- more coming soon
- A. A., "Renormalization group trajectories between two fixed points", arXiv:0910.1063v1 [math-ph], contribution to the proceedings of the XVI International Congress on Mathematical Physics, Prague, August 3-8, 2009.
- A. A., "On the volume conjecture for classical spin networks", arXiv:0904.1734v1 [math.GT].
- 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.
- A. A., "Renormalization group trajectories between two fixed points", slides of invited lecture at the International Congress on Mathematical Physics, Prague, August 2009.
- A. A., "Field theoretic cluster expansions and the Brydges-Kennedy forest sum formula", slides of my April 2008 talk for the conference "Combinatorial Identities and Their Applications in Statistical Mechanics", at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
- A. A., "The combinatorics of classical invariant theory revisited by modern physics", slides of my Feb 2007 talk at the Montreal CRM workshop "Combinatorial Problems Raised by Statistical Mechanics".
- A. A., "On the Hadamard-Foulkes-Howe conjecture and multidimensional resultants", slides of my Sept 2005 talk at the 55th Séminaire Lotharingien de Combinatoire in Bertinoro.
- A. A., "Combinatoire du logarithme et renormalisation en physique", slides of my May 2003 talk at the Journées du LIPN Combinatoire, Informatique er Physique, at Université Paris 13.
- A. A., "Multivariable power series, reversion and Lagrange-Good inversion via quantum field theory", slides of my Oct 2002 talk at the 49th Séminaire Lotharingien de Combinatoire in Ellwangen.
1 - A. A., and J. Chipalkatti, "The Higher Transvectants are Redundant". Ann. Inst. Fourier (Grenoble) 59 (2009), no. 5, 1671--1713. preprint version .
2 - 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 .
3 - A. A., and J. Chipalkatti, "On the Linear Combinants of a Binary Pencil". Glasgow Math. J. 51 (2009), no. 3, 481--498. preprint version .
4 - A. A., "A complete renormalization group trajectory between two fixed points". Comm. Math. Phys. 276 (2007), no. 3, 727--772. preprint version .
5 - 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. (.pdf) .
6 - 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 .
7 - A. A., and J. Chipalkatti, "On the Wronskian combinants of binary forms". J. Pure Appl. Algebra 210 (2007), no. 1, 43--61. preprint version .
8 - 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 .
9 - A. A., and J. Chipalkatti, "The bipartite Brill-Gordan locus and angular momentum". Transform. Groups 11 (2006), no. 3, 341--370. preprint version .
10 - 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 .
11 - 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 .
12 - A. A., "Feynman diagrams in algebraic combinatorics". Sém. Lothar. Combin. 49 (2002/04), Art. B49c, 45 pp. (electronic). preprint version .
13 - A. A., "A physicist's proof of the Lagrange-Good multivariable inversion formula". J. Phys. A 36 (2003), no. 36, 9471--9477. preprint version .
14 - A. A., "The Jacobian conjecture as a problem of perturbative quantum field theory". Ann. Henri Poincaré (2003), no. 2, 199--215. preprint version .
15 - A. A., J. Magnen, and V. Rivasseau, "Bosonic monocluster expansion". Comm. Math. Phys. 229 (2002), no. 2, 183--207. preprint version .
16 - A. A., and V. Rivasseau, "Explicit Fermionic tree expansions". Lett. Math. Phys. 44 (1998), no. 1, 77--88. preprint version .
17 - 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 .
18 - 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 .
"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.