# Recent Results in Extremal Matroid Theory

### Joseph E. Bonin

### The George Washington University

**Thursday, November 20, 1997**

**4:00-5:00 PM**

**Room 102, Bradley Hall**

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
collinear?

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.