Preface to this Mores entry

I cannot remember what the reason for this was, but I recently opened my DPhil thesis and came across my acknowledgements section. I was struck again by how many people I loved during my time in Oxford and so I was moved to share it on this website. It is traditional for a DPhil candidate to acknowledge their supervisors, family and friends at the beginning of their thesis, but it is often a very brief, albeit heartfelt, tipping of the hat. I wanted to convey a fuller sense of the relational journey as well as my deep gratitude to those who kept me going. And given that a mathematical thesis is rarely very personal, an extended acknowledgement section afforded me the opportunity to stamp my thesis with some of my character and the character of those I love. It was also a pleasure to write.

Note that the first three chapters of the thesis are titled 'Introduction', 'Notation and preliminary results' and 'Surveys'. The next five chapters have technical and mathematical titles. The final chapter is titled 'Future directions'. The titles of the opening and closing chapters are relevant to the specific dedications in my acknowledgements.

After my acknowledgements, I included a further dedication. I am sentimental and I could not help myself.

Acknowledgements

The last three and a half years have been full of unrivalled joys—romance and magic, mythology and history, mathematics and theology, friendship and faith, learning and more learning. They have also been full of contrasts—sunshine and grey, warmth and loneliness, triumph and defeat, fun and struggle, laughter and farewells. At the end of it all, I have so many people to thank, some of whom I name below individually and others in groups. I am grateful to each and every one of you.

Chapter 1 is dedicated to God who is revealed through Jesus Christ for His mercy and kindness throughout the past few years and His gift of true life throughout eternity. He is the 'introduction' of all things. Without Him, my time in Oxford and this thesis in particular would be of no lasting value to me. My gratitude to Him is endless.

Chapter 2 is dedicated to Mum and Dad. They have very much provided me the 'preliminary results' needed for this DPhil, supporting me with the love and resources necessary. I owe them my life and all my accomplishments are theirs also.

Chapter 3 is dedicated to my supervisors, Charles and David, since they introduced me to the field of research 'surveyed' in this chapter. I am deeply indebted to them for their tireless investment of time and energy into me and my work through their helpful discussions, exhortations to persist, suggestions for improvement, and meticulous proof reading. As one of Charles' last students and one of David's first, I hope this thesis does their brilliance and patience justice.

Chapter 4 is dedicated to the OUTTC of 2017/18. The university table tennis club has been a huge part of my time in Oxford throughout all three and a half years. This chapter came together in 2017/18, the academic year our team got promoted up a league and despite the awfulness of lengthy drives to away matches, I treasure all the hours of contact that we played.

Chapter 5 is dedicated to the Incredibles. The Smash, Overcooked, Chinese movies, and general chimping out really kept me going during the time I proved the majority of the content in this chapter. May the chat endure forever.

Chapter 6 is dedicated to the snek squad. This chapter is the only one remaining from the year I first arrived in Oxford. That time of transition and establishment of roots into a new environment was made easy by the official language of snek squad—banter and memes. I pray that we all reach S-tier eventually.

Chapter 7 is dedicated to the folks of Summer Scriptorium. The bulk of this chapter was proved in the libraries of Funfield, Lincoln, St Anne's, and Pembroke. I look back upon the summer of 2019 as an idyllic and dreamy time, the perfect combination of friendship, learning, and sunshine. It is times like this that give me glimpses of the age to come.

Chapter 8 is dedicated to St Ebbe's Church. The final stretch is often the hardest. It was not so for me, in large part due to the encouragement of my church family through Publicum and T2. I genuinely felt their excitement for me as I neared the finish line.

Chapter 9 is dedicated to my fiancée Rach. Having said 'yes', she will henceforth be a part of all my 'future directions'.

Thanks go to the proof readers of all my individual chapters—Mattie, Helen, Christiaan, Dom, Jef, eMiLiEn DuPoNt, Andi, Mr. Chip, and Kane. The errors are all my own. Special thanks to Hansen Chen—though I do not know you personally, I give you my warm thanks for providing the appropriate Green’s function used in the proof of Lemma 5.1.1 following a helpful discussion on StackExchange.

Further heartfelt thanks go to my DPhil examiners Jan Kristensen and Lassi Paunonen for their careful reading and constructive feedback because of which this thesis is much improved. Jan has been a huge encouragement to me all throughout my DPhil candidacy. Lassi provided extensive comments which happily showed to me his keen interest in my work. The idea for Example 6.6.1 comes from him.

Finally, especially affectionate thanks and hugs go to the fellow DFail-er, the monkey-brother-botlane-partner, the a n g e r y warrior, the charioteer, the other JC, the Hearthkeeper, and the Anointed Tadpole who sticks closer than a brother. You have all made Oxford strange and wonderful in your own particular way.

Dedication

Since I believe this thesis as a whole is greater than the sum of its parts...

To Mark and Zoe.

Two of my greatest delights at all times as well as two of my sharpest sorrows whenever we must say goodbye.

They are the beloved children of my beautiful sister Joy and her husband Pedro, the coolest man on earth.

____________________

Posted on this website 06.03.24, Auburn, Sydney, Australia.

Originally written circa March 2020 (I regret not dating my acknowledgements more precisely at the time), Oxford, United Kingdom.

Updated circa May 2020, Wentworthville, Sydney, Australia.

Love is giving of Self to Other that understands what it is to receive.

Love is receiving by Self of Other that understands what it is to give.

Love outdoes for Other’s sake.

Love is outdone for Other’s sake.

Love is sacrifice, forgiveness, self-denial, and yet, greatest mystery:

Love rules eternal, above the stars and beneath the sea.

Promise is the most wonderful magic humans possess.

Promise is the most terrible magic humans possess.

For a promise made is a world created.

But a promise broken is a world destroyed.

To make a promise is to hold one’s soul in cupped hands.

To break a promise is to feel one’s soul drip through leaky fingers.

To keep a promise is to look down upon one’s soul and see,

The reflection of the stars upon the sea.

What does marriage,

The rule that says one plus one is one,

What does marriage say of love plus promise?

With spoken words of unspeakable doom,

Marriage takes the divine power of love,

And binds it with human rings of promise.

Marriage binds love by promise;

Yet love, bound by promise, is not bound but free!

For promise trusted is fear removed,

And fear removed is love unleashed,

And love unleashed, through ordinary life,

Creates the stars and stills the sea.

____________________

19.05.23, Auburn, Sydney, Australia. A wedding reading written for two dear friends (the meaning of whose names include the Pleiades, eternal ruler and son of the sea) married in Hanbury, United Kingdom on the 12th of June, 2023.