Speaker: Prof. N. S. Narasimha Sastry, IIT Dharwad
Title: Ovoids in finite projective 3-space
Date & Time: 5th July 2017, at 11 am
Venue: Ramanujan Hall
Abstract: In a finite projective 3-space considered as an incidence
geometry, an ovoid is the analogue of the sphere in Euclidean 3-space,
introduced independently by Segre and Tits. Elliptic quadrics are
generic examples of ovoids. A projectively nonequivalent family of
ovoids were constructed by Tits which is closely related to the
Suzuki groups and Moufang sets. These are the only known families of
ovoids.
Apart from being objects of intrinsic interest, they are fundamentally
related to some important combinatorial structures like inversive
planes, generalised quadrangles, permutation polynomials, group
divisible designs, etc. Their classification and understanding their
distribution in the projective 3-space are the fundamental problems
regarding them. However, several first questions about them are yet
to be settled. To name a few: the structure of the intersection of
any two of them, packing the projective 3- space by ovoids, the number
of such objects, up to projective equivalence.
As an introduction to this topic, we discuss some interesting results
and mention some open problems.
I will make an effort to keep the talk elementary.