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Abdelmalek Abdesselam, Research Page


Areas of interest :

I am a mathematical physicist working on:

  • Constructive quantum field theory.
  • Rigorous renormalization group methods.
  • Mathematical statistical mechanics.
  • Combinatorics related to Feynman diagrams and cluster expansions.
  • Classical invariant theory, and applications of the classical symbolic method to problems in algebraic geometry and representation theory.

    • Publications and Preprints


    Editorial activities :

    Annales Henri Poincaré.

    Journal of Mathematical Physics, (2013-2015).

    Annales de l'Institut Henri Poincaré D, Combinatorics, Physics and their Interactions.


    Membership in professional societies:

    International Association of Mathematical Physics .

    Americal Mathematical Society.


    Co-organizer for the workshop "Recent Mathematical Developments in Quantum Field Theory", July 24-30 2016, held in Oberwolfach, Germany.

    Co-organizer for the thematic program "Combinatorics, geometry and physics", June 2-July 31 2014, held at the Erwin Schrödinger International Institute for Mathematical Physics, Vienna.

    Organizer for the workshop "Harmonic Analysis and the Renormalization Group" held at the University of Virginia, April 18-21 2014.

    Co-organizer for the conference "Recent Mathematical Advances in Classical, Quantum, and Statistical Mechanics" held at the University of Virginia, March 8-9 2013, on the occasion of the retirement of Larry Thomas.

    Co-organizer for the Quantum Field Theory Session at the XVIIth International Congress on Mathematical Physics held in Aalborg, Denmark, August 6-11 2012.

    April 2008 Cambridge conference I co-organized : Combinatorial Identities and Their Applications in Statistical Mechanics.

    Some links and references on forest and tree formulae in constructive field theory.


    Slides of talks :

    - A. A., "Exploring conformal invariance with hierarchical models", slides of talk at the Analysis, Quantum Fields, and Probability seminar, October 2021. Video of the talk.

    - A. A., "Pointwise multiplication of random Schwartz distributions with Wilson's operator product expansion", slides of talk at the conference "Quantum field theory, renormalisation and stochastic partial differential equations", Cambridge, UK, October 2018.

    - A. A., "A proof of Wilson's epsilon expansion for a toy model of three-dimensional conformal field theory", slides of talk at the Probability Seminar of Columbia University, New York, Sep 8 2017.

    - A. A., "On a Toy Model for Three-Dimensional Conformal Probability", slides of short talk at the Seminar on Stochastic Processes 2017, Charlottesville, March 8, 2017.

    - A. A., "A Toy Model for Three-Dimensional Conformal Probability", slides of Colloquium talk at the University of Maryland given on Feb 1 2017, College Park MD, USA.

    - A. A., "Vers une théorie probabiliste des champs conformes en dimension trois", slides of Colloquium talk at the University of Lyon 1 given on Jan 18 2016, Lyon, France.

    - A. A., "Towards three-dimensional conformal probability", slides of talk given at the conference "Constructive Field Theory: from Condensed Matter to Quantum Gravity. A conference in honor of Vincent Rivasseau", Paris, France, November 2015.

    - A. A., "Proof of a 43-year-old prediction by Wilson on anomalous scaling for a hierarchical composite field ", slides of talk given at the conference "Constructive Renormalization Group: A Conference in Memory of Pierluigi Falco", Roma, Italy, June 2015.

    - A. A., "On the ground state energy for massless Nelson models", slides of talk given at the conference "QMath11 Mathematical Results in Quantum Physics", Hradec Kralove, Czech Republic, September 2010.

    - 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.

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