January 4, 2026 · 2:16 pm

2025 Booklist

Pratchett – Wyrd Sisters
I’m not going to review individually the various Discworld books I’ve read. If you haven’t read any Pratchett, I strongly recommend reading the Colour of Magic and deciding from there how many Discworld books you want to read.

The Best Australian Science Writing 2024
I bought this back in 2024 (not cool – what if I wrote the best ever Australian Science writing on December 31 and then it couldn’t be included!) and decided not to give it as a present. I found it an interesting potpurri of articles.

Pratchett – Pyramids

Silver – On the Edge
The author is the guy who became famous because of the 538 blog covering polling for the 2008 US presidential election (happier times). I found the poker stuff interesting enough, but the book couldn’t keep up interest as it moved into other topics. Skip this.

Robbins – In Search of Kazakhstan
This is a lighthearted and enjoyable easy-reading travelogue from the days of Kazakhstan that now are closer to the breakup of the USSR than the present day. Did you know apples are from Kazakhstan? You do now. Extra fact: Despite me already having a poor opinion of the Soviet regime, this book managed to lower it.

Crichton – Jurassic Park (reread)
The book is always better than the movie. And this one is a good movie.

Hotten – Bat, Ball and Field
Hotten used to blog at The Old Batsman but like many bloggers has moved to substack. This will give you a glimpse of his writing style.

O’Reily – A Thoroughly Unhelpful History of Australian Sport
Why does Titus O’Reily not have a wikipedia page? A mix of humour and history of the Australian sporting landscape. Worth looking at if you have an interest in the latter.

Pratchett – Guards Guards

Studwell – How Asia Works
A book about the economics of development in 20th century Asia, attempting to explain the relative economic trajectories of various countries studied. Talks about land reform, protectionist policies for industry and financial deregulation. Does get a little repetitive hearing these for the n-th time, but I think I learned something.

Kuang – The Poppy War
The first book in an ambitious fantasy trilogy that is set in a fictional country that very clearly is China, though all place names are fictionalised. I picked this up after having read (not in 2025) and enjoyed her Babel novel. Good enough that I went to read the sequel, and the third book in the trilogy is on my to-read list.

Pratchett – Moving Pictures

Tough – Solo
Jenny Tough sets out to run (yes run) across mountain ranges in six continents. This is completely bonkers. A simple and enjoyable quick read.

Pratchett – Eric

Rhinehart – The Dice Man
The main character in this book is a psychiatrist who makes decisions in his life by rolling dice. Which can range from sensible to absolutely bonkers depending on the nature of the decisions you are trusting to fate. No prizes for guessing where on the spectrum this is – you’re going to struggle to get a novel out of using a D6 to decide whether to get the chicken or the beef on a flight.

Pratchett – Reaper Man

Kuang – The Dragon Republic
The sequel to The Poppy War (above). Read this if and only if you read and enjoyed The Poppy War.

Rushdie – Haroun and the Sea of Stories
This is, simply, a beautiful well-written story. Suitable for all ages. Afterwards, I started his more famous Satanic Verses and found it much harder going, it seemed hard to believe it was from the same author. Absolutely recommend.

Pratchett – Witches Abroad

Tesh – Some Desparate Glory
Very good Science Fiction.

Watterson – The Complete Calvin & Hobbes Book I
Yes I’m counting this as a book.

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December 14, 2025 · 1:54 pm

Providence Restaurant Guide

Xaco Taco (south of downtown, walking distance). A favourite. It’s good to be in a place again where you can get good Mexican food. Tacos are their main dish (including happy hour tacos between 3-5pm). Their bowls are a great value option, and I’ve heard good things about their margaritas as well. Thanks to Stephen for suggesting this on the first day. 5/5.

Cielito (Thayer St). If you want good Mexican food on a smaller budget then this is the place to go 5/5.

Coldstone Pizza (downtown). Best pizza in town. 5/5.

Quitos (Bristol). Seafood restaurant. Get there by cycling along the East Bay bike path. If you’re a long term visitor to ICERM, Recycle-a-bike is a good place to find a bike for the duration of your visit. They lose half a point because the salmon wasn’t quite worth full marks. 4.5/5.

Mokban (downtown). Korean restaurant. Easily the best Asian cuisine I’ve found in Providence. 4.5/5.

