(Algebraic Geometry, Algebra and Number Theory Seminar)

Date/Time/Room: Friday Dec 6, 2002, at 3:30 pm in PKH 487 at UTA
                                  Refreshments will probably be served.

Speaker: Michael Williams, Ph.D., Raytheon

``Characteristic-2 Orthogonal Geometries, Symplectic Spreads, And Non-Associative Division Algebras''

Abstract: Finite fields of characteristic 2 provide a framework for the construction and study of exponential numbers of non-isomorphic orthogonal and symplectic geometries. We will discuss the up and down process used to generate orthogonal geometries, symplectic spreads, and semifield planes. The non-associative division algebras are intimately related to the geometries and are used to prove inequivalence. The up and down construction also provides the machinery to generate exponential numbers of boring translation planes. Motivation for the study of the non-associative division algebras has coding-theoretic roots. The application to binary Kerdock codes and to Z(4)-linear Kerdock codes will briefly be discussed.


  If you are travelling from out of town, then a map of UTA may be found at Note that PKH is the triangular building in the south-central region of the map next to the "garage" & is on Nedderman Drive between College St & West St. Parking is available in the nearby (just south of PKH) parking lots with a UTA permit. Visitor (free), & metered, parking is available by Davis Hall (marked DH in South West part of map). A parking garage (expensive) is next door to Pickard Hall (use West St to get to it). Note that if heading south on Cooper, then no left turn is allowed to Nedderman Drive. Recommended route from UNT: eventually head south on Hwy 360, west on Abram, south on Pecan, west on Nedderman. Then use map. From TCU: east on I30, exit Cooper, south on Cooper (but there is currently construction on Cooper and so the possibility of heavy delays, so you might prefer to use Fielder, heading South to Abram, and then East to Cooper); then use map. From anywhere else: good luck! Note that PKH 487 is on the 4th floor of PKH; turn right out of elevator.

Questions, etc on arrangements/directions? Contact Michaela Vancliff. Please RSVP if coming from out of town, since, if you are a little late, we will delay the start of the talk for you.