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Honors Thesis Geometric Objects with a More Combinatorial Flavor Submitted by Committee on Undergraduate Honors Work

OF HONORS THESIS GEOMETRIC OBJECTS WITH A MORE COMBINATORIAL FLAVOR We are studying geometric objects, defined over finite fields, with a more combinatorial flavor and present the results of the investigation of classification problems in geometry and combinatorics. Objects called BLT-sets, living in a vector space over a finite field, are of great interest to finite geometry, as they provide access to most of the objects that have been studied for a long time (translation planes, generalized quadrangles, flocks). On the other hand, there are objects that are invariant under a Finite group. An example are the Coxeter groups, which act as symmetry groups of root systems, and have been classified. They turn out as symmetry groups of BLT-sets. Andreea Erciulescu Department of Mathematics Colorado State University Fort Collins, Colorado 80523 Spring 2011