The University of Montana
Mathematical Sciences Colloquium

Extremal questions are studied in many branches of mathematics. For instance, in graph theory we might ask: How many edges can a graph on n vertices contain if it has no subgraph isomorphic to the complete graph K_m? In projective geometry we might ask: How many points can a subset of a projective plane of order q contain if no k of the points are colinear?

Matroid theory is an abstraction of graph theory, projective and affine geometry, and several other branches of mathematics. Questions of the type posed above can be asked about matroids. We will address several such questions and present some intriguing problems and conjectures in this area.

This talk will include enough background on matroid theory, starting with the definition and motivating examples, to be widely accessible.

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