Antonios (Fox Point, or on Thayer St). Pizza by the slice. You want to go here only on Wednesdays, when the pizza is only $3.24/slice, otherwise you’ll pay through the nose. The Fox Point location is superior to the Thayer St one. Look for the square pizza with pepperoni and white dollops of cheese. 4/5.

Den Den (north of ICERM). Another Korean restaurant. I went here once early on and my memory is a bit hazy. Decent food, if not as good as Mokban. 4/5

East Side Pockets (Thayer St). Felafel (and other culturally similar foods). An inexpensive way to fill up. 3.5/5.

Jahunger Providence (Fox Point). Uighur cuisine. Only the second Uighur restaurant I’ve ever been to, so I’m expecting many people may not have had their cuisine. If that’s the case, you should try it and see if it’s for you. 3.5/5.

Congress Tavern (downtown). Look, you’re not here for the food, you’re here because it’s a bar and you’re hoping for a decent burger or similar while you drink. On that note, they do a reasonable job. One unusual thing they do serve is lobster nachos. And these are genuinely good, if you can stomach the steep asking price. 3.5/5.

Geoff’s Superlative Sandwiches (south of ICERM). Standard place to go for a sandwhich. Their menu is extensive, there’s a second blackboard with a beginner version if the first one is overwhelming. Surely you can find something you like here. 3.5/5.

Sura (downtown). Don’t bother going here. It’s not bad, it’s just that Mokban across the road is better. 3.5/5.

Livi’s Pockets (downtown). On the plus side, service was very fast. On the minus side, it felt like a lot of money for a wrap that wasn’t anything special. It’s the same owner as Livi’s Burritos in the same arcade., but the latter was closed so I didn’t get to try that. 3/5.

Baja’s Taqueria (Thayer St). We went for burritos here so I ordered a burrito. I think that personally this is the wrong thing for me to order at a Mexican place, so I’m not rating this one very highly. 3/5.

Filini’s I’ve had one very good slice of pizza here, one very ordinary slice, and half a sandwich that didn’t agree with me. Not worth hoping that you’ll find one of their better pizzas. 2.5/5.

Plant City (south of ICERM). As the name suggests, vegetarian. I had one wrap on their menu and decided that Geoff’s is preferable. 2.5/5.

Jolly Roger Cafe (south of ICERM). I went once here and didn’t vibe with the place. 2.5/5.

Cielito (downtown). Mexican food. I went once and felt I paid too much for a dish that wasn’t really all that tasty. 2/5.

The Malted Barley (downtown). Their main dish is pretzel sandwiches. Yes you heard that correct (the pretzels are the bread, not the filling). The only thing I consider worth eating here is their soup, and only if it’s the clam chowder. Anyway, you’re not here for the food, you’re here because of the trivia, but we learned that this isn’t even the right place to go for trivia – check out The Point Tavern in Fox Point instead. 1/5.

Dune Brothers (south of downtown) So the USA doesn’t seem to understand fish and chips. The price here is something like four times what it costs at home. Given the sticker shock, I went for something else and was seriously disappointed. 0.5/5.

Mala Noodles (Thayer St) This place is crap. 0/5.

Greg’s Breakfast and Lunch (by the Washington secondary trail) Back in my cycle touring days (which lasted until I put my bike on a Fung Wah bus and went home), I had a breakfast in the same set of shops as this place (I think not at Greg’s though). It was a great breakfast, meaning large or immense, but also not in the pejorative sense. So I went to Greg’s wistfully hoping for more of the same. The food was very standard American diner fare. What is really dragging down this review is the ambience. They were playing the radio, and their choice of radio station was a Christian station. Even if you took the lyrics away from the music, looking purely at the rest of the musical composition, it was the lamest possible music you’ve ever heard. I subscribe to the Red Symons rating theory where zero is not a lower bound. -1/5.

Track 15 (downtown) Track 15 is a glorified food court. Apparently the only option there that is edible is the Indian, but if you know me, you’ll know that that is not going to be my first choice of cuisine. They lose marks because when I ordered, I was asked for my phone number. That’s already completely inappropriate, but if the age/gender roles were reversed would be outright creepy. -2/5.

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November 16, 2025 · 5:16 pm

The Last DECRA

What The DECRA is a grant for early career researchers, funded by the Australian Research Council. It’s a three year fellowship, providing both salary support and research funding.

