MathematicsSeminar 
Rocky Mountain Algebraic Combinatorics Seminar
Hyperovals, Cyclotomic Sets, and their relations in AG(2,$q$)
Philip DeOrsey
University of Colorado, Denver
In a projective plane of order q=2^{e}, a hyperoval is a maximal set of
points no three of which are collinear. The search for, and classification
of, hyperovals has been an active research area for many years. The most
common way to represent hyperovals is with an opolynomial in PG(2,q).
We will discuss a new representation of hyperovals in AG(2,q), when the
points of AG(2,q) are viewed as elements of GF(q^{2}). We call this
representation a ρpolynomial.
Due to the structure of ρpolynomials we can show that the range can be
partitioned into cyclotomic sets of the form

Strongly regular graphs from large arcs in affine planes
Tim Penttila
Colorado State University
Tits constructed generalized quadrangles from ovals in Desarguesian projective planes in 1968; AhrensSzekeres and Hall constructed generalized quadrangles from hyperovals in Desarguesian planes in 1969 and 1971. Payne constructed generalized quadrangles from qarcs in Desarguesian planes of order q in 1972 and 1985. All of these generalized quadrangles have strongly regular concurrency graphs. Without the hypothesis that the planes be Desarguesian, we construct graphs with the same parameters.
This is joint work with Elizabeth LaneHarvard and Stanley E. Payne.
Weber 223
4–6 pm
Friday, May 9, 2014
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University
This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.
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