An Efficient Algorithm for Determining...
April 18, 2023
An Efficient Algorithm for Determining...

Polarized morphisms are important objects in various mathematical and computational fields, and their composition is a fundamental operation. In this talk, we present a new algorithm to efficiently compute the composition relationship of two polarized morphisms using the concept of dynamical canonical height. Our approach utilizes the properties of dynamical...
On Sub-semigroup Generated by Finitely...
August 29, 2023
On Sub-semigroup Generated by Finitely...

In the realm of category theory, an endomorphism represents a map that preserves an object's structure. This opens the door to exploring the (semi)-group structure of $\mbox{Hom}(X)$, the collection of such endomorphisms. A pivotal concept in this exploration is the Tits alternative, which classifies linear groups generated by two elements....
Introduction of SageMath
May 01, 2024
Introduction of SageMath

Polarized morphisms are important objects in various mathematical and computational fields, and their composition is a fundamental operation. In this talk, we present a new algorithm to efficiently compute the composition relationship of two polarized morphisms using the concept of dynamical canonical height. Our approach utilizes the properties of dynamical...
On Tits Alternative and its...
June 20, 2024
On Tits Alternative and its...

In the realm of category theory, an endomorphism represents a map that preserves an object's structure. This opens the door to exploring the (semi)-group structure of $\mbox{Hom}(X)$, the collection of such endomorphisms. A pivotal concept in this exploration is the Tits alternative, which classifies linear groups generated by two elements....
Why is it so hard...
December 29, 2024
Why is it so hard...

We study the composition relations of rational functions, focusing on two main aspects. First, we establish a stronger version of the Tits alternative for endomorphisms of the projective line, proving that for almost all rational functions $f$ of degree greater than 3, the semigroup generated by $f$ and any fixed...