Last Thursday I deposited my thesis. This is one of the final steps of my Ph.D. – the last one being the defence, which will be in December. I owe that fact that I’ve made it this far to a lot of people, below I have copied the Acknowledgements from the beginning of my thesis dissertation.

First, I must thank my advisors Jesús Montes and Enric Nart. I would like to thank Jesús for the original idea behind my thesis and his encouragement. It is clear that I wouldn’t be here without the support and assistance of Enric. In accepting me to be his student, I think he was more conscious of the way ahead us than I was. Thanks to his advice, support, and mentorship, today I can venture to call myself a mathematician.

I would like thank Jürgen Klüners for hosting me in Paderborn and providing invaluable advice and a fantastic experience while I was there. The company and friendship of Inga, Thorsten, and Friedrich made my visit so much more enjoyable, I thank you all!

To my friends and workmates at the UAB, the last four years have been an incredible experience, and it’s been wonderful to share it with all of you, especially Jens Bauch, my fellow “student of the Montes algorithm”.

I want to thank everyone in the Barcelona number theory group. Especially to my fellow students, Carlos, Elisa, Iago, Jens, Nuno, and Piermarco, and to my fellow seminar organisers Montse and Piermarco.

A la familia Martínez-Trujillo-Zaguirre-Heras, mi familia aquí en el hemisferio del norte. Me habéis aceptado como uno más de la familia con vuestro amor y apoyo. Quiero agradecer a Mari Carmen y Manolo, quienes especialmente han hecho de Granada mi segunda casa.

To Thea and Bruce, you are my parents, my mentors, and my friends. Thank you for the unconditional support you’ve given me, growing up and then in the nearly ten years since I packed up and left to live on the other side of the world. To my brother Evan, and to Steph, it’s always fantastic to see you guys and catch up on our lives apart. Let’s see if we can spend a few years living on the same continent at some point!

I have, of course, left the most important person to last. To Andrea who, through the entirety of our respective theses, has been my constant companion, partner, friend, and more. There are too few words in any language to describe what you mean to me. I would not have made it here without your love! Thank you for everything!

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