Description
Mathematics Colloquium
Speaker: Prof. Peter Beelen, Technical University of Denmark
Title: A new family of maximal curves.
Day, Date and Time: Wednesday, 24th January 2018, 4 PM
Venue: Ramanujan Hall
Abstract:
Let C be an algebraic curve defined over a finite field with q elements. The
Hasse-Weil bound gives an upper bound on the number of rational points on
C. An
algebraic curve is called maximal if this upper bound is attained.
On of the most important examples of a maximal curve is the Hermitian
curve, which
can be defined by the equation x^q+x=y^(q+1) over the field GF(q^2) with q^2
elements. It has genus q(q-1)/2 and it is not hard to show that any
maximal curve
over GF(q^2) has genus at most q(q-1)/2. One of the main open problems in
this area
is to classify (the genera of) all maximal curves for a given finite field
GF(q^2).
In a recent work together with Maria Montanucci, a new family of maximal
curves was
discovered. In this talk I will give an introduction to the topic as well
as present
this new family of curves.