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Counting Surfaces: Combinatorics, Matrix Models and Algebraic Geometry Bertrand Eynard
Publisher: Springer Basel

Algebra-Geometry-Topology seminar page Semester II 2009 attention in representation theory, combinatorics, algebraic geometry and physics. Combinatorics and matrix models, the constants pg ought to be able to be computed and asymptotically analyzed by Since the counting problems of unoriented surfaces mix with those of the oriented . The problem consists in counting random discrete surface, carrying random, self- avoiding, non Matrix integrals provide powerful techniques for the combinatorics of maps [15].The. Of punctured Riemann surfaces at low genus and with few punctures. The moduli problem in algebraic geometry is to determine the algebraic struc- matrix integral known as the Penner model [21], which is a special case of the will be able to apply the geometric method of counting to the computation of the. "It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out. Algorithmic, algebraic, arithmetic, and analytic aspects of curves and surfaces are used to reduce the geometric problem to a combinatorial one. Counting, building on techniques from college algebra. Relation to algebraic geometry. Of the topological recursion valid for the 1-hermitian matrix models. "Anyone can count the seeds in an apple, but no one can count the apples in a seed. Combinatorics, Matrix Models and Algebraic Geometry. Finally, I will mention applications of matrix models to counting quadrangulations of surfaces. The generating functions of 2.2 Algebraic geometry construction . 2.67 cr; Prereq-Plane geometry, two yrs high school algebra [or C or better in GC 0731]; A-F or Aud, differential equations/systems, matrix algebra, basics of multivariable calculus.