Algebraic Curves with Many Rational Points over Finite Fields

Explore algebraic curves with many rational points over finite fields in this 49-minute conference talk by Maria Montanucci. Delve into the construction of maximum curves, automorphism groups, and the generalization of the GQ curve. Learn about semigroups, the GK curve, and the geometry of maximal curves. Discover the decoding process for maximal curves and gain insights into future developments in this field. Engage with topics such as notation, point counting over FQ, lifting automorphisms, and the foundations of this mathematical area. Conclude with a Q&A session to further enhance your understanding of this complex subject.

Introduction
Notation
How many points over FQ
Construction of maximum curves
The automorphism group
Lifting the automorphisms
Generalization of the GQ curve
Semigroups
GK curve
Why was it a conjecture
Geometry of a maximal curve
Decoding a maximal curve
Whats next
Developments Foundation
Questions