. Inst. Fourier (Grenoble) 59 (2009), no. 5, 1671--1713. Preprint version . Published version.

  18. A. A., A. Procacci, and B. Scoppola, "Clustering bounds on n-point correlations for unbounded spin systems". J. Stat. Phys. 136 (2009), no. 3, 405--452. Preprint version . Published version.

  19. A. A., and J. Chipalkatti, "On the Linear Combinants of a Binary Pencil". Glasgow Math. J. 51 (2009), no. 3, 481--498. Preprint version . Published version.

  20. A. A., "A complete renormalization group trajectory between two fixed points". Comm. Math. Phys. 276 (2007), no. 3, 727--772. Preprint version . Published version.

  21. A. A., "Towards a complete renormalization group trajectory between two fixed points", contribution to the Oberwolfach Report for the 2006 meeting "The Rigorous Renormalization Group" organized by: C. Kopper, V. Rivasseau and M. Salmhofer. Oberwolfach Rep. 3 (2006), no. 2, 1061--1063. Published version. Oberwolfach version.

  22. A. A., Short appendix for the article "On the Jacobian ideal of the binary discriminant" by C. D'Andrea and J. Chipalkatti. Collect. Math. 58 (2007), no. 2, 155--180. Preprint version . Published version.

  23. A. A., and J. Chipalkatti, "On the Wronskian combinants of binary forms". J. Pure Appl. Algebra 210 (2007), no. 1, 43--61. Preprint version . Published version.

  24. A. A., and J. Chipalkatti, "Brill-Gordan Loci, transvectants and an analogue of the Foulkes conjecture". Adv. Math. 208 (2007), no. 2, 491--520. Preprint version . Published version.

  25. A. A., and J. Chipalkatti, "The bipartite Brill-Gordan locus and angular momentum". Transform. Groups 11 (2006), no. 3, 341--370. Preprint version . Published version.

  26. A. A., "A computational solution to a question by Beauville on the invariants of the binary quintic". J. Algebra 303 (2006), no. 2 (Computational Algebra), 771--788. Preprint version . Published version.

  27. A. A., "The Grassmann-Berezin calculus and theorems of the matrix-tree type". Adv. in Appl. Math. 33 (2004), no. 1, 51--70. Preprint version . Published version.

  28. A. A., "Feynman diagrams in algebraic combinatorics". Sém. Lothar. Combin. 49 (2002/04), Art. B49c, 45 pp. (electronic). Preprint version . Published version.

  29. A. A., "A physicist's proof of the Lagrange-Good multivariable inversion formula". J. Phys. A 36 (2003), no. 36, 9471--9477. Preprint version . Published version.

  30. A. A., "The Jacobian conjecture as a problem of perturbative quantum field theory". Ann. Henri Poincaré (2003), no. 2, 199--215. Preprint version . Published version.

  31. A. A., J. Magnen, and V. Rivasseau, "Bosonic monocluster expansion". Comm. Math. Phys. 229 (2002), no. 2, 183--207. Preprint version . Published version.

  32. A. A., and V. Rivasseau, "Explicit Fermionic tree expansions". Lett. Math. Phys. 44 (1998), no. 1, 77--88. Preprint version . Published version.

  33. A. A., and V. Rivasseau, "An explicit large versus small field multiscale cluster expansion". Rev. Math. Phys. 9 (1997), no. 2, 123--199. Preprint version . Published version.

  34. A. A., and V. Rivasseau, "Trees, forests and jungles: a botanical garden for cluster expansions". Constructive physics (Palaiseau, 1994), 7--36, Lecture Notes in Phys., 446, Springer, Berlin, 1995. Preprint version . Published version.


Other:

- A. A., P. Blanchard, J. Feldman, A. Jaffe, J. Jona-Lasinio, C. Kopper, J. Magnen, and V. Rivasseau, "Roland Sénéor". International Association of Mathematical Physics News Bulletin, July 2016.

Ph.D. Thesis :

"Explicit constructive renormalization" june 1997, (in French). Chapter I has a quick introduction to BPHZ renormalization from a mathematical standpoint. The papers in Chapters II and III which have been published since, have been removed (see hep-th/9409094 for the preprint version of the paper in Chapter II and hep-th/9605094 for that in Chapter III). Chapter IV presents a nonperturbative analog of Zimmermann's forest formula.

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