Andrea Bonucci

Intro

Hi! My name is Andrea and I am a mathematics student interested in the following subjects:

I've written my Bachelor thesis on the combinatorial aspects of surface Cluster algebras and applications to Frobenius' conjecture; which has been awarded a 9 out of 10 grade, which you can read here! As far as other interests, I'm an avid gym bro and have currently been on a bodybuilding track since Semptember 2022, and I also really enjoy travelling!

On the side I am also learning Kona, in order to optimize my Python script (for calculating expected move of a stock using option prices), as well as applying it to the high-frequency trading sector. For fun, I am also doing ProjectEuler problems (friend key: 1885079_du9SO9rxCr4OmSodYjJS96zZHxH1cGKy). Here are some solutions written in Kona!

Work

Combinatorial aspects of surface Cluster algebras and applications to Frobenius' conjecture.

Four Color Theorem

Abstract: In 1852 Francis Guthrie was coloring in a map of the United Kingdom, when he noticed that to color in any map, he could use as little as four colors. This observation reached mathematician Augustus De Morgan, who in turn shared it with the mathematical world. The Four-Color Theorem emerged: a conjecture stating that to color in any figure with regions, where regions sharing a common boundary are colored differently, four colors would suffice...

Frieze Patterns of Integers and Triangulated Polygons

Abstract: This report seeks to examine finite frieze patterns of non negative integers, introduced in the early seventies by Coxeter. There are two primary aims of this paper. Firstly, it aims to prove the bijection between triangulations of convex n-gons and frieze patterns of order n discovered by Conway and Coxeter and discuss the construction of a frieze pattern from its associated convex polygon.

Finitely generated modules over principal ideal domains

Abstract: The purpose of this report is to give a detailed description about the structure and behaviour of finitely generated modules over principal ideal domains (PIDs), that are especially nice rings. This type of analysis is particularly important if we apply it to the ring of integers, ℤ, which is a PID; as it allows for a proof of the Fundamental Theorem of Finitely Generated Abelian Groups.

Mathematical Modeling of Stochastic Systems: Forensic DNA

Abstract: In this report we will focus on nuclear DNA, which is found in almost every cell of our body, subdivided into chromosomes. It is known that each of us has 23 pairs of chromosomes. One pair is indicative of our gender, i.e., men have one X-chromosome and one Y-chromosome, while women have two X-chromosomes.

Mathematical Modelling of a Shock Absorber and Spring System

Abstract: Driving comfort and safety are essential considerations when behind the wheel. A shock absorber is typically used to keep the wheels in good contact with the road, absorbing and dampening any sudden motion. This project aims to develop a mathematical model of a shock absorber and draw conclusions regarding its optimal design.

Mathematical Modelling of a Prey vs Predator model

Abstract: As the number of endangered and extinct species continues to grow, it is becoming more and more important to understand how animals interact with each other in an ecosystem. Throughout this paper will explore how the populations of two species can change in density over time or under different experimental conditions...

About

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Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';