New Zealand is a wild place. As far as we know humans only settled in New Zealand in the 13th century AD. They were Polynesians who came in canoes from small Pacific islands far away to the East. There were no land mammals except for some small bats. The Polynesians brought with them rats and dogs and various crops, some of which grew in New Zealand and became staple foods (including, famously, kūmara, the sweet potato, a major historical puzzle).

It’s now about two weeks since I arrived in Christchurch, New Zealand. I am here as an Erskine Fellow teaching the first half of an undergraduate course on Coding Theory at the University of Canterbury. The city is quite large and very spread out. It reminds me in different ways of both the UK and the US. Not having a car is fairly limiting though the bus system is good. Everyone gives a big “Thank you!

Water and ice En un sueño lejano, como un recuerdo en la niebla, aparece Borges. Escritor de Buenos Aires, ciego. Escritor no del amor sino del espanto. Aparece como el capitán de un equipo de rugby arengando a sus compañeros en el vestuario: “Muchachos, a ver si nos entendemos, el hielo existe” Transición de fase lo llaman los físicos, como la muerte. Un día sos, al otro día no. El agua fluye, el hielo se queda donde está.

An old paper (Über hypergeometrische Funktionen, deren letztes Element speziell ist) by W. Heymann (from a talk by Wadim Zudilin) discusses the value of an ${}_2F_1$ at special $t$’s. He does $t=-1/3,1/4,1/5$ and related values and mentions Gauss for $t=1,-1,1/2$ and Kummer for $t=-1/8,1/9,8/9$. For example we have this identity $$ F_h = F \left( -\frac{h}{2}, -\frac{h}{2} + \frac{1}{2}, h + \frac{3}{2}, -\frac{1}{3} \right) = \frac{2}{3} \cdot \left( \frac{8}{9} \right)^h \cdot \frac{\Gamma \left( \frac{1}{3} \right) \cdot \Gamma \left( h + \frac{3}{2} \right)}{\sqrt{\pi} \cdot \Gamma \left( h + \frac{4}{3} \right)} $$ If we take $h=1/2$ we get an HGM defined over $\mathbb Q$, we get the gamma vector $[-4,1,1,2]$ and corresponding Weierstrass model $$ y^2+xy=x^3+\frac t{64}x.

This book, published in 2007, is a discussion of various mathematical experiments in Number Theory using the computer. The main computational tool used is the sophisticated package PARI-GP. Maybe the best way to describe the book in more detail is to just quote its preface. Preface -------- There is a long and distinguished tradition in mathematics, perhaps even more pronounced in number theory, whereas a chance discovery of a pattern or identity between numbers arising from unrelated calculations leads to the development of whole new fields (this is precisely how Gauss phrases it in a diary entry).

This project got started at a fabulous workshop held in Benasque, Spain (in the mountains, a few hours drive from Barcelona) in 2009. I wrote this post in my blog after returning from another workshop there on p-adic analysis in 2007. In my own notes I added: The place is truly amazing. Mountains falling over you as you walk down the street. The plan of the 2009 workshop was to explore ways to compute exotic L-functions, not arising from elliptic curves or usual modular forms.

One of the joys of cooking (of living!) in Italy is the variety of products you can find in the market. Supermarkets tend to be small (navigating them at peak time a challenge) and the selection limited but the quality is always very high. You could basically buy anything with your eyes closed and not be dissapointed (or ruin your appetite or your health if repeated). I am thinking specifically of the farmer’s markets in the public squares and the incredible variety of vegetables and especially herbs you might find.

I am not sure where I got this from. I do remember my aunt, the writer Alicia Plante, back in Buenos Aires, mentioning a recipe of baked fish with blue cheese that I prepared a few times. In the US I adapted it using big mushrooms instead of fish. But maybe I got the idea somewhere else. 1 Get some big round mushrooms, for example, shitake mushrooms. I read that one should never wash the mushrooms with water as they get ruined somehow but gently remove any impurities with a soft brush.

After a fair number of iterations this is the result of my cooking pasta with greens. At home we just call it Pasta Verde. This version is with Swiss chard but a real nice combination is dandelion leaves (tarassaco in Italian) and Swiss chard (bieta). You can see how the various steps follow those for cooking a risotto. 1 Start preparing about an hour in advance a thick broth to use to cook the pasta.