Yesterday I defended my Ph.D.

It all went really well and I had lots of people come along to support me, which was fantastic.

Thea, Bruce, Evan and Steph also all came from Australia (by way of various length routes) as well.

Now it’s time to relax a bit and enjoy the Christmas holidays. Research will continue, but that’s something for next year.

I’ll write a bit more about the defence later on.

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Thesis defence

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Next week I’ll defend my Ph.D. thesis, titled “Triangular bases of integral closures”, and written under the direction of Jesús Montes and Enric Nart.

It will be on Thursday the 11th of December, at 18:00 CET (that’s 6:30pm in Barcelona for those of you not used to 24-hour time).

It’s a public event, so you’re all welcome to attend. In fact, I’d love to see everyone there.

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Down time

I had decided that when I deposited my thesis, I’d take a day or two off, not go in to uni and just relax and recover a bit.

That didn’t really happen, between a course I’m taking at the UB, classes I’m teaching and exams I’ve had to correct, somehow time is rapidly disappearing and now I’m on to preparing for my defence.

Well, after the defence then.

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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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Happy Birthday Andrea

Yesterday was Andrea’s birthday.

We started celebrating last weekend (yep, Andrea is catching onto the Stainsby-Wilson week-long birthday). A quick trip to Granada for the weekend to celebrate with Andrea’s family.

It was great to get away from Barcelona for a few days and catch up with the family. Especially Bruno, who’s talking more and more.

Yesterday we went out for lunch at a sushi restaurant in Sant Cugat. The food was fantastic and there weren’t too many people, being midweek.

Then we had a quiet afternoon between a bit of shopping and resting at home, all in all a relaxing day.

I’ve got some more news from today, but that’s to come.


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Bruce once told me a story from when he was working at an agency, sometime just before I finished school I think.

He was working on ideas for a client with a junior creative team. They were both young, probably first “real job”, and the copywriter was a bit obnoxious.

At one point during their brainstorming session, when Bruce had come up with a succession of good angles, the young copywriter turned to him and said, “wow, you’re really good at this!”

I don’t know whether Bruce pointed out that he’d been doing it a long time, or just thought it.

Today I got the corrections for a couple of chapters of my thesis dissertation back from my advisor.

He’d taken what I’d spent a week or so writing, pulled it to pieces and put it back together again in a much clearer, more elegant way. I imagine it took him an hour.

I have to remind myself that he has also been doing this for a long time.

Experience does have it’s advantages.

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On the brink of disaster

Yesterday I had one of those moments that’s probably the worst nightmare of any PhD student who’s writing their thesis dissertation, and doubly so in mathematics.

Reading through a proof I’d first written some three years ago, I found an error.

What at first seemed to be a small issue, when investigated, turned out to be major.


Mathematical proofs are like towers, each proof sits on top of others, which rest on others and so on, all the way down to axioms that define the basis of everything else.

Well, my entire thesis is sitting on top of a couple of theorems, and it was in the proof of one of those that I found the error.

To put this in perspective, if this theorem turned out not to be true, over 40 pages of mathematical proofs and my entire thesis would be worthless, sitting on a base that wasn’t even there.

Of course, I never really expected that to be the case, but writing a proof can be a tricky thing, and it’s often hard to tell how long it will take to finish one.

Anyway, a day and a half later and while I don’t have it all written out, I’ve got the structure of a new proof sorted out and am confident that I’ve covered everything this time.

As an added bonus, it looks like I can prove something that’s a bit stronger than the original theorem and if that’s the case, it will make the last chapter I have to write a bit more straight forward.

It’s the silver lining that’s important after all.

Note: The xkcd comic is a tenuous link at best, but how could I resist sticking a proof based comic here?

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Keep calm and


I’m not normally one for jumping on internet memes, but when a fellow damned and suffering soul, I mean another PhD student currently in the process of writing her thesis dissertation, sent this, I felt I had to stick it up here.

If you’ve never heard of the Keep Calm and Cary On posters, have a look at the Wikipedia page and then come back and laugh with me.

Perhaps I’ll print one of these out and stick it up in my office.

This post can also serve as a sign that I’m still alive, just a bit busy writing and running example computations to write much more here at the moment.

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Working holiday visas

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I saw on Twitter today that Spain and Australia are in advanced talks to finally agree on a working holiday visa programme between the two countries. This came from the account of the Spanish embassy in Australia, so I imagine it’s fairly legitimate, although I haven’t been able to find any recent news about it elsewhere.

Here’s my translation:

We are confident that an agreement with Australia on Work and Holiday visas can be signed by the end of the year!

I think this is great. There is precious little relationship between Australia and Spain and it would be great to see more possibilities open up in this area. It certainly would have been a nice option to have when I first moved to Barcelona.

I’ve never understood why there was no agreement for working holidays visas between Spain and Australia, but today I read something that makes sense, although we’re moving into hearsay and rumour territory now.

Apparently it’s all got to do with Christopher Skase. The Australian businessman who declared bankruptcy and then fled to Mallorca. Somehow (read: bribes with lots of other peoples’ money) he managed to have his extradition from Spain denied based on health issues – even after he was obviously better – and Australia wasn’t happy about this.

So, the reason that there were no working holiday visas is that Australia has been in a tiff about corrupt spanish officials letting Skase off the hook, and more than 10 years after he died (and 20 years after the fact), they’re only just getting over it now.

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Thesis progress

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While working on my thesis dissertation, I regularly commit changes to a code repository. This gives me peace of mind – I push the repository to a couple of different servers – and allows me to easily go back and recover things that I’ve deleted.

It has also made it possible for me to create an animated visual representation of my progress.

I submitted the link to Hacker News a couple of days ago and it made it to the front page for a couple of hours. Here’s a screenshot of it at number 11 (which is the highest it got as far as I know):



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