[Turkmath:3869] Sabanci University Mathematics Colloquium - May 23, 2019

[Michel Lavrauw]

You are cordially invited to the Mathematics Colloquium on Thursday 23 May 2019  at 13:40 in the FENS building on Sabancı Campus in room G029.

Speaker: Sudhir Ghorpade (Indian Institute of Technology)

Title: Maximum number of zeros of systems of homogeneous polynomial equations over finite fields.

Abstract: Let F be a finite field. We will consider the following question:
Given a system of a fixed number of linearly independent homogeneous polynomial equations of a fixed degree with coefficients in  F, what is the maximum number of common zeros they can have in the corresponding protective space over F? 
The case of a single homogeneous polynomial (i.e., hypersurface) corresponds to a classical 
inequality proved by Serre in 1989. For the general case, an elaborate conjecture was made by 
Tsfasman and Boguslavsky, which was open for almost two decades. Recently significant progress in this direction has been made and it is shown that while the Tsfasman-Boguslavsky Conjecture is true in certain cases, it can be false in general. Some new conjectures have also been proposed. We will give a motivated outline of these developments. If there is time and interest, connections to coding theory or to the problem of counting points of sections of Veronese varieties by linear subvarieties of a fixed dimension will also be outlined. Parts of this talk involve joint works with Mrinmoy Datta and with Peter Beelen and Mrinmoy Datta. 


Kind regards,
Michel Lavrauw