Fernando Rodriguez Villegas
Recent Writing
C'est le moment des braves: Goodbye KarimNovember 1, 2025
C’est le moment des braves
So would Karim write to Ralph at precisely midday, to say it was time for lunch. Every working day for years.
So Ralph told us, the many people crammed in the Parrochia di San Michele Arcangelo in Sgonico, during Karim’s funeral. A laic ceremony.
Outside, the massive trees with their large yellowing leaves were already in winter. The air was wet. The bright yellow contrasted with the dark color of people’s clothes and the heavy silence and the concentrated and sad look of people’s faces.
read moreNew Zealand II: Arthur's PassJuly 27, 2025
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).
read moreNew Zealand I: ChristchurchJuly 20, 2025
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!
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Water and Ice
Belluno
How to eat a maritozzo
Two nights at Cattinara (in Spanish)
All WritingRecent Math
Giochi imparzialiFebruary 3, 2026
These are the slides of my talk (in italian) for high-school students at ICTP.
read moreRamanujan MotivesOctober 27, 2025
These are the slides of my (online) talk at the 2025 meeting “VIII Encuentro Regional de Teoría de Números” held at La Rocha, Uruguay.
read moreSpecial parametersOctober 8, 2024
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.
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Experimental Number Theory
HGM
The Mathematics of the Football
Counting quiver representations over finite fields
All MathRecent Cooking
Scoplit pestoMarch 10, 2025
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.
read moreMushrooms with blue cheeseNovember 15, 2024
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.
read morePasta verdeNovember 2, 2024
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.
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