Description

Title: Ovoids in PG(3,q) and Algebraic codes

Speaker; Prof. N. S. Narasimha Sastry, Formerly from ISI Bangalore and IIT Dharwad

Day, Date and Time: Tuesday, 20th December 2022 at 2 PM

Venue: Ramanujan Hall, Dept of Mathematics

Abstract: Ovoids in PG(3,q) are the Incidence geometric analogues of spheres in Euclidean 3-space. If q is odd,

Baralotti and Panella showed independently that elliptic quadrics are the only ovoids in PG(3,q). Further, an ovoid

and its set of tangent lines determine each other. However, if q is an odd power of two, then apart from elliptic

ovoids (which exist for all q), PG(3,q) admits one more projective class of ovoids which are not projectively equivalent

to elliptic ovoids. They were discovered by Tits, using the graph - field outer automorphism of PSp(4,2^{2n+1!}), and its

stabilizer in PSp(4,q) (called the Suzuki simple group, the same as ^2 B_2(q) in Lie notation) was discovered earlier

by Suzuki as the final piece in the long series of works on the classification of finite Zassenhaus groups by Zassenhaus,

Ito, Feit and Suzuki. Further, the set of tangent lines of two ovoids can coincide even if they are projectively nonequivalent.

These are the only families of ovoids in PG(3,q) known and classification of ovoids in PG(3,q) is a major problem in Incidence

Geometry. Because of their connections to many other combinatorial structures ( like inversive planes, generalized quadrangles,

group divisible designs, ...) and the very exceptional behavior of the Suzuki simple group and the Tits ovoid, understanding the properties of ovoids in general, and their distribution in PG(3,q) in particular, are of considerable significance.

In this talk, I will present some facts known about ovoids in general, their distribution and the role of algebraic codes in

understanding them. An effort will be made to clarify all the basic notions involved.

Description

Ramanujan Hall, Department of Mathematics

Date

Tue, December 20, 2022

Start Time

2:00pm IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Sun, December 18, 2022 1:30pm IST