Who You are eligible to apply up to 5 years post-PhD, and has allowances for career interruptions. You must have the support of an Australian university, but you do NOT have to be currently employed at an Australian university.

When For funding commending in 2027 (for which the default PhD award date is 1 March 2021), applications will be open early in the new year, with anticipated results announcement in September-October.

Why Last? I’ve been told it’s the last. The ARC isn’t great at actually announcing things like this. (this is what I can find). So if you’re eligible, and want to live in Australia, apply this round!

Is it a good deal? Yes (personal experience).

What does an application look like Here’s mine. It’s a sample size of one.

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July 21, 2025 · 2:54 pm

IMO 2025

I went to this year’s IMO (no not as a contestant, I’m ineligible) on the Sunshine Coast. I have to lead with this image, which is the pattern of tiles on the floor at the Sunshine Coast airport.

The image contains a very mild spoiler to problem 6 on this year’s exam. The uncanny coincidence is too awesome to not mention it.

My role was on the problem selection committee, which means I was involved in selecting the shortlist, which involved getting to the Sunshine Coast much earlier than the contestants (never a bad thing to be next to a QLD beach in winter), getting a few days off, then recommencing academic work with jury meetings and coordintion.

Here’s a picture from nearby Mount Coolum, taken on a hike during the break period.

When initially approached, I was a little apprehensive about how my rustiness with olympiad mathematics would affect my opinions and capability to work on the shortlist, but I think things turned out fine. I would be willing to do this again if asked. Coordination felt very different to the shortlisting process, it involves a lot of work in a short time period, some of which can be stressful, but is of essential importance to making an IMO run smoothly. I think I enjoyed the whole process more because I was on the PSC beforehand, and would be less likely to accept to attend a future IMO in a coordination only role than I would as a PSC role.

Here is an awesome T-shirt. I want one.

The Australian Maths Trust took the opportunity to have an alumni reunion event on the final morning. They had this swag to give away, highlighted by copies of Australian Scenes (no longer published in dead tree form) dating back to 1992. I took the opportunity to complete my collection from the years in which I competed.

Unfortunately the publicity around this IMO in more mainstream media tended to focus on the unverifiable claims of the AI community rather than the feats of the students involved. Any organisation between the IMO and AI companies was a shambles, with nothing being organised in advance to force any integrity onto the AI companies, and inappropriate requests for coordinators to mark AI scripts, including after the closing ceremony with some in person approaches by individuals with laptops.

To end on a more positive note, here’s a reunion photo taken after the closing ceremony. All of us were at IMO 2001 and all of us were graduate students at MIT together.

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December 23, 2023 · 4:44 am

The spin Brauer category

Alistair Savage and I have uploaded our paper The spin Brauer category to the arXiv.

The Brauer category only sees the representations of \mathfrak{so}_N, which come from representation of the group \mathrm{SO}(N). In particular, it misses the spin representation S (which is a tensor generator of the category of finite dimensional \mathfrak{so}_N-modules). The starting point of this paper is to define a new category, the spin Brauer category, which sees the spin, and hence all, representations of \mathfrak{so}_N. Here is the abstract:

We introduce a diagrammatic monoidal category, the spin Brauer category, that plays the same role for the spin and pin groups as the Brauer category does for the orthogonal groups. In particular, there is a full functor from the spin Brauer category to the category of finite-dimensional modules for the spin and pin groups. This functor becomes essentially surjective after passing to the Karoubi envelope, and its kernel is the tensor ideal of negligible morphisms. In this way, the spin Brauer category can be thought of as an interpolating category for the spin and pin groups. We also define an affine version of the spin Brauer category, which acts on categories of modules for the pin and spin groups via translation functors.

If you go to the arXiv and download the source, you will see the following line:

%\toggletrue{details} % To include details (default is false)

If you uncomment this line (and fix the bibliography, which for reasons unknown to me appears at the start when you download source), and then compile the file yourself, you will see a version with more details.

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November 24, 2023 · 12:28 am

We’re hiring (2023 edition)

We’re hiring!

Two permanent positions in pure maths. One in geometry/topology, one open for all areas of pure mathematics. Applications are through mathjobs (link to Job 1, link to Job 2), and are due December 18 (AEDT).

