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.

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.

Description

Ramanujan Hall, Department of Mathematics

Date

Wed, January 24, 2018

Start Time

4:00pm IST

Priority

5-Medium

Access

Public

Created by

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Updated

Sun, January 21, 2018 5:24pm IST