This project focusses on two problems in matroid theory. The first is to show that the size functions of minor-closed classes of matroids are either infinite, exponential, or polynomial. The second is to show that the size function of a minor-closed class C is bounded by a linear function if and only if there is a finite upper bound on the critical exponent of matroids in C. Matroid theory is a natural generalization of graph theory and projective geometry, and thus ocupies a central place in combinatorial theory.
