University of Delaware
Discrete Mathematics Seminar

Applications of pencils of conics
Keith Mellinger
University of Mary Washington
Tuesday, May 1, 2012
Ewing Hall 336 5.00 - 6.00 pm

ABSTRACT: In recent years I have been interested in how conics in the classical projective plane PG(2,q) can be used to construct interesting geometric objects. This talk will survey some of my work in this area. The first application is to semiovals where I will briefly describe the notion of a pencil of conics and some previous work that can be used to construct large semiovals. Interestingly, the pencil ideas translate very nicely to other geometric constructions. We examine objects called anti-blocking sets as well as the construction of special conic pairs that can be lifted to caps in higher dimensional spaces. All of these ideas employ a common technique which we will describe. My collaborators range from an undergraduate student, an unemployed ex-fed, and another overworked/underpaid college professor.