Combinatorics and Physics: the use of heaps of pieces
Prof. Xavier Viennot
CNRS, Bordeaux, France.
The relation between combinatorics and theoretical physics has been particularily active and fruitful in the last few years. It is classical to relate statistical physics and algebraic graph theory.
I will present more recent and less classical interactions, mostly based on the use of the notion of "heaps of pieces", giving a "geometric" and combinatorial interpretation of the algebraic notion of commutation classes of words of the so-called Cartier-Foata monoids (called trace monoids in theoretical computer science).
The combinatorial tour in this domain will include topics like directed animals, Baxter hard hexagons model, solid-on-solid model, and the so-called 2D lorentzian triangulations in quantum gravity.