abstracts of the 3 talks in Chennai, February and March 2012  "Quadratic algebras, combinatorial physics and planar automata"   (talk CMI, Chennai, February, 6) abstract: For certain quadratic algebras Q, we introduce the concept of Q-tableaux, which are certain combinatorial objects drawn on the square lattice. These tableaux are equivalent to notion of planar automaton. Planar automata is a new concept (not to be confused with cellular automata) which formalize the idea of recognizing certain "planar figures" drawn on a 2D lattice.  Examples are with two quadratic algebras well known in physics: the most simple Weyl-Heisenberg algebra defined by the commutation relation UD=DU+Id (creation-annihilation operators in quantum mechanics) and the so-called PASEP algebra defined by the relation DE=ED+E+D, in the physics of dynamical systems far from equilibrium. The associated Q-tableaux are respectively towers placements, permutations and the so-called alternating, tree-like and permutation tableaux. Other examples include non-crossing configurations of paths, tiling, plane partitions and alternating sign matrices. "Combinatorial operators and quadratic algebras"   (talk IMSc, Chennai, March 1) abstract: The Robinson-Schensted-Knuth correspondence (RSK) is an ubiquitous bijection between permutations and pairs of Young tableaux having the same shape, and is related to the representation of the symmetric group. First, I will recall briefly the classical ways to define this correspondence: Schensted's insertions, the geometric interpretation, and the "local" rules (or growth diagrams) defined by S.Fomin. This last construction is associated to a "combinatorial" representation of the simple Weyl-Heisenberg algebra defined by the commutation relation UD=DU+Id (creation-annihilation operators in quantum mechanics). I will apply the same "philosophy" to another quadratic algebra coming from the physics of dynamical systems far from equilibrium, i.e. the PASEP algebra defined by the relation DE=ED+E+D. A combinatorial representation is defined in relation with the combinatorial theory of orthogonal polynomials and some background from computer science (operators for data structures). The analogue of the RSK correspondence is a bijection between permutations and certain combinatorial objects called alternative tableaux, giving interpretation of the stationary probabilities of the physics model PASEP. I will finish with some extensions to other quadratic algebras, in relation with hot subjects in physics and combinatorics.  "The combinatorics of some exclusion model in physics"   (talk at IIT Madras, March 2) abstract: The PASEP model (partially asymmetric exclusion process) is a toy model in the dynamics of particles moving in a strip and has been extensively studied by physicists. They gave explicit expressions for the stationary probabilities of the associated Markov chain, in relation with some orthogonal polynomials and some quadratic algebras. More recently, combinatorists gave combinatorial solutions for this model. I will give an introduction to this hot and active subject, which is at the crossroad of physics, probability, algebra, combinatorics and computer science.