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October 21, 2023 · 11:55 am

Ublock origin filters (unimelb/mathoverflow/stackexchange)

Motivated by recent changes to the mathoverflow cookie popup spam, I recently learned something about Ublock origin filters. In particular, a URL X matches *X. Now my custom filters file contains the lines


unimelb.edu.au##.tealium_explicit_consent.tealium_privacy_prompt


##.js-consent-banner.r16.l16.b16.bar-lg.fc-white.bg-black-600.sm\:p16.p32.sm\:w-auto.ws4.z-nav-fixed.ps-fixed.ff-sans


##.wmx12.mx-auto.jc-center.ai-center.d-flex.px12


##.js-dismissable-hero.ps-relative.fc-black-300.bg-black-600.py24.sm\:d-none

So the first line above matches every unimelb.edu.au website, independent of the prefix before unimelb. While the last three match every website, so I can use this set of three filters not just on mathoverflow, but on every site in the stackexchange network.

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October 14, 2023 · 1:32 am

The Jacobson Density Theorem

I’ve never been at ease with the Jacobson density theorem, every proof that I’d seen felt somewhat weird and never had any stickiness in my mind. So I came up with my own proof, I hope you like it.

The Theorem (Jacobson Density Theorem}
Let k be a field and A a k-algebra (yes unital). Let S be a finite dimensional simple A-module and D=\operatorname{End}_A(S) (which is a division algebra by Schur’s Lemma). Then the canonical homomorphism from A to \operatorname{End}_D(S) is surjective.

Proof
First, without loss of generality (replacing A by a quotient), we can assume that S is faithful.

Let us first deal with the case when A is a division algebra. Then S=A. And D=A as well, acting by right multiplication. And we are done.

Since A is not a division algebra it has a non-zero element a which is not invertible.

If a is not nilpotent, then the minimal polynomial m(x)\in k[x] of a factors as x^np(x) where n,\deg(p(x))>0. In particular it has two coprime factors, so by the Chinese remainder theorem k[x]/(m(x)) has a non-trivial idempotent. In particular, A contains a non-trivial idempotent.

If on the other hand a is nilpotent, then we can find v,w\in V with av=0, aw=v and v\neq 0. Since V is irreducible, there exists b\in A with bv=w. Then (ba)v=0 and (ba)w=w. So ba is not nilpotent, and we can run the argument of the previous paragraph again to conclude that A contains a non-trivial idempotent.

Let e be this non-trivial idempotent. We will use the fact that eS is an irreducible eAe-module. This is part of a general fact, that S\mapsto eS is a bijection betwen simple A-modules S with eS\neq 0 and simple eAe-modules. Furthermore, from the nature of the constructions of both directions of this bijection, we can conclude that

    \[\operatorname{End}_A(S)\cong \operatorname{End}_{eAe}(eS).\]

Now we can perform an induction on dimension. The inductive hypothesis tells us that eAe \to \operatorname{End}_{D}(eS) and (1-e)A(1-e)\to \operatorname{End}_{D}((1-e)S) are both surjective. To finish, given the symmetry between e and 1-e, it suffices to show that given any D-hyperplane H with eS\subset H and any D-line \ell\subset eS, there is a nonzero element in A with kernel H and image \ell. (I thought about this step myself in terms of matrices, but actually writing it up like that feels a little gauche).

The inductive hypothesis applied to (1-e)A(1-e) allows us to find a nonzero element c\in A with ker(c)=H. Pick nonzero v\in \im(c) and w\in \ell. Since S is simple there exists d\in A with dv=w. Then dc does the trick and our proof is complete.

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September 10, 2023 · 12:35 pm

Kanchanaburi, 14/08/23

Wake up to find out what my hotel calls an “American Breakfast”. This turns out to invovle toasted white bread with jam, fried eggs, mango, juice and tea/coffee. The mangos in Thailand are good, the white bread could be improved upon.

Tuk-Tuk to the bus station (80THB). Some words are exchanged between my tuk-tuk driver and someone at the bus stop and I am asked if I want to take a minibus. I agree. I realise now that based on my experience with the bus to Erawan Falls the next day, I am getting a faster and more comfortable ride than the bus would give me, for only 125 THB. Hellfire Pass is my destination this morning, and I am the first passenger dropped off. I’m not sure what the final destination of my minibus is, perhaps the Three Pagodas border crossing?

In WWII, the Japanese used forced labour (both POWs and civilians) to build a rail link to Burma. Hellfire pass is one section of the rail corridor where an interpretive centre and an audioguided hike along the rail corridor has been set up by the Australian government, free of charge. There are no longer any rail tracks along this part of the route, the British ripped out all the rail westward of Nam Tok at the conclusion of the war.

Unlike most visitors, I did the full hike, which is not as difficult as it is made out to be. I’m glad I’m not in a tour group – one arrives after me and the participants don’t get quite enough time to do the full hike and get the full experience. The audioguide has lots of stories told by POWs and the track has some nice views across the valley towards Myanmar. I also see my first monkeys of the trip, and after conversing with a local it seems that monkeys are as common in Thailand as kangaroos are in Australia.

I wholeheartedly recommend visiting this place.

After finishing Hellfire Pass, I bum a ride with a local to Namtok Sai Yok Noi waterfall. This seems to be a place more for children than adults. Though I must say, the chance to cool off under the waterfall is a great relief in this weather. Lunch is had here, from the other side of the main road.

There are two ways now to return by public transport, by bus or by train. I choose the latter (100 THB for foreigners), and walk to Nam Tok station, a walk which is not of any interest whatsoever. The train back to Kanchanaburi is more scenic than the bus, and on the more scenic portion of the trip I’m joined by some tour groups. The highlight is the section around Krasae Cave (you do get to briefly see inside the cave from the train) right next to the river. And the rest of the journey is enjoying riding through the countryside in a civilised manner, with the windows open as much as possible and no A/C in sight.

Back in Kanchanaburi, the train crosses the Khwae Yai along the famous bridge, full of tourists who have to get out of our way. There’s a station immediately after the bridge, which is where I alight.

Next stop is the JEATH war museum. This one got added to the agenda essentially because of the location, and being Thailand, entry is cheap. There’s a section dedicated to the 2nd World War, as you expect, but also some other stuff related to older history of Thailand. As well as some surprising exhibits like a section on the winners of the Miss Thailand beauty pageant. Because why not. The JEATH museum also comes with some nice views of the bridge over the River Kwai and the surrounding area as in the below picture.

Dinner is next, but that is beyond the scope of this blog. And Erawan falls beckons the next morning.

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July 5, 2023 · 2:20 pm

Okinawa

1. Ta-taki Falls.

This is a short hike along a river to reach a pretty waterfall spot. And when I say along a river, I really mean you are walking through the actual river. There’s a place to hire shoes for the hike at the trailhead carpark. If you’re unsure, you need to hire them. Wear bathers, as you’ll want to have a swim at the pool under the waterfall, as well as giving you more flexibility on your route during the walk. A unique hike, highly recommended.

2. Bitter Melon

Those of you who grew up eating this may wonder what I’m even making a fuss about. There’s this vegetable in Okinawa (and some other places) called bitter melon. When you first taste it, it seems a little strange, but not overly offensive. And then the aftertaste hits you and you wish you had made wiser life choices. Best to avoid this food, although that isn’t always easy, some places are nasty and will do things like hide bitter melon inside tempura.

3. Satsukimaru

We found this lovely little restaurant in Oku, in the northern part of Okinawa. Good cheap food, even if they did do the bitter melon in tempura trick. Small and cozy, you can see the entire restaurant in the picture. Highly recommended.

4. Onishidake (Mt. Onishi)

There is supposed to be a hiking track to the top of Mt. Onishi. We stopped the car and went for a bit of a walk along a side road, but couldn’t find the trailhead. It wouldn’t surprise me if the trail has been neglected and become severly overgrown. If any reader stumbling across this post has more information, please do share it.

5. Mt. Fuenchiji

Skip this. There’s some telecommunications equipment and no view.

6. Katsuudake (Mt. Katsuu)

This one is a short steep hike from the car park to the summit, which is sure to work up a sweat, at least in the humid summer months. You can see that beautiful views will be possible from the below photo, but to see them all, you’ll have to go visit yourself. It is possible to continue hiking beyond the peak but we didn’t look into this. Highly recommended.

Practicalities: I needed to produce my international drivers licence to rent a car in Japan. 40 AUD for someone to look at my license and write down details on some document + 12 AUD for a photo. I should muscle my way into this industry, it seems like a nice profit making machine.

Acknowledgements: Thanks to Iva Halacheva for the photos